V

 

RELATIONSHIP BETWEEN FLUID FLOW

IN CELLULOSE AND THE GENERATEO

ELECTRIC ENERGY WITH APPLICATION
TO WATER MOVEMENT IN PLANTS

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
MOUNIR A. MORCOS
1969

N
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Alichitqan 31;.11:

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This is to certify that the

thesis entitled

RELATIONSHIP BETWEEN FLUID FLOW IN CELLULOSE AND
THE GENERATED ELECTRIC ENERGY WITH APPLICATION
TO WATER MOVEMENT IN PLANTS

presented by
Mounir A. Morcos

has been accepted towards fulfillment
of the requirements for

_Ph_'D'_ degree in M ° '

     

or professor

Date -fi/ (CZZZ 6?

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ABSTRACT

RELATIONSHIP BETWEEN FLUID FLOW IN CELLULOSE AND
THE GENERATED ELECTRIC ENERGY WITH APPLICATION
TO WATER.MDVEMENT IN PLANTS

by Mounir A. Morcos

The concept of electro-osmotic flow in plants was examined.
The engineering bases of fluid flow inside xylem vessels were
studied, and the nature and the role of the electric potential
and current in plants were investigated.

A review of the fundamental bases of plant anatomy and
physiology was done to examine the limits imposed by them on
the vascular tissues and the whole intact plant. The finding
of many of the early and latest experiments in the area of
electro-osmosis, was interpreted by the zeta potential concept.

A model representing xylem vessels was developed. The flow
of energy through this model was analyzed mathematically. The
energy balance equation for the model was solved for dissipated
energy, which was considered to be the source of the generated
electric energy.

The relationship between the dissipated energy and the elec-
tricenergy was examined by forcing water to pass through a
cellulose pad of filter papers. Different water heads were
applied, and voltage, current, flow rate were measured and re-
corded. The tested fluids were: distilled deionized water at
23.8°c and at 30.00c, COZ-saturated water, (0.005M) and (0.01M)

KCl solution.

Mounir A. Morcos

The results showed that the source of electric energy may
not be an "intrinsic constant quantity" of the material and the
liquid such as zeta potential. The electric energy may be a
product of the flow process itself.

A theory "The Electron Accumulation Theory”was developed to
relate the generated electric energy to energy losses due to
the dynamics of water flow through porous materials.

Applying these results to the plant, showed that ”electro-
osmosis", according to its definition, does not play a role in
sap movement in xylem vessels.

Physiological processes in plants which may be explained by
the "Electron Accumulation Theory" include a negative charge
existing on root hair surfaces as a result of the flow of soil
water to the cortex of the root.

The structure of xylem vessels permits xylem sap to keep
high tensile stresses. These tensile stresses, combined with
the electric behavior of the flow, may cause the xylem sap to
act as a communication system along the whole height of the plant.

Equations for energy dissipation which can be solved by
using numerical techniques were developed.

Approv
jor rofessor

Approved we“ @L

Department Chairman

RELATIONSHIP BETWEEN FLUID FLOW IN CELLULOSE AND
THE GENERATED ELECTRIC ENERGY WITH APPLICATION
TO WATER MOVEMENT IN PLANTS

By

/

Mounir A. Morcos

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Agricultural Engineering

1969

se/7r/
1/4770

ACKNOWLEDGMENTS

The author is greatful for the assistance of all who helped
him in this study. He is extremely appreciative for Dr. Chester
J. Mackson (Agricultural Engineering) for his continuous assis-
tance and encouragement, and for the suggestion of the topic of
this research.

To Dr. Klaus Raschke (Atomic Energy Commission), the author
expresses his gratitude for the time, instrumentation, and his
constructive criticisms.

To Dr. Bill A. Stoute (Agricultural Engineering), Dr. George
E. Merva (Agricultural Engineering), Dr. Harold Davidson (Horti-
culture), and Dr. Rolland T. Hinkle (Mechanical Engineering), the
author expresses his sincere appreciation for their guidance,
encouragement, and helpful suggestions.

The author wishes to thank Dr. Carl W. Hall, Chairman of the
Agricultural Engineering Department for his assistance in so many
ways.

Special thanks are due the people of U.A.R. Cultural and
Educational Bureau for their help whenever needed. Appreciations
are extended to many graduate students at Michigan State University,
especially Mr. Samir Mansy and Mr. John Gerrish for their valuable
suggestions.

The author also appreciates the help of Mrs. Sharyon Morgan

in the typing of the manuscript.

ii

To:
My family, my wife Eugeni, and my daughter

Hanan, for their many sacrifices.

iii

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS-ooooooo ........ ........ ................... ii

DEDICATION................. ......... .. .................... iii

LIST OF FIGURES....................... .............. ...... vi

LIST OF APPENDICES..... ...... .............. ............ ... viii
Chapter

I INTRODUCTION....................... ............ ... l

I.A Nature of the Problem....... ................. 1

I.B Objectives ...... . ........ . ................... 2

II REVIEW OF LITERATURE .............................. 4

II.A The Structure of the Plant. ................. 4

II.A-1 The Structural Unit of Plant Tissue ...... . 4

II.A-2 The Conducting Tissues of the Plant ....... 8

11.3 Sap Translocation............. ............ .. 14

II.B-l Root Pressure Theory............ ........ .. 14

II.B-2 The Cohesion Theory......... ........... ... 15

11.0 Assimilates Translocation................... l8

II.D Electrical Potential in Plants .............. 22

II.E Background Theories................ ........ . 28

III MATHEMATICAL ANALYSIS OF FLUID TRANSLOCATION INSIDE

XYLEM TISSUE..................... ........... . 39

IV EXPERIMENTAL ANALYSIS............... .............. 57

V DISCUSSION OF RESULTS ....... ...... ............... . 64

V A The Source of the Natural Electrical Potential 64
V.A-1 First Theory..................... .......... 65
V.A-2 Second Theory "Electron Accumulation Theory" 68
V.A-3 The Validity of "Electron Accumulation Theory" 69
V B The Relationship Between Fluid Flow and The

Electric Phenomenon........... .......... 72
V.B-l Electric Responses to the Tested Fluids.... 72
V.B-2 Numerical Evaluation of Electric Responses

to the Tested Fluids......... ........... 87
V.B-3 The Role of Electric Energy in Plant ....... 97

iv

Chapter Page

V.C The Role of Xylem Vessel Wall Structure

in Plant 0 O I O O O O O O O O O O O O O O O 00000000000000 1'03
V.C-l The Generation of Electric Energy .......... 103
V.C-2 The Existance of High Tensile Stresses

in Xylem Sap........ .................... 104

V.C-3 The Existance of a Communication System
in Plants.... ...... ... .................. 108
VI SUMMARY AND CONCLUSIONS ........................... 112
VI.A Summary ..................................... 112
VI.B Conclusions ..... . ......... . ................. 113
VII RECOMMENDATIONS FOR FURTHER STUDY ................. 115
SELECTED REFERENCES ................ . ...................... 117
APPENDICES ........................... ..... ................ 122

LIST OF FIGURES

Figure Page
1 The Major Parts of the plant ........ . ........ . ..... 5
2 plant Cell ......................................... 7
3 The Pit ............................................ 7
4 Cell Wall Construction ............................. 7
5 Xylem Tissue ....................................... 10
6 Phloem Tissue ............... .... ................... 11
7 Sieve Plate ........................................ 11
8 The Microstructure of the Root ..................... 12
9 The Microstructure of the Stem ..................... 12

10 The Microstructure of the Leaf ..................... 13
11 Root Pressure Theory ....... .... .................... 17
12 The Cohesion Theory ................................ 17
13 Patterns of Water Uptake ........................... 17
14 Effect of Cuts on Water Path ....................... 17
15 Cytoplasm Streaming ................................ 19
16 Mfinch Mechanism ............. ... .................... 19
17 Pressure Flow Mechanism (Mfinch Mech) in Plant ...... 19
18 The Physiological Processes in Plant ............... 40
19 Xylem Tube Model ................................... 42
20 Energy Flow Through Tube Wall ...................... 42
21 Flow Work Through a Tube Section... ................ 42
22 Schematic Diagram of the Used Apparatus ............ 58

vi

Figure Page

23 A. The Apparatus Used To Determine The Electrical
Current and Voltage. Showing The General Set Up
Instrumentation, and Faraday Cage............... 59

B. A Close Up of the Cellulose Pad in the Plexi-
glass container................................. 59

24 Effect of Water Flow Through Cellulose Pad ......... 66
25 Effect of Pressure Head on Electrical Potential.... 66
26 Schematic Diagram Represents The Source of Electri-

cal Potential in the Cellulose Pad............ 70

27 The Effects of the Flow of Distilled Deionized
Water (23.80c) in Cellulose Pad, on the
Voltage, Current and Electric Energy .......... 77

28 The Effects of the Flow of Warm Water (30.00c)
in Cellulose Pad, on the Voltage, Current
and Electric Energy ....... ..... ..... .......... 78

29 The Effects of the Flow of CO -Saturaged Water
in Cellulose Pad, on the Voltage, Current
and Electric Energy....... .................... 79

30 The Effects of the Flow of (0.005M) KCl Solution
in Cellulose Pad, on Voltage, Current, and
Electric Energy.. ........ . ............ . ....... 80

31 The Effects of the Flow of (0.01M) KCl Solution
in Cellulose Pad on the Voltage, Current

and Electric Energy........... ................ 81
32 Electric Energy and Dissipated Energy as Function
of (4p)2.. .................... . ............... 82

33 The Generated Electric Energy of the Fluid Tested.. 83

34 The Effect of the Distance Between Downstream
Electrode and Pad Surface, on Voltage and
Current ............. . ......................... 84

35 The Effects of Flow of Distilled Deionized Water
(22.60c) in a Glass Fiber Pad on Voltage,
Current, and Dissipated and Electric Energy... 86
36 Flow Pattern During the 24 Hours of the Day........ 98
37 vapor BUbble FormationOOOOOOOOO00............OOOOOO 109

38 The Apparatus Used in Testing the Existence of
Tensile Stress in Water Column................. 109

vii

Appendix

LIST OF APPENDICES

Table A.1

The Effect of Flow of Deionized Distilled

water Through Cellulose Pad (23.80c)..

Table A.2
The Effect of Flow of Warm Deionized Dis-
tilled Water Through Cellulose Pad
(30.0°c) ...............................
Table A.3
The Effect of Flow of CO Saturated Water
Through Cellulose d (23.40c)........
Table A.4

The Effect of Flow of (.OOSM) KCl Solution
Through Cellulose Pad (23.80c) ........

Table A.5

The Effect of Flow of (.01 M) KCl Solution
Through Cellulose Pad (23.8°c) ,,,,,,,,

Table A.6

The Effect of the Distance of Down Stream
Electrode From the Pad ,,,,,,,,,,,,,,,,

Table A.7

The Effect of Flow of Deionized Distilled
Water Through Glass Fiber Pad (22.60c)

viii

Page

123

124

125

126

127

128

129

I. INTRODUCTION

I-A. Nature of the Problem:

Fluid translocation in plants is one of the topics which
receives a lot of interest and research in the field of plant
biology. The nature of this process is still not completely
understood. The translocation of sap in trees explained by
many theories: capillarity, imbibition, vital pumping, and
finally the cohesion theory. The translocation of assimilates
has been explained by: diffusion, protoplasmic streaming, chang-
ing turgidity, and finally by mass flow along a gradient of
hydrostatic pressure.

The natural electric current which was observed in living
plants, has attracted the attention of many scientists. Some
investigators related this current to translocation of sap, and
tried to force the sap to move inside the tissues of the plant
by applying an external electric current or potential. Others
offered new theories about the role of electro-osmosis in the
translocation of sap and assimilates. To study this electro-
osmosis concept, or the use of electrical potential in general,
many experiments have been performed. However many of the in-
vestigators attacked the problem with little considerations of
either the limits imposed by both the anatomy of vascular
tissues and the whole intact living plant, or the physical
laws controlling any process of fluid translocation. To deter-
mine the role of electro-osmosis in fluid translocation inside

the plant, the study must be based on both these limits and

those physical laws which have been extensively studied in other
fields of science. The role of electro-osmosis may have great
potential and may make many contributions in plant production,
as many scientists have predicted. However, this study is in-
tended to investigate this role from the engineering point of
view. It will investigate the engineering bases of fluid flow
inside the plant, and try to determine if there is, in fact,

any significant role of the electrical potential in the flow of
fluids inside the plant.

Since sap and assimilates translocation is a fluid flow
process, a physical model representing plant vascular tissues
will help in studying this fluid flow process which might take
place in this model, and will help in constructing the physical
equations which can represent these processes.

The degree of agreement between these equations and the
result of experiments performed will show the validity of the
model, and at the same time, the role of electro-osmosis in

fluid translocation in plants.

I-B. Objectives:
1. Constructing a physical model representing the plant
tissues.
2. Studying the physical processes of fluid flow in that
model.
3. Constructing the equations which describe the flow

process.

4. Evaluating these equations experimentally to determine
their validity and the validity of the concept of electro-

osmotic flow in plants.

II. REVIEW OF LITERATURE

II-A. The Structure of the Plant:

According to Fuller (1963), the body of most flowering
plants is composed of four kinds of structures: roots, stems,
leaves, and flowers. The first three are the vegetative parts
and their functions center upon the intake of raw materials,
the manufacture of food, and the utilization of food for growth
and development. The flowers are the reproductive parts and
are concerned with the formation of seeds, Figure l.

The roots are non-green in color and their principal functions
are the absorption of water and nutrients from the soil, the
anchorage of the plant body in the soil, the conduction of materials
upward into the stem and downward from the stem and leaves, and
sometimes, the storage of considerable quantities of food.

Stems arise usually as branched continuations of the root system
and their primary functions are the conduction of materials
upward, downward and transversely, the production and support of
leaves and flowers, and sometimes, the storage of food. The
chief function of leaves is the manufacture of food. This pro-

cess is known as photosynthesis.

II-A-l. The Structure Unit of Plant Tissue:

The smallest structural unit of plants is the cell. Plant
cells are extermely varied in size, structure and functions.
In general, a plant cell, figure 2, is constructed of:

l. The cell wall which enclose the living substance.

TERMINAL BUD

 

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.| d
\\ ’ [”45 ......FLOWER
ea,

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5%\ AXILLARY BUD
BRANCH
LEAF
/
I STEM

CONDUCTING TISSUES

fl PRIMARY ROOT

SECONDARY ROOT

 

 

 

 

 

 

 

 

 

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ROOT HAIR 4

 

ROOT CAP

 

FIG. I. THE MAJOR PARTS OF THE PLANT.
FULLER,II963I

2. The protoplast, or the living component of a single
cell, which consists of the cytoplasm with the nucleus
and other component embeded in it.

3. The ergastic substances, which are the nonliving
materials present within the cell, such as liquids,
crystals and other solid bodies.

1. The Cell Wall

Cell walls have a layered structure: the middle lamella
which is a pectic substance, the primary wall which consists
chiefly of cellulose, hemicellulose and pectic materials, and
the secondary wall which is deposited upon the primary wall
after the cell attains its final size and consists chiefly of
cellulose. The secondary wall layers do not develop at certain
points to form the pits, Figure 3, which facilitate the passage
of water and dissolved materials. Lignin, which is a polymer
of high carbon content, may be present in all three wall layers,
Esau (1965).

Cellulose occurs in the form of long chain molecules with
length as great as five microns. A cellulose molecule has a
maximum width of 8 X. Cellulose molecules are combines into
micelle with diameter of 100 X and contains about 100 cellulose
molecules in a transaction. The micelles form a bundle called
microfibril which is 250 X wide and contains about 2000 cellulose
molecules. Microfibrils are combined into macrofibrils 0.4
micron wide and containing 500,000 cellulose molecules in a

tranSection, Figure 4. These macrofibrils are oriented into

,. .., - ,-.-—rniddle lamella — — —— -—middle lamella

I '. . ‘ - .- -"'v" /
. H m: C. ." . ...... .. 9"...
I 3 .‘ . I, "" a. as. . ... a a
. a. ' ‘ e.‘
...- o
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FIG. 2 - PLANT CELL FIG. 3 - THE PIT

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layered
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two olucbse

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FIG.4- CELL WALL CONSTRUCTION
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two or three layers, almost perpendicular on each other, Preston
(1965).

Cellulose does not dissolve in water, but it absorbs water
in large quantities and therefore, most all walls are in a highly

hydrated or saturated condition.

2. Protoplast:

Consists of many components: the nucleus embedded in the
cytoplasm, the cytOplasm layer, and a vacuole filled with cell
sap inside the cytoplasm layer. The cytOplasm layer is surrounded
by two membranes, the endoplast around the vacuole, and the
ectOplast between the cytoplasm and the cell wall. Both mem-
branes control the passage of materials into and out of the
living protoplast.

There are cytoplasmic connections between cells. The cell
walls possess minute pores through which extend fine thread of
cytOplasm called plasmodesmata. These plasmodesmata provide a

means for the interchanging of materials of adjoining cells.

3. Ergastic Substance

These were previously mentioned.

II-A-Z. The Conductinngissues of the Plant:
The conducting tissues of plants are, the xylem and the

phloem tissues.

1. Xylem Tissue:

The function of xylem tissue is mainly to translocate water

and dissolved materials from the soil to the leaves. The components
of this tissue are the tracheids, vessels, ray parenchyma cells,
fibers, and xylem parenchyma, Figure 5. The vessels and tracheids
are constructed of dead cells which lack protoplasm at maturity.

The inside diameter of xylem vessel ranges from 20p to 400” in

trees. In vines it may be as much as 700u in diameter.

2. Phloem Tissue:

The function of phloem tissue is to conduct food from the
leaves to other parts of plants. The components of this tissue
are the sieve tube members, companion cells, phloem parenchyma,
ray parenchyma cells, and phloem fibers, Figure 6.

Sieve tubes, like xylem vessels, are vertically elongated
rows of cylindrical cells. However, the end walls of the sieve
tubes contain numerous perforations, and the cells contain living
protoplasm, but the nuclei are absent at maturity, and the cytOplasm
is continuous from cell to cell through the sieve plates of the
end walls.

The length of sieve tube ranges from 550 micron with pitted
fine-porous plates, to short membered tubes have a length of
about 135 microns with transverse wide-meshed plates. The average
diameter of sieve tube is 23H. The diameter of the pores in the
sieve plates ranges from a fraction of a micron to 15 micron,
and are associated with callose, a polymer of glucose residues,
Figure 7. Figures 8, 9, and 10 show the location of these

tissues in the root, stem and leaf reSpectively.

       
    
  
 

    

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FIG.6 - PHLO'EM TISSUE
FULLER,( I963)

   

pore content;

     

middle lamella cytoplasm

 

FIG. 7- SIEVE PLATE
ESAU, (less)

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FIG. 8- THE MICROSTRUCTURE

 

 

 

 

 

 

 

 

 

 

FIG. 9 - THE MICROSTRUCTURE

”sumowes"— FULLER,(I963I

A EPIDERMIS

B CORTEX

C ENDODERMIS
D PERICYCLE
E XYLEM

F PHLOEM

G CAMBIUM

OF THE ROOT

EPIDERMIS

CORTEX

BUNDLE CAP FIBERS
PHLOEM

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INTERFASCICULAR
CAMBIUM

XYLEM

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FIG IO- THE MICROSTRUCTURE OF THE LEAF

PEAR LEAF”- ssAu . (uses)

l4

II-B. Sap Translocation:
Salisbury (1966), summarized the two main theories of sap
translocation: the root pressure theory, and the cohesion

theory.

II-B-l. Root Pressure Theory:

In this theory, the dissolved salts from the soil solution
diffuse through the apoplast of the cortex of the root. The
apOplast includes the cell walls and the intercellular spaces.

The symplast, which is the living part of the cell, then accumulates
these ions actively by moving them across the act0plast by its
metabolic processes. This metabolic activity is due to the ample
amount of available oxygen in the cells nearest the surface of

the cortex tissues of the root. These ions can move via the
symplast toward the inside root, where the oxygen tension is

much lower and the processes of accumulation are much less
efficient. These ions then begin to leak out into the surrounding
apoplast and into the water-filled xylem tubes. Such an increase
in concentration would then put into effect the process of osmosis,
with the semi-permeable endodermal layer of cells acting as the
semipermeable membrane of an osmometer, Figure 11.

Crafts (1961) pointed out that sap exudation from root
pressure is not abnormal flow contingent upon cutting, for if
the atmosphere was allowed to become saturated, solution would
appear in droplets at the hydathodes and drips from the plant.

However, Fisher (1949), suggested that the pressure in the trunk

15

of a tree is sub-atmospheric since when holes were bored at the
base of a tree, sap flow did not occur but water poured into
the hole was absorbed.

Kozlowski (1964) pointed out that there still are many
arguments against the importance of root pressure to sap ascent,
and it is generally considered not to play a primary role in

ascent of sap.

II-B-Z. The Cohesion Theory:

If water evaporates from the leaves at a fairly rapid rate,
root pressures are not expected to develop at all, and the plant
seems to act simply as a water conduit between the soil and the
air. The actual movement of water through the stem is in response
to hydraulic gradients, but these in turn are established by the
free-energy gradient. Under atmOSpheric pressure, there is a
steep gradient from low to high, "Diffusion Pressure Deficite",
"DPD", and from high to low free energy, going from the soil
water through the plant into the atmosphere, Figure 12. The‘
term, "DPD", is defined as the difference between the osmotic
pressure, "0P", and the Turgor pressure, "TP", which is that
pressure exerted against the cytoplasm and hence the cell wall

as a result of osmosis.

DPD = OP - TP

As water evaporates and is removed from the leaf, it will be

pulled up in the xylem elements. Rather high tensions may be

16

developed in holding the column of water together between the
roots and the leaves. Kozlowski (1964), indicated that the
cohesion theory has been re-examined and re-evaluated in the

light of recent data, and many objections have been raised.

These objections include the impossibility of existence of tensive
channels in presence of free air bubbles, inadequacy of tensile
strength of water, failure of stem pressures to decrease pro-
portionally with increase in height, and insufficient evidence

for existence of continuous water columns.

Preston (1938), pointed out that many vessels were found
filled with gas, and Scholander (1955), has proved that vapor
bubbles in the vine did not prevent the movement of the trans-
piration stream. 0n the other hand, the existence of continuous
columns of water has been acknowledged by many investigators as
Haines (1935), and Gibbs (1935).

Dealing with the pattern of water movement, Rudinsky (1959),
showed that patterns of water uptakes in unilaterally injected
conifers varied greatly among species. He gave five distinct
patterns, and attributed them to anatomical differences in xylem
structure. The most complete distribution of water into the crown
was provided by a system of spiral ascent and the least effective
by a vertical ascent, Figure 13. Kozlowski (1963) showed that
patterns of dye uptake varied greatly with species.

Greenidge (1955), observed that dye solutions moved up to
horizontal saw cut in tree stems, and then were transferred

laterally into regions above the incisions, Figure 14.

phloem
xfiem

: pericycle
. casparian strip

' endodermls

epidermis

 

root hair
/

FIG. ll -ROOT PRESSURE
THEORY

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vertical ascent spiral ascent

-FIG.|3- PATTERNS OF
WATER UPTAKE

 

 

 

 

 

 

 

 

 

‘ I air 90°]. RH
K { DPD = '40 0"“.
.y f
7 \I I low free energy
"I f ’ g/
.\ /
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I :\ DPD=IO-l5 atm.
// A
' t
/—-- roo s
/I \/ DPD=5-6 otm.
\. /-—-—soil water near
field capacity
q ‘_ DPD=OJ atm.
high free energy
FIG. l2 - THE COHESION
THEORY
iii
:55:
2;.
it
"14.3
' III
#1".
I3?
without cut with horizontal cuts

FIG. l4- EFFECT OF CUTS
ON WATER PATH

18

II-C. AssimiIates Translocation:

Salisbury (1966) discussed the translocation of assimilates
from point of origin to point of utilization. The point of origin
is usually a photosynthesizing cell or a cell that converts
insoluble starch to soluble sugar. Substances move by diffusion,
but two mechanisms may be considered to increase the rate of
translocation. The first is the cytoplasmic-streaming hypothesis,
Figure 15, in which a substance can diffuse from the streaming
cytoplasm of one cell to the other. This mechanism is untenable
for mature sieve tubes, because the cytoplasm does not stream in
these phloem cells. The other mechanism was suggested by Mfinch.
This mechanism permits bulk flow of assimilates through the sieve
tube. The mechanism itself consists of two osmometers connected
by a tube and surrounded by water, Figure 16. One osomometer
contains a high concentrated solution, while the other contains
a much more dilute solution. The first osmometer will take up
water by osmosis, developing a pressure on both osmometers which
increases the free energy of the water in the second osmometer
and forces water to diffuse from it. This results in a flow of
material from the first to the second osmometer.

This pressure flow mechanism can be applied to a plant by con-
sidering the producer cell as the high-concentrated-solution osmometer,
the consumer cell as the other osmometer,the symplast as the connecting
link, and the surrounding solution in the apOplast as that in
the Mflnch mechanism, Figure 17. The plant system never reaches

equilibrium because sugars are continually being produced and

dilute concentrated
solution solutipn

  
   

 

 

 

 

 

 

 

FIG. l5-CYTOPLASM STREAMING FIG. l6- MUNCH MECHANISM

I‘ C04

 

1

, ' : 5-1.: --producer cell
high osmotic potential

 

 

 

 

',_--consumer cell
low osmotic potential

 

FIG.I7- PRESSURE FLOW MECHANISM (MUNCH MECH.)
IN PLANT

20

used up.

Manson (1928), showed that the removal of the bark stOpped
sugar transport whereas separation of bark and wood did not, and
that transport took place into the loosened flaps of bark.

Loomis (1945), in a study on translocation of sucrose in
maize, stated that neither the active diffusion nor the pressure
flow mechanism will explain the polarized type of movement where
sugars are moved from leaves containing 0.3 per cent sucrose
through tissues containing 7 or 8 per cent sucrose.

Gauch (1953), showed that small concentrations of boron
greatly facilitated the absorption and transport of applied
sucrose. He proposed that boron reacts with the sugar to form
a sugar-borate complex which moves through cellular membranes
more readily than nonborated sucrose.

Crafts (1961), pointed out that one weakness of Mfinchs' and
others past work was their failure to realize that the phloem is
a distribution system and that its function is not to carry foods
only from leaves to roots; its role is to provide organic nutrients
for every living nonphotosynthetic cell of the plant.

Spanner (1958), put forward a new theory that involves a
bulk flow of the sieve-tube contents actuated by a mechanism
located at the sieve plates. The motive force proposed is
electro-osmosis. Spanned claimed that the three requirements
for electro-osmosis, namely a charged membrane, a membrane
potential difference, and a porous structure in the membrane -

are present in the sieve plate. Spanner attributed maintenance

21

of the potential difference to a cycle movement of potassuim ions
into the sieve tube above the sieve plate and thence out of the
tube below the plate. The return motion of potassium ions takes
place in companion cells or possibly in phloem parenchyma. The
starting device for this mechanism would be:

1. discharge of sugar into the sieve tubes

2. uptake of water osmotically leading to a vertical surge

in cells neighboring the sieve tube, and

3. flow of potassium ions along the direction of flow

in the sieve tubes and counter to this direction in

the neighboring cells.
Once established, this circulation would electrically polarize
the sieve plate causing rapid electro-osmosis through the plate.
Thus each sieve plate would contribute its energy to the flowing
stream.

Crafts (1961) criticized electro-osmosis theory because of
the recognized low permeability of tonoplast of companion cells
and phloem parenchyma, and the lack of an explanation for the
ready reversibility of phloem exudation.

Crafts (1961) mentioned the results of Tammes (1957) in
which he gave the composition of sieve-tube sap of Arenga

saccharifera as:

 

Sucrose: about 15 per cent
Nitrogen: total 410 mg per liter

Potash: 1200 mg per liter of K+

22

Phosphate: 98 mg per liter of P03-

Magnesium: 96 mg per liter of Mg2+

Calcium: 10 mg per liter of Ca2+

Hipton (1955), mentioned that when phloem exudation takes
place by mass movement of a solution through sieve tube strands,
the strands might be sufficiently permeable to allow a flow of

solution at a linear velocity of 200 to 500 cm per hour.

II-D. Electrical Potential in Plants:

The phenomenon of the existence of a natural electric poten-
tial in plants has been observed by many investigators. Fenson
(1957), mentioned that Kinkel in 1878 suggested that water trans-
port was the cause of plant electricity. Waller (1925), referred
to Haake who in 1892 was the first one to observe alternations
of potential in plants due to a change of illumination. Haakes'
conclusion was that oxygen respiration and carbonic acid assimila-
tion are prominently considered in the electric current in
plant. The movement of water possibly has a share in the caussative
conditions of the electric current, but its influence is but
slight. Waller (1925), gave the same observation. By illuminating
one half of the surface of a greem leaf and shading the other
half, he found that photo-electric response was mainly dependent
upon the metabolic activity of chlorophyll. He mentioned that
photo-electric current varied in magnitude and direction in
different leaves. He also observed that photo-electric current

occurred in some cases in the absence of chlorophyll.

23

Lund (1931), observed that in normal unstimulated condition
of Douglas fir, the main apex of a lateral branch maintained an
electro-positive conditions to all points below it. After several
experiments, Lund (1931 b) concluded that the cortex of the Douglas
fir is the origin of the E.M.F. and that the orientation of the
radial. E.M.F. in the cortex is Opposite to that in the wood. On
other experiments on the Douglas fir, Lund (1932), found that the
electric polarity of the apex could be decreased, reversed or made
equal to zero by means of changing its temperature.

In some earlier experiments, Lund (1927) observed the
electropositivity of regions of greater growth to more basel
regions. March (1928) observed the same phenomenon on growing
roots. In his discussion on the possible origin of continuous
bioelectric current in root tips, Lund (1928), concluded that it
was a result of oxidation-reducation potentials developed by the
respiratory mechanism of the cell. These potentials were deve10ped
at cell surfaces, internal, external or probably both, resulting
in typical polarization phenomena. Scott (1967) mentioned that
almost always the interior of the cell is more negative in
potential than the external solution by 70 to 150 millivolts.

March (1928) agreed with Land and adds that the E.M.F. of a
given length of onion root is the algebraic sum of E.M.F.'s of
the individual cells of such length. Lund (1930), also con-
cluded that the inherent electric potential existing on the leaf
of Bryophyllum must be equal to the algebraic sum of a complex

system of E.M.F.'s of individual cells.

24

Burr (1942), observed a potential difference between the
base and the apex of the seedling growing root during development,
with the base positive and the growing point negative. He men-
tioned that this potential was complicated by fluctuations which
presumably represented the diversion of energy from the electrical
reserves of the organisms. On other experiments, Burr (1944) found
that as fruits grew larger, the potential gradients tended to
decrease.

Burr (1944) in his experiments on young maple trees, where
two electrodes were introduced between the bark and the cambium
on the trunk of the tree, five feet apart, observed natural
electric potential in the trunk with the upper electrode positive.
He noticed also that in the early morning from two to four hours
before sunrise, the potential difference was maximum, then it
dropped without interruption until the afternoon. After sunset
the potential increased again.

Burr (1945), in other experiments, observed that during
winter months, the upper electrode in the tree was positive.
During the summer months, the tree showed a reversal in polarity.
By carrying on the same experiments the following year, he found
that during December, the upper-electrode was positive, while in
January the upper electrode became negative and in February it
became positive once again. Burr (1947) observed that in Fall
and Winter, when the tree became dormant, the upper electrode

became increasingly positive. In early Spring the potential

25

tended to fall and the polarity reversed. In Spring and Summer,
the potential reversed once again, with the upper electrode
positive. Before the leaves fell in the Fall, the potential
started to rise markedly. Part (1948) concluded that the apex of
a healthy tree is usually more positive than the base.

Fensom (1957), after reviewing many of the earlier experiments
concluded that these published reports did not show any obvious
correlation between transpiration and potentials. He mentioned
also that since many of these experiments showed that bio-poten-
tials might be accounted for in terms of membrane permeability
as well as by the oxidation-reduction systems of metabolism,
there has been a quite reasonable tendency to attribute potentials
to tran3port rather than the reverse. Fensom (1958), on a study
on the sunflower, showed that a correlation existed between
tranSport pattern and bio-potential patterns.

Fensom (1963), in his experiments on three kinds of trees,
found that there was yearly and daily rhythms of electrical
potential. This potential was due to the effect of electro-
osmosis or streaming potential, and was influenced by major
temperature changes, by heavy rain, and by many other factors
inherent inside the living tree. Fensom (1962) showed that
artificial flow through open channels of woody tissue produced
changes in electrical potential. Fensom (1959) interpreted the
electrical potential differences which were found in dead wood
when it was wetted, as resulting from local differences in ion

concentrations which cause Donnan potential.

26

The existence of these natural electrical potentials,
caused many investigators to try to utilize this phenomenon to
affect the biological processes inside the plant. Blackman (1924),
showed that by stretching insulated wire above the crop at a
height of about seven feet, and positively charging it to a
voltage of 40,000 to 80,000 volts with a discharge rate of .5
to 1.0 milliamper per acre, the increase in yield of oats was
between 30 and 50 percent. In another experiment carried on Pot-
Culture, Blackman (1924 b), found that the percentage of increase
in the dry weight of Maize was 27 percent.

Plowman (1909), observed that an electric charge of positive
sign inhibited the vital processes of plant protOplasm, while
negative electric charge stimulated such processes. Collins
(1929), observed that current which was supplied by suspending
a charge network above maize plants with current intensity of
10"9 amperes per plant did not show any significant response.

Murr (1963), by positively charging a suSpended wire mesh electrode
over the plants with 30 to 75 Kvolt/m, found that the treated
plants produced less growth, a leaf tip burning phenomenon occured,
and the whole plant appeared deeper green when compared with the
control plants. On further discussion of this effect, Murr (1965)
believes that this effect may not be electrostatic but may be
attributed to lethal current densities caused by corona discharge
from cells near the tip.

0n the other hand, several researchers tried to direct

current inside the plant. Knight (1914), found that direct

27

current of a density of 10.6 to 10.4 amperes had no effect upon
the respiration of the germinating peas. Breazeale (1951),
showed that ion absorption by plants is an electrical phenomenon.
When a negative lead of -2.23 volts was connected to the tomato
plant and the positive to the metal container, the cation uptake
was greatly increased. When the negative lead was attached to
the metal container and the positive to the plant, absorption
of cations was not influenced by the electric current. Breazeale
(1953), in other experiments, showed that the uptake of Na, K,
and Ca was actively stimulated by applying the electrical current.
Berry (1943) observed that the response of the inherent
electrical potential of onion roots to an applied direct current
depended upon the direction and magnitude of the applied current flow.
When the current was directed from the top to the base of the plant
the positivity of the natural electrical potential decreased.
Clark (1938), showed that the negative apical polarity of
Avena coleoptile was increased on stimulation by alternating
current. At the same time, he showed that the inherent potential
had no apparent causal relation to polar auxin transport in
plant. Rosene (1937) noticed that the longitudinal potentials
of the branches and stem of the Douglas fir were modified by the
application of an electric current from an external source.
Scott (1967), after reviewing many experiments,concluded
that many attempts have been made to modify the rate of plant

growth either by the application of electrostatic fields or by

28

the passage of electric current through the tissue. Most of
these treatments have either had no effect or have caused reduced
growth and sometimes tissue damage.

Fensom (1962) showed that artifically applied voltages pro-
duced two effects. First a small and temporary disturbance in
sap flow, second a sudden large surge of sap flow into the stem
after prolonged electrical stimulation of up to 45 volts. This

was accompanied with artificial guttation.

II-E. Background Theories:

 

Collins (1961), explained the phenomena of streaming potential
and electro-osmosis. When two chambers containing water are
separated by a plate of porous material, and a difference in
electrical potential between the chambers is maintained by metal
electrodes placed on each side of the porous place, a flow of
water occurs from one side to the other. This phenomenon is called
electro-osmosis. Liquids other than water also exhibit this
behavior.

Conversely, when water or other liquid is forced through a
porous plate by a pressure differential, an electrical potential
difference across the plate is observed. This potential is
called streaming potential.

Both of these phenomena are associated with the existence
of charged layers at the solid-liquid interface. These layers
behave as two parallel surfaces of opposite electrical charge

separated by a distance of molecular dimension. The potential

29

difference between these two layers is called the zeta potential
(c).

If the charged double layers are treated as a condenser with
parallel plates, 3 distance dm apart, the zeta potential can be
related to the charge e on a plate as

c = edm

DE
0

where D = the dielectric constant of the liquid

—12 2 2

so = 8.85 x 10 (coulombs) / newton - (meter) in M.K.S.
units
When applying electric potential E across the plate, the electric
force FE which will diSplace the charged layer will be gE per unit
1:

area.

where = the thickness of the plate

t
E = applied electromotive force in e.s.u.

and the total force will be given by integrating g§_ over the
t

pore surface, which is proportional to the bulk volume of the

porous plate.

a:
ll

.EE (cAt) = ceAE
t

where c = the proportionality constant for pore surface (cm-l)

A area of the plate
As the electric force diSplace the charge, the fluid is dragged
along with the charges. For a steady flow, the displacement force

FE and the viscous force F“, which Opposes the flow, must be in

3O

equilibrium. But Fu is prOportional to pore surfaces, velocity

u and visocosity u of the liquid

r11
II

Buu (At) = Buqt

where B proportionality constant with permeability considered

q = uA = volume flow

At equilibrium ceAE = Buqt

c e A E = C"3’50 A E

q = _ ——

B u t Bdm t

 

This equation gives the magnitude of electro-osmotic flow rate.

Mason (1950), discussed the electrokinetic theory of fibers.
He mentioned that the fundamental quantity of this theory is the
zeta potential which in the beginning was considered to be of
a simple nature, but has since been the center of considerable
controversy. The theory says that a solid in contact with polar
liquid acquires an electric charge. By the absorption of cations
or anions having a specific affinity for the solid, the excess
charge of opposite sign accumulates as a diffuse ionic layer in
the liquid adjacent to the solid. This mobil charge causes the
potential difference which is known as the zeta-potential. If
the liquid is caused to flow through a cellulose fiber pad, by
the application of a pressure gradient, a flow of electric charge
occurs.

Mason (1950) gives the relation between the current I, capillay

path length 1,.pressure difference Ap, and pad resistance R by

31

Helmholtz-Smoluchowski equation:

= V _ DC

 

 

Ap RAp - 4np1 E
where 5 = pore factor
V = the streaming potential

However, Mason (1950) pointed out that the origin of the

electric charge in cellulose in contact with pure water is obscure.

Neale (1946) mentioned that most chemical neutral solids
acquire a negative charge in contact with water and concluded that
this is due to an intrinsic property of water to expel electrons
from itself.

Fensom (1957) indicated that the two expressions commonly used
to describe electrokinetic movement of liquids in narrow passages
are the Helmholtz-Smoluchowski equations. For electro—osmosis,
where an applied E.M.F. produces flow of liquid.

= ACDC
41m 1

E (1)

q

 

where AC = the cross section area of a capillary tube.

For streaming potential, where there is a pressure causing flow
of liquid which produces a difference in electrical potential
between the ends of the flowing column:

V a D C Ap (2)
4 n ulkc

32

where kC = Specific conductivity of liquid

Fensom (1957) gave the value of these parameters in xylem tissue as:
D = 80 u = 0.01 poise C = 0.013

From these values, and by considering the velocity of the liquid to

be u = q , he solved the first equation for u as:

A
c

u = 0.92 x 10‘4 E

1
This equation means that 4500 volts would be required along
150 cm of tracheal tube to give flow velocity of 10 cm per hour.

To solve the second equation, he used Poiseuille equation:

Ap , 891p = 128 glu a 32n1 u u
r 4 D 4 D2

 

rc = capillary tube radius

DC = capillary tube diameter

He estimated the value of V to be:

- 2
V a 8D; _ 2.9 x 10 1
k n2 k D

CC c

ONE:

This equation means that a flow rate of 10 cm per hour in

tracheal diameter of 20 microns with kc = 2 x 10"6 ohm‘1 will give

33

a streaming potential of l millivolt.

From these equations, Fensom (1957) believes that the stream-
ing potential will be significant only if tranSpiration rates
are high, if liquid conductivity is very low, or if the xylem
tubes are small in diameter.

Fensom (1957) pointed out that if the observed potentials are
assumed to be metabolically maintained, then the electro-osmotic
pump can move the water with a speed of 36 cm per hour if the
potential difference is 100 millivolts and the flow passes through
10 barriers each of 1 micron thickness. These barriers exists
across xylem vessels when they are new, and act as electro-osmotic
pumps to move water and small ions.

Lundegardh (1951) explained the existence of electrokinetic
potential across a membrane separating two solutions by the
activity of hydrogen ions on each side of the membrane.

R T +
V= g 1 (H) 2
Me n (HI) 1

where Rg = gas constant
T = absolute temperature
e = charge

and (H+) 1 and (H+) 2 are the activities of hydrogen ions on
side 1 and 2 respectively.

According to Osterle (1964), the irreversible thermodynamics
of electro-osmotic flow can be summarized by the conversion of

electric power into hydraulic power. When a liquid electrolyte

34

flows through an insulating circular tube, the direction of the
potential difference AV, current I, pressure difference Ap, and
flow rate q, will correspond to that conversion of electrical
power I AV into hydraulic power qu.

The dissipation rate (Dr) associated with the mode of conversion

is:

D = IAV - qu
r

The forces AV andAp and fluxes I and q will be linearly related as

 

 

Ap = a AV - RH q
I = CE AV + a q
where a = cross-coefficients which are identical by Orsager's
reciprocal theorem
R = viscous resistance, R _ 8 u 1
U U “ 2
Ar
0 A
CE = electric conductance; C = E
E 1
CE = electric conductivity

If the pressure differential were zero, an applied electric field
would move the fluid through the tube with a uniform velocity uO

expressed by:

u _ b AV
0 ' o 1

 

where bo = the electro—osmotic mobility of the liquid with respect

to the wall

35

b = E (—Wo)

where E the permittibility of the liquid

We = the electro—kinetic potential

With the use of the simple parallel plate condenser relationship,

where q = the surface density of the charge counter to the
charge absorbed on the tube wall
d = the apparent thickness of the double layer on
the tube wall

Also a can be solved by the previous equation to be:

with a, R and C known, the irreversible thermodynamic description
of electro-osmotic flow is complete.

Fensom (1959) related streaming potential and electro-osmosis
to the hydrogen ion and hydronium (H3O+). This ion moves the
fastest in plant electrolytes with (HO-) next and (K+) third.

The hydronium ion has a diameter of 1.6 X.while that of hydrated
potassium ion is 3 X. Hydronium ion must be present in appreciable
concentrations wherever respiratory acids are being produced.

Fensom (1959) summarized the process of producing the hydrogen

ion by the following equation.

36

water + acid :::::; radical + H 0+

3

The hydrogen ion will be increased in any process that:
a) increases acid concentration as in respiration
b) decreases the concentration of the free radical
c) decreased H30+, as happens by the translocation of
H30+ away from reaction zone by its free migration
through the plasmalemma.
On the other hand, hydrogen ion will be absorbed if acid is
being removed as happens in evaporation of CO from the surface

2
of a mesophyll cell in the leaf in the dark

+ -
H30 +Hco3 :7. HCO +1120 4:... 2H20+CO

2 3 2

Fensom (1959) showed the role of hydrogen ion in electro-osmosis

by considering a system consisted of membrane separating two
solutions of l/lO M (K Cl) and 1/10 M (H Cl). Ions will attempt

to get through the holes of the membrane. The (Cl-) ions will

have the same potential on the two sides of the membrane, while
(H30+) and (K+) will attempt to pass to the opposite side. Because

(H 0+) moves faster, it will cause a positive charge on the opposite

3
side (streaming potential). However, since the membrane has
negative charge (zeta potential), the previous streaming potential
will cause electro-osmotic flow of (K+) ion on the opposite dir-
ection. These two flows, which are opposite in direction will

be balanced after short time. But if the holes in the membrane

were too small for (K+) ion to pass, this electro-osmosis flow

will be stopped.

37

Tyree (1968) suggested the use of the Onsager equations of

irreversible thermodynamics.

J a L d2 +L dE
pp d1 PE d1
I L d + L dE
= EP __2_. __.__
d1 EE d1
where J = flux of solution in cm3 sec_ per cm2 of tissue
2
I = flux of current in amp / cm of tissue
dp_ = the hydro-kinetic pressure gradients in (Joules cm_3)
d1 1
cm-
Igg = the electrical potential gradients in volt cm-1
d1
and LEP’ LPE’ LPP and LEE are constants. These are called the

Onsager coefficients.
Tyree (1968) relates the hydro-kinetic pressure gradients

to the electrical current by the equation:

dP _ A I

—-..—- —

d1 2 ALEP

and to the electrical potential by the equation

511: LEE dE
d1 L d1

38
where L = the hydraulic conductivity of the xylem.
PP

Dainty (1963) also expressed the electro-kinetic phenomena in
terms of irreversible thermodynamics and Onsager coefficients. He
discusses three models: the Helmholtz-Smoluchowski model, the
frictional model, and the model of Schmid. All these models assume

linear relations to fit the principles of irreversible thermo—

dynamics.

39

III. MATHEMATICAL ANALYSIS OF FLUID TRANSLOCATION
INSIDE XYLEM TISSUE

The plant as a biological system is very complicated. How-
ever, Figure 18, simplifies the plant system and the physiological
processes that occur inside.

Translocation of fluids occurs mainly in two kinds of tissues:
the xylem and the phloem. The xylem tissue, which this study
concerns itself with, extends from the roots to the leaves. It
begins at the root hair zone where the conditions are:

l. The xylem tubes are newly developed.

2. The existing fluid is a low concentrated solution.

3. The water potential of this solution is higher outside

than inside xylem vessels.
At its leaf end, the conditions are:

l. The vessel ends are closed and are surrounded with living
cells.

2. High rate of transpiration during the day, and therefore,
water solution in the surrounding cells exists under
negative potential, lower than that inside xylem vessels.

Inside the root and the stem, between the root hair zone and
the leaves, xylem vessels are surrounded by living tissues which
differ in their water potential during the day and night.

To study the fluid flow process inside the xylem, and to
determine its relationship to the natural electrical potential

which exists in it, a representative model has been deve10ped.

4O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C ... _ H20
2 g _____ MINERALS
§ :. ......... 02
g .............. C02
( ‘W _____ CARBOHYDRATES
g E * --------- __..._... ASSIMILATES
g g “““ ’ _.I.__I,__ ENERGY
< W HEAT
3
g.- E
T : *
I ' I
_ Y Y 5 ,
PI 1W
LEAVES RES manou
I
I 1 I I I
I : I i ASSIMILATION
I I ! 5 .
I g | I
I ' =
I IN”
W
STEM
I A I I
. . H
I I | ,
I I - '
I I I I
I I . =
I 1 IN .
‘W
ROOTS }
I
III
.I LI
l 2 .
' E
' I
I;
THE SOIL

 

 

 

FIGJB. THE PHYSIOLOGICAL PROCESSES
IN PLANT.

41

‘The model, Figure 19, consists of a long porous and permeable
tube closed at both ends. The surrounding of this tube can be
divided into three regions. The lower one is the high water poten-
tial region, which represents the root hair zone. The middle region
is the longest one, and its water potential differs according to
the rate of the other physiological processes. This region repre—
sents the surrounding parenchyma, fibers, and cambium cells in
both the root and the stem. The third one is the low'water
potential region which represents the surrounding tissues inside
the leaf.

It is assumed that the analysis of what occurs in this model holds
for all xylem vessels. It is further assumed that what occurs
in the xylem tissue is a summation of that which occur in the
individual xylem tubes.

The inside and the outside radii of the tube are ri and r0
respectively, therefore, the thickness of the tube wall is (ro-ri).
The length of the tube is represented by 1. The pores in the
permeable wall are of two kinds: a) narrow ones which are gaps
between the three cellulose layers of the secondary wall, ‘For
this study, they are assumed to be circular in cross section with
diameter equal to (Sc, b) wider ones with diameter 6p which represent
the pits in the*wall.

If a square segment of the wall is considered, Figure 20,
the energy balance through it will be:

Energy in + Energy dissipated or generated

= Change in wall internal energy + Energy out

42

- -- / low water poIonIIaI zone

\I
\ ~- 2M /
\QL‘T / (Ihe leaf)

 

 

....... \I/?
1 ; I
5 ~41
E I“?
5 l FIG. 20
i . i ENERGY FLOW THROUGH
\ i I .4 TUBE WALL
\\ . //
\ /
(the stem)
(the root)

 

 

   

 

 

---"??? 1' \Whlgh water potantlol ' Oz
' I
j/_J.\t zone (root hoIrI
/ "
FIG. 2|
FIG.I9- XYLEM TUBE MODEL FLOW WORK THROUGH A

TUBE SECTION

43

The "Energy in" term is AQx and can be defined as:
AQx = -Lp dA _%j):__
where: AQx = the energy which flows in the x direction per unit
time. It can be considered as flow work, with dimen-
sion (dyne-cm/sec).
L = rate of flow of energy, or rate of flow of work, with
dimension (dyne - cm/sec - cm — unit Ap)
dA = area of wall piece, with dimension (cmz)

p = water potential with dimension (dyne/cmz)

§p_ = water potential gradient in the direction x
3x

The term "Energy out" Qx‘+ dx can be eXpressed as:

AQx+dx=—[Lp dA 32 + 3 (LI) dA ap)dx]

8x 3x 8x

There is no source for generating energy from the view point of
fluid dynamics, but there is energy dissipation due to the
friction between the inside surfaces of the pores and the fluid,
and perhaps between solute molecules and water. The dissipation
rate per unit volume of pore space in the wall material is A0.
This dissipation rate is a function of fluid viscosity, temperature,
and velocity gradient at the inside surfaces of the pores.

A52 = f(U, T, du, 090000000)

dx

To simplify the analysis, A0 can be considered as an average rate.

Therefore,

44

Energy dissipated = A0 ¢ dA dx
where ¢ = the porosity of the wall material.
The term "Change in internal energy", can be eXpressed as:

Change in internal energy = dA dx ¢ U 32
81

where U energy needed to change one unit volume of wall pore

Space, one unit of potential

T time in seconds

Therefore, the energy balance equation becomes:

-Lp dA 32 -A6 ¢dA dx = ¢U dA 32 dx -[:Lp dA 32

8x 3T 3x
+ a (L dA 32 ) dx] (1)
3x p 8x

Canceling, Equation (1) becomes

 

 

a (L 32 ) -¢AQ = ¢ U 32 (2)
3x p 3x 3r
Lp can be considered as Lp = P - one unit Ap

one unit length

where P = the rate of volume flow per unit area under the existing

conditions with dimension.(cm3/cm2-sec)

To simplify the analysis, Lp can be considered as a constant under
certain conditions. Although, as mentioned previously, it varies
according to the rate of volume flow, it can be considered as a
constant since the volume of flow does not change as long as the
potential differences does not change. This is the case if the

analysis is made for a short period of time. On the other hand,

45

the whole tube wall can be considered as constructed of one
material having the same characteristics at any point. Therefore,

equation (2) becomes

fi-A=LL_QL <3)
3x2 L L 8T
p P

For three dimensional model, and by applying the same analysis,

the equation becomes:

 

JELT‘ 2.22..+_33£_'$_§_Q_=¢U 3p (4)
2 a 2 2 L L 31
3x y 32 p p

For cylindrical coordinates, the equation becomes:

 

2
_3__R_+_1_.._3_IL+_1__§_2L+_§3L‘_9AQ_ =
2 r 3r 2 2 2 L
3r 1' 39 32 p
LU 3p (5)
L 3T

However, the conditions around the tube wall in the horizontal plane,
can be assumed symetrical. Moreover, the flow of energy in the z
direction, inside the wall itself, is of lower order than that in
the r direction, because §p_ << §p_

82 Sr

Therefore, 322 and 822 can be neglected, and equation (5)
2 2
ea 32

becomes:

 

_.§_Z_E_+l_‘1P_T_ff§£=<PU 3p (6)
2 r 8r L L 8T
3r p P

The plant is not in a steady state condition because of the dynamic
physiological processes. As mentioned previously, the change in
the internal energy of the tube wall, during a Short period of

time, can be considered negligable, and the term 32 approaches

3T
zero. Therefore equation (6) becomes
A.
(122 +1 dp-¢Qr=0 (7)

 

This equation can be solved for AOr by multiplying it by r and

considering the boundary conditions.

r dzp + QB. _ ¢Aer (8)
2 dr L
dr P
with boundary conditions:
p = po at r = r0
p = p1 at r = r1
.92 = 0 at r = 0
dr

d 2 d

dr r dr r

Then: (1 [r g2]_ “er (9)
dr dr ‘ L

47

AQr is an average value, but if r < r1, AQr = 0

Therefore, integrating equation (9) gives:

A. 2
r dp = ¢ Qr (r — r?) + c (10)
—-*-- 1 1
dr 2 L
P

Dividing by r and integrating once more gives:

 

 

O 2- 2 2
p _ ¢AQr [ (r r1) —r1 ln L]+ cl 1n r + c2
2 Lp 2 r1 (11)
Considering the condition 92_ = 0 at r = 0
dr
2 2
0 (0) = Q (0) (0 — r1) + c1 c1 = 0
2 L
P
Considering the condition p = pi at r = r1
2 2 2 r
Pi=___9'__(_0)__ (rl-ri) r i+c
2 L 2 i In ;—' 2
P 1
c2 = p1
Considering the condition p = po at r = r0
¢A° 2 2
p = Qr [Ito-ti) _r 1n: ro]+p.
P
A. 2 2 r
p—pi= ¢Qr [(r “ri) ”Zr 1“. __0_]
° 4 L r
p i
4 L
A0, = __ p LPOTPi) , (12)
¢ [( 2 - 2) - 2r r j
to ri iln

48

Since AOr is the dissipating rate within one unit of volume of

pore space, therefore the dissipation rate for a section of the

. **
tube of length dz will be = er

dér** - 4 LP (p0 _ pi)

 

 

 

—fi' 5‘- 7T_—"-‘_— 0
I [0' r3) - 2:, in r..]
O Y;
**
. 4NL
er - p___(p0 - 3.1) dz (13)
21‘2 In r0
1 ——
T
1_ __.._. 1
2 2
r - ti

and the dissipated energy for the whole length of the tube will
be

* **
. _ 1 .
or -J{o dor

 

 

*
('2 =f1 do”. ””113 (Po-P1) dz (14)
r o o
2 r
Zri 1!]. “fi-
1' 2”.“‘2'
r " r
o 1

This dissipated energy occurs as a result of fluid flow in and

out of the wall of the tube.

L is the rate of flow of energy and it is prOportional to the
P

volume flow rate. On the other hand, "Poiseuille" equation relates

the volume flow to the potential difference (po - pi).

P -P = 3.1.1.1; or q= (Po-Pin“
o i 4 8 I u

Therefore, L can be written in terms of (p — p ) as:
P 0 i

 

 

L = P ‘_one unit Apfi N
p ' one unit length
P = ( po - pi) _ C
u
‘where C = constant, with dimension cm
Therefore,
L = C (pO - pi) per unit Ap ~ (15)
P u unit length

Ihiserting this expression for L in equations 12, 13, and 14 gives:

 

 

 

 

p
° 2
Qr - ac (po - p1) >0 (16)
¢U 2 2
(rz-r)-(2r lnro)
o i i ';—
i
.** p p2
er = 4n c ( o - 1) _ _" dz >0 (17)
u 2r lnl:g
r
1_ i
r2 _ r:

 

 

Qr = f; 317-9 (p0 " pi) d2
2 r
u 21' In .2
1 r
i
1-
2 _ 2
r0 r1

 

 

Q*=4nc f1 (po-Pi)2 dz >0 (l8)

1' T“— o _._._.__..__.___..-

2 r

O

21' In -I.----

1_ i
2 2

r - r

However, there is other energy dissipated due to the friction of
fluid with the inside surface of the tube. This energy loss can
be estimated by considering a section of the tube, Figure 21, of
height dz located at the bottom of the tube. The energy balance
for it will be:
Energy in + Energy dissipated inside the wall
= Change in the internal energy of the wall
+ Energy dissipated on wall surface + Energy out
The term "Energy in" consists of two items, Qz and AQr. Qz
is the energy flow in z direction. But Qz = 0 since the tube is

closed at the bottom. AQr is the flow of energy in r direction.

AQr=-Lp dA g2 =-21Ir dz L «32
dr p dr

r

f°AQrg§ = fpo 2an dz dp

r1 r P1

AQ =_ 2N Lp (p0 - pi) dz
r v _

r
0
In—
I

i

 

51

 

A0 = _ 2n C (p - pi)2 dz (19)
r “*Efrrrr' o
o
u ln “'
r1

The term "Energy dissipated inside the wall itself," has been com-

puted to be:

** 2

 

 

dOr = 515; (po-pi) dz (19)
u
2 1'0
2r 1n -"
I'
1.. i
2 2
r0 — ri

The term "Change in internal energy" can be drOpped out for the
same reasons mentioned previously.

The term "Energy dissipated on the inside surface of the
tube," 02 is a function of flow temperature, viscosity and velocity

gradients at tube inner surface.

02: f (U, T,51_L_1)
dr

However, the dissipated energy is prOportional to the inside

surface area of the tube, and equals:

Oz (2n r ) dz
1

The term "Energy out" Q is eXpressed as:
z-+ dz

sz+ dz = Q2 +.%E__ (Qz) dz

52
Therefore, the energy equation becomes:

2
Q + 31C (Po " Pi) dz- 4" C (p0 - pi)2 dz =
z ._.___

 

 

 

 

 

 

 

 

 

 

H In ro u 2r2 1n rO
— i —_
r1 r,
1
1-
2 _ r2
0 r '
Q + 3Qz +Q 2nr dz 0 1 (20)
z 3 z i
z
Canceling, equation (20) becomes
d 2
Q2 = 2n C (p - p ) - 4n C (p0 - pi)2
d O i
r r
z u 1n._g u 2r 1n _9
r1 1 r1
2*2
ro - ri
- O 2nr. (21)
z 1
Integrating equation(21) gives:
1 p 9-2 1 p 92 d
Q1=27ICfO(O- 1)dz-4IIC [O _(__o___- 1) Z
N U 2
ln ro 2r In ro
T i T
i i
1-
r - r
o
- 2n 121 ri Qz dz (22)
Since Q = 0 at z = 1, because the tube is assumed to be closed

at both ends, therefore,

53

 

 

 

2 .
gig]; (Po—P1) dz+2nfgziqzdz=
2
zri 1n _:_9_
I_ 1
2 2
r _
o 1.i
1 2
2n c [0 (go - Pi) dz (23)
U r
lnI—Q
r
1

i. e., the total loss of energy inside the tube wall material and

on the inside surface of the tube equals

£10
11

 

[3) (1:0 - Pi)2 _ dz (24)
1'

111.2

r
i

While the energy dissipated only by the friction of fluids on the

inside surface of the tube is:

7
l . .7,
n n 1 _ _
2 f r 0 dz 2 C j (p p ) [,. ._1___

 

 

ln-Jz
r
i
12 ] dz =
r
2r In _11
‘1
' ‘ “2 2
r0 - r1
1 r0
2 2 n.__
2n CJf; (po - pi)2[ (to - r1 — Zfig, fig) ] dz (25)
u r0 2
1n —— (r - r1 - 2ri 1n.:g )
r1 r

54

These energy equations were solved for the dissipated energy for an
important reason. If the natural electric potential in xylem
comes from sap flow process, it must be a result of a conversion
of some of the energy to electrical energy. Referring to the model,
the sources of this electric energy may be one or more of the
following:

1) the friction of fluid and the wall

2) the chemical concentration gradient inside the tube

3) the zeta potential

4) some biological processes in the surrounding tissues,

i.e., an external source of energy outside the tube.
In all cases, the existence of electric energy within the model
is a result of dissipation of some of the available energy.

If the performed experiments show a relationship between the
electric energy and the dissipated energy, equations 24 and 25
can be used to determine the magnitude of the generated electric
energy.

The proportionality factor between the two kinds of energy
will depend on the mechanism responsible of generating this
electric energy. This factor can be determined experimentally
also.

Practically, equations 24 and 25, can be used to determine
the dissipated energy due to the sap flow process in the xylem
tissue of the plant. Next, the prOportionality factor can be

used to determine the generated electric energy. The magnitude

55

of this electric energy, the flow rate and direction, and the

pore diameters, at any location in the xylem tissue, will help in

estimating solute movement and the surrounding tissues reaction.

The two expressions: (p - pi), and L , which were used in
o

P

the analysis, can be further defined as follows:

a) The term (p - pi) is the water potential difference
0

b)

L

P

between the two sides of the tube wall. It is not just

the hydraulic pressure difference, but it is a combined
term consisting of the hydraulic pressure difference,

the osmotic pressure difference, and any other chemical

potential differences. The dimension of this term is

(dyne/cmz).

The term L is the rate of flow of energy, or the rate

P

of flow work. It can be determined experimentally by

 

g/A .
dp/dx
___l__ [ Thickness X volume of flow per second X
(po - pi) Area
fluid potentia1]= l [ cm X cm3 X dyne ] =
Ap 2 sec 2
Cm cm

dyne - cm
sec—cm—one unit Ap

 

can also be determined by equation (15).

The coefficient C in equation (15) can be estimated by referring

to ”Poiseuille" equation:

 

4 4
C = c*[a6cfi+fib 6p ]
(r -r)
O i

where a, b, and c* are preportional constants

57

IV. EXPERIMENTAL ANALYSIS

The relation between the dissipated energy, flow rate, and
the electrical potential differences, which have been observed
by many investigators, can be determined experimentally. The
source of this electrical potential, according to the previous
review of literature, is due to the zeta potential. This concept
can be investigated experimentally.

AS the mathematical analysis was done for a model repre-
senting the xylem vessels, the experimental analysis will be
performed on a model made of material representing the wall of
the xylem vessels. Filter paper "Whatman No: l" was used since
it is made of pure cellulose. The reason for using this filter
paper is to avoid any interference of the living cytoplasm or
any of the biological processes which occur in the natural stem
of the plant, thus enabling the study of only the effect of fluid
flow on the development and magnitude of this natural electrical
potential.

A fluid was forced through a pad of filter paper. Elec-
trodes located on each side of the pad were used for measuring
the generated voltage and electric current. Figure 22
shows the schematic diagram of the apparatus used, and Figure 23
shows the actual appartus.

The pad .9 cm thick, was constructed of 50 Sheets of filter
paper. It was kept in a plexiglass box, the inside of which
was coated with paraffin wax. The box had a circular hole on

each side. A glass tube of one inch inside diameter was fixed

mDF<m<nE< 0mm: m1... m0 Z<mo<5 o:.<s_m:om INN .oE

       
   

332.8

:23...»

        
       

..20560
3.25.? .3339.

  

|l'.

\ >833

\

3:32.. Lowe: 39:02» /:o
:0 out :00 Each-n: 509.353.. overdo

Alv

    

59

 

FIG. 23 A. The apparatus used to determine the
electrical current and voltage. Showing

the general set up, instrumentation, and
Faraday cage.

 

FIG. 23 B. A close up of the cellulose pad in
the plexiglass container.

60

to each hole. With the pad in place the plexyglass box was

sealed with the paraffin wax to eliminate any air or water leakage.
Therefore, fluid was forced to pass through the glass tubes with
the pad between them.

The unit was placed inside a Faraday cage to eliminate any
electrical effect from the surroundings. For the same reason,
shielded wire was used to connect the electrodes with the measuring
instrument.

Tests were performed using the following fluids:

1. Pure distilled deionized water at 23.80c

2. Solution of 0.005 M of KCl

3. Solution of 0.01 M.of KCl

4. C02 sautrated water

5. Warm distilled deionized water at 30.00c

Provisions were made to allow doing some changes during the
performance of the experiments, such as: the change of pressure
head, the change of the distance between the electrodes and the
surface of the cellulose pad, and the change of the direction of
the flow.

Silver - Silver chloride electrodes were used. The coiled
wire electrodes were prepared as follows:

1. The base of the electrode was insulated by a thin glass

tube filled with paraffin wax.

2. The wire was coiled, then coated with the silver chloride

layer. This coating was performed by immersing the

coiled end of two electrodes, facing each other, in 1%

61

HCl acid. The other ends of the electrodes, which were
in contact to a 1% volt battery, were reversed each 30
seconds for 6 complete cycles.

3. The coiled end was washed with deionized water before

the electrode was used.

The electrical measurements were done by a "Keithley 150 B
Microvolt Ammeter" having a voltage range from 0.01 microvolt to
1.0 volt, and an.amperagerange from 0.01 nano ampere (nano ampere =
10.9 ampere) to 1.0 milliampere. The values measured were
recorder on a "Keithley 370 strip recorded", having Speeds of
.75, 1.5, 3, 6, and 12 inch per minute, and same speed values
per hour.

The pressure head difference was measured by a "Merian mercury
manometer".

The distilled deionized water, which was used in all the
experiments, was made by passing distilled water through a resin
column to eliminate any anion or cations from the water. The
resistance of this water was found to be more than 3MB.

The fluide used in the experiments, were kept in C02 - free
air, and water samples were also collected under COZ-free air, except
in the cases where CO2 saturated water was used.

In each experiment, a series of different pressure heads,
ranging from 0.2 to 20.0 inches of mercury was used, and voltage,
current, volume flow rate, fluid conductivity and pH were measured
and recorded.

For each fluid, the experiment was repeated at least three

62

times, to assure the reproducability of the results. The elec-
trodes were always reprepared before performing any experiment
since the decay or the breakage of the silver chloride layer
causes unstable readings.

From the data obtained, the following calculations were made:

 

Pressure head cm H20 = (in Hg) x (2.54) x (13.537) = (in Hg)
x (34.38)
Pressure head dyne = (cmH20) x (.99737) x (980.67) = (in Hg)
2
cm
x (33631)
Volume flow rate cm3 - (m1 ) x (l ) x l x =
sec_cm2 (min) (60 n(1.27)2
(ml x
(min) .002583

This value equals also the velocity of flow

Mass flow rate gm - (volume flow rate) x (.99737) =
2

sec-cm

_(_uL1__)_ x (.002577)
(min)

Potential energy dyne - cm 8 (dyne) x (flow velocity) = (in Hg)
sec (cmz)

x (ml ) x (86.8779)
(min)

Kinetic energy dyne - cm = (flow velocity)2 x (mass flow rate) x (l/2)=
sec

(ml )3 x (.860 x 10’8)
(min)

63

Dissipated energy dyne - cm .2 (Potential energy)
sec

Electric energy dyne - cm = (m.V) (10-3) (u A) (10-6) (107) =
sec

(m.V) (u A) (104)
Ratio of Electric energy = (m.V) (u A) x (1.151 x 10-4)

Dissipated energy (in Hg) (ml )
(min)

 

 

These figures are for water at 23.8°c. In the case of warm
water or KCl solutions, the appropriate figures were used for

each case.

64

V. DISCUSSION OF RESULTS

The source of the natural electric potential in plants is
an important question to be answered. The relationship between
this electrical potential and fluid flow process is also impor-

tant.

V A. The Source of the Natural Electrical Potential:

 

In an attempt to determine the source of the natural electri-
cal potential, a series of preliminary experiments were performed.
Distilled deionized water was forced through a cellulose pad, by
applying an external pressure. The generated voltage, due to
fluid flow, was measured, and is shown in Figure 24.

In each experiment, it was noticed that a sudden negative
electrical potential, of about -250 millivolts appeared when the
cellulose pad was completely wettcd. This negative potential
decreased fast during the first two minutes, then continued to
decrease gradually until it reached zero, about 15 to 25 minutes
later. The time needed to reach zero voltage, depended upon the
rate of water flow. The time required to reach zero decreased
as the flow rate increased. In each case, the downstream elec-
trode was the negative one.

After reaching zero, the voltage built up gradually, but it
stopped increasing when it reached a certain reading which depended

upon the flow rate. This building up voltage reversed the polarity

65

of the electrodes. Therefore, the downstream electrode became
positive.

Whenever the flow of water was stopped, the voltage rapidly
decreased to zero :,10 millivolts. The longest time required to
reach zero was about 10 hours, but in most the cases, it was a
few minutes.

On the other hand, when the direction of flow was reversed,
the electrical polarity was also reversed. Thus, the downstream
electrode was always positive. The magnitude of voltage remained
relatively constant, but of opposite Sign. When the flow rate
was increased, the voltage increased, Figure 25.

As the distance between the upstream electrode (negative)
and pad surface was increased, the voltage decreased.

As the distance between the downstream electrode (positive)
and pad surface was increased, the voltage increased. However,
any increase of the distance more than 4 millimeters did not affect
the voltage magnitude.

For either electrode, the current dropped when the distance
between the electrode and pad Surface was increased.

There are two possible explanations for the existence of this

electric potential. Each depends upon a different theory.

V A-l. First Theory:
The active (OH) group in cellulose molecule, has the ability

to form hydrogen bonds with two water molecules. Water molecule

66

 

 

 

 

 

 

 

 

 

 

+ my
4 o
, o
. 2
+200i -;, flow was flow direcIion
. ’ slapped was reversed
1 flow dwecnon
I '00“, l was reversed
O‘WH... ....... .. 1. his-..
. T *\/T r- fi‘ ' l .. l I‘
4 I 2 Mime hour
— I00;
—200
cellulose pad flow was
completely wetled stopped
—300,
FIG. 24 -THE EFFECT OF WATER FLOW IN
CELLULOSE PAD
+m.V.
1:. flow rate
+ 200; g was increased
13 flow rate flow rate flow was
4 4m|./min. was Increased stopped
1 "0‘" rate flow role
I 2 mI./min. 6mI./min.
+ IOQ: fl
. ow was
j slapped I
04 ........... , ........... r ........... 11 n ”new
1 5 6 7 time ”hour"

 

 

 

FIG. 25 - THE

EFFECT OF WATER FLOW RATE

67

is a dipole. Therefore, when the cellulose is wetted, water mole-
cules arrange themselves with the positive poles toward the oxygen
atom of the active (OH) groups of cellulose molecules. This keeps
the negative poles directed outward, which gives the wetted
cellulose molecule a negatively charged surface.

Water has 10'7 of its molecules dissociated in (H+) and (HO-)
ions. (H+) ions are attracted towards this negatively charged sur-
faces of cellulose, and they form a positively charged layer
adjacent to cellulose surfaces.

When water was forced to pass through the cellulose pad, this
positively charged layer of (H+) ions was dragged with the flow
which caused the observed electric potential.

However, if that is the case, then there is no reason for the
drop in voltage when the distance between the upstream electrode and
pad surface was increased. There is no reason also, for the increase
in voltage when the distance between the downstream electrode and pad
surface was increased. Moreover, the sudden negative potential which
was noticed when the cellulose pad was completely wetted means that
the cellulose caused the ionization of water. The (H+) ions of the
ionized water molecules were attracted to the oxygen atoms of the active
(OH) groups of cellulose, while the (HO-) ions were washed away with
the flow. This process will leave the cellulose with positively charged
surfaces, which does not agree with previous work done, Neale, (1946).

This strange observed behavior of the electrical potential
lead to the second explanation of the source of this electric

phenomenon.

68

8V A-Z. Second Theory: "Electron Accumulation Theory":

When water flows in capillary passages, it is subjected to
great shear stresses due to the sliding of each molecule layer
over the other. This shear stress will be greater near the inner
wall surfaces, due to the greater value of velocity gradient there.

The dissipated energy, due to this shear stress, is not
completely lost in form of heat. A part of this energy is con-
verted to electric energy.

The sliding of two layers of water molecules over each other,
breaks the bonds between these two layers, and causes some elec-
trons to be expelled to the surrounding. When the sliding layers
are'close to cellulose surfaces, some of these electrons are ex-
peled to these cellulose surfaces.

By the accumulation of electrons on its surfaces, the cellu-
lose becomes negatively charged, while the water molecules, which
have expelled the electrons, become positively charged.

Moreover, it is known that the loss of energy from water
molecules at the inlet of any passage, is greater than the loss
at the exit. The reasons for this are:

l. The changes in flow stream lines at the inlet are greater

than the change at the exit.

2. The deveIOpment of velocity profile, which starts at the

inlet, results in the decrease of shear stress magnitude

from the inlet towards the exit.

69

Therefore, this greater energy loss at the inlets of water

passages causes more electron accumulation at the upstream side

of the cellulose pad. Figure 26 represents that schematically.

V A-3.

The Validityiof "Electron Accumulation Theory":

The results of the experiments performed support this theory.

The validity of this theory can be substantiated by re-examining

the behavior of the electric phenomenon with reSpect to the change

of flow and electrode conditions:

1.

The downstream electrode was always positive, while

the upstream electrode was always negative. This was

a result of the greater accumulation of electrons on

the upstream side.

The voltage dropped when the distance between the up-
stream electrode and pad surface was increased. This
voltage drop occured, because the upstream electrode

did not, any more, measure the difference of the accumu-
lation of electrons on the two sides of the pad. Instead,
this electrode acted as one plate of a capacitor, with

the pad side as the other plate.

The voltage increased when the distance between the
downstream electrode and pad surface was increased.

This voltage increase occured, because this electrode

got rid of some of the effect of the accumulated electrons
on the upstream Side of the pad, Therefore, the voltage
reading was between the accumulated electrons on the upstream

side of the pad, and the partially positively charged water

molecules.

70

 

 

 

 

 

\_ ‘ “ “‘4‘“ ‘ “‘/
\\-‘ /
If..." \—
/—'—__- \

 

/—
the change in stream lines \

 

velocity profile development

 

 

    

 

 

IlIII t f _
e A=enerqy dissipated at the inlet
B=enerqy dissipated ot the exit
pressure
|drop //|
A
peItIt a ‘ /él
I dissipated energy
. flow
4—-— electron accumulatIon <————

direction

 

 

 

the source of electric energy. -' .. - J

 

 

 

FIG. 26- SCHEMATIC DIAGRAM REPRESENTS THE
SOURCE OF ELECTRICAL-POTENTIAL IN THE
CELLULOSE PAD.

71

4. Beyond 4 millimeters, the distance between the down-
stream electrode and pad surface did not have any effect
on the voltage. Beyond this distance, the effect of
the accumulated electrons became negligeable,thus the
voltage stayed constant.

5. The current drOpped when the distance between pad surface
and either electrode was increased. This is expected
because the electrical resistance was also increased.
However, the drop in current with the increase in voltage
at the same time, supports this theory.

Another test of this theory was made by performing another

series of experiments, in which (0.01 Molar) KCl solution was
used instead of water.

If the hydrogen-bonds are assumed to be the source Of the
negatively charged surfaces of cellulose, or if the zeta potential
is assumed to be the source of the electric double layer, the
voltage Should increase, or at least its magnitude Should remain
constant, when KCl solution was used. However, this did not occur.
When KCl solution was used, the voltage drOpped to a very small
magnitude.

According to "Electron Accumulation Theory", this voltage
drop must be expected, because of the high conductivity of this
solution. This high conductivity did not permit the accumulation
of large quantity of electrons on the cellulose pad. Instead,

it caused their discharge.

72

It can be concluded here, that the source of the electric

energy is not an "intrinsic constant quantity"

of the material,
such as the zeta potential. This electric energy is generated
by the dynamics of water flow, which has the ability to convert
one form Of energy to another. As the dynamics of flow process

dissipates some of water's potential energy in form of heat

energy, it converts some of the energy to electric energy.
V B. The Relationship Between Fluid Flow and The Electric Phenomenon:

V B-l. Electric Responses to the Tested Fluids:

The preliminary experiments were followed by a series of
quantitative experiments. The tested fluids were:

1. Distilled deionized water at 23.8°c and 30.00c

2. KCl solution: 0.005M and 0.01M

3. COz-saturated water.

For each fluid tested, the cellulose pad was washed by a flow of
distilled deionized water for 48 hours, followed by the tested
fluid for 48 hours.

The results of these data are shown in tables: A.1 for
water at 23.80c, A.2 for warm water at 30.0°c, A.3 for C02-
saturated water, A.4 for (0.005M) KCl solution, and A.5 for
(0.01M) KCl solution. These data were expressed graphically in
Figures 27, 28, 29, 30, and 31 respectively.

For each fluid tested, a series of three experiments were

73

performed, but only the data of the first of these experiments
was tabulated and represented graphically. The other two exper-
iments gave similar data, but the magnitude of this data was
always lower due to the decay of the silver chloride layer of the
electrodes. The performance of three experiments assured the
reproducability of the obtained results.

Table A.1 and Figure 27, show the effect of water flow on
voltage and current across the cellulose pad. Flow rate increased
linearly with the increase in water potential difference (Ap),
while the increases in both the electrical potential and current
were close, but not exactly linear with reSpect to (Ap). The
dissipated energy was a parabolic function of Ap. Figure 32-A
Shows the parabolic relation between the dissipated energy and
(Ap)-

The relation between the electric energy and (Ap) was nearly
parabolic. The deviation of this relationship from being parabolic,
may be due to a decrease in the rate of electron accumulation on
cellulose surfaces as the later became overcharged with these
electrons. Voltage and current curves, Figure 27, Show that the
rate of increase of voltage and current declined as Ap increased.

When warm water at 30.00c was used, Table A.2 and Figure 28,
this reduction in the rate of electron accumulation also occured.

An increase in water temperature, increased the kinetic

energy of water molecules. Therefore, the dissipated energy

74

increased, and so the electric energy. Figure 32-B shows that

the dissipated energy was a parabolic function of Ap. It also
shows that the electric energy when warm water was used, departed
more from being a parabolic function of Ap. This deviation from
the parabolic relation may be due to the same previously mentioned
reasons.

Table A.3 and Figure 29, Show the effect of flow of C02-
saturated water in cellulose pad, on the vOltage, current, dissi-
pated energy, and electric energy. Figure 29 shows that the
relationship between Ap and voltage, current, and flow velocity
was linear. The similarity of both the dissipated energy and
the electric energy curves was great. Figure 32-C shows that
these two kinds of energies were related to each other, and were
parabolic functions of (Ap).

The magnitude of the electric energy dropped to 1/10 its
magnitude when COZ-saturated water was used instead of water.
According to the "Electron Accumulation Theory", the higher elec-
tric conductivity of COZ-saturated water caused the discharge of
electrons from cellulose surfaces. Thus, the voltage dropped to 1/20
its magnitude when COZ-Saturated water was used instead of water°

On the contrary, the current reading was doubled. A possible
explanation of that, is that some cations of the fluid were
attracted towards the negatively charged cellulose surfaces.

Some of these cations caused the discharge of some of the

accumulated electrons, while others, being dragged with the flow,

 

 

fl I‘m-1.1. .W’S...\ ire-H. l

 

75

caused the high current reading.

The drop in electric energy was due to the decrease in
voltage, which was previously mentioned. The magnitude of the
electric energy was 1/10 its magnitude, when COz-saturated water
was used instead of water. That means that 90 per cent of this
electric energy was utilized in moving more cations with the
flow. In other words, 90 per cent of the electric energy was
converted into kinetic energy for moving these cations.

As previously mentioned, fluid samples were taken before and
after the fluid tested passed the cellulose pad. The pH and con-
ductivity of these samples were measured. The data were insigni-
ficant because the used pH meter, gave almost the same reading
(:_.O4) for the sample which were taken before or after passing
the cellulose pad. The conductivity meter gave exactly the
same readings for both kinds of samples. This was because the
sensitivity of the available meters was less than it should be
to Show this slight changes in cation concentrations. Therefore,
these data were neglected.

When (0.005 M) KCl solution was used instead of water, the
velocity, voltage and current were in linear relationship with
(Ap), Table A.4 and Figure 30. The current increased five times,
while the voltage dropped to about 1/100 its magnitude,when KCl
solution was used instead of water. The result was a drOp in

the electric energy to 1/20 its magnitude for pure water. By

76

following the same reasoning, it can be said that 95 per cent of
the electric energy was utilized in moving more cations with the
flow.

The use of (0.01M) KCl solution also caused the drop of the
electric energy, Table A.5 and Figure 31. The relationship of
flow velocity, voltage, and current vs. (Ap) was linear. The
voltage drOpped to about 1/200 of its magnitude when (0.01 M) KCl
solution was used instead of water. The magnitude of the current
was doubled. Thus the electric energy dropped to about 1/100 of
its magnitude for pure water. This means, once again, that 99
per cent of this electric energy was utilized in moving more
cations with the flow. Figure 32-D shows the relationship
between the electric energy and the dissipated energy for both
concentrations of KCl solution. It also shows the parabolic
relationship between the two forms of energy and (Ap).

All energy curves, for all the fluids tested, were drawn
together in Figure 33, to Show the relative magnitude of the
electric energy for all fluid tested.

On the other hand, Table A.6 and Figure 34, represent the
effect of the distance between downstream electrode and pad
surface on voltage and current magnitude. This was previously

discussed.

77

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FIG.32- ELECTRZIC ENERGY AND DISSIPATED ENERGY AS FUNCTIONS
OF (0p) .

83

 

 

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FIG. 33 - THE GENERATED ELECTRIC ENERGY OF THE
FLUID TESTED.

84

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

KID. m.V. (A) pA Kn. m.V. (B) pA
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0 LC 20 3.0 0 l0 2.0 30
FIG. 34 - THE EFFECT OF THE DISTANCE BETWEEN DOWNSTREAM

ELECTRODE AND

PAD SURFACE, ON VOLTAGE AND CURRENT.

85

Another experiment was performed, using glass fiber filter
paper instead of cellulose filter paper. In this experiment,

a pad constructed of 20 sheets of filter paper was used (filter
discs NO. 5270-D grade 934 AH, Arthur H. Thomas Company, Phila-
delphia, Pa.). Distilled deionized water at 22.60c was used with
this glass fiber pad. The voltage and current were measured by

a ”Multi Function Unit," Model 3444A DC, Hewlett Packard, with
voltage range from 0.01 millivolts to 1000 volts, and current
range from 0.01 microamperes to 1.0 ampere.

The data of this experiment were tabulated in Table A.7,
and were expressed graphically in Figure 35.

Table A.7 and Figure 35 show that the use Of glass filter
paper instead of cellulose filter paper caused the increase Of
voltage, current, dissipated energy and electric energy. Figure
35 shows that both the electric and dissipated energy are
related, and are parabolic functions of Ap.

Table A.1 and Table A.7, show that when Ap was 2 672 x 103
dyne/cm2 the voltage and current readings were for a cellulose
pad 235 millivolts and 0.29 microamperes; and for a glass fiber
pad 4200 millivolts and 6.50 microamperes. Both the voltage
and the current were about 20 times greater when glass fiber
pad was used in place of a cellulose pad. The two tables show
also that the dissipated energy was about 72 x 103 ergs when a
cellulose pad was used, and about 159 x 103 ergs when a glass

fiber pad was used. The electric energy was 0.68 erg in case of

86

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87

a cellulose pad, while it was 273 ergs in case Of a glass fiber
pad. Finally, the flow rate was 0.107 cm/sec in case Of
cellulose pad, while it was 0.236 cm/sec in case of glass
fiber pad.

A comparison between the data of the two tables can be
explained as follows. The flow passage appeared to be
bigger in diameter in the glass fiber pad, which had a higher
flow rate. However, the greater flow rate resulted in a
larger rate of energy dissipation, probably caused by greater
friction losses. The final result was a greater accumu-
lation Of electrons on the glass fiber surfaces, which in
turn caused the high readings Of voltage and current.

V B-2. Numerical Evaluation Of Electric Responses to
the Tested Fluids:

A further investigation Of the response of the gener-
ated electric energy was done numerically. In this numerical
analysis, the data of the distilled deionized water, Table
A.1 was used.

The maximum flow rate, Table A.1, was 106 x 10.3 cm
per second. This reading corresponds to flow rate Of 6 cm

per minute, which is within the range of the actual sap

88

movement in xylem tissues. The voltage reading correspond-
ing to this flow rate, Table A.1, was 235 millivolts, and
the current was 0.29 micro-amperes.

The nonlinearity Of voltage and current curves, Figure
27, was considered in the previous discussion, to be a re-
sult of the overcharging of cellulose with the expelled
water electrons. If there was a means to cancel the re-
pelling effect of the accumulated electrons, voltage and
current curves should be linear with respect tO p. That
means that the number Of the expelled electrons from water,
should be greater than what was actually measured.

When KCl solution was used, the conductivity of this
solution caused the discharging of the accumulated elec-
trons from cellulose surfaces. Therefore, there was no
overcharging with electrons, no repelling effects of elec-
trons, and no limits on the number of electrons which could
be expelled from water as it passed in the pad.

To estimate what the current reading should be if its
relationship with p was linear, a tangent line to the first

portion Of the current curve was drawn, Figure 27. The current

89

reading on this tangent line, which corresponds to flow rate of
106 x 10"3 cm/sec., is 0.39 microamperes. This reading was

converted to a number Of positive charges as follows:

-19

1 electron-charge = 1.602 x 10 coulomb

0.6 242 x 1019 e

1 coul

l Ampere-sec. l coul.

0.6 242 x 1019 e

0.6 242 x 1013 e

0.6 242 x 1013 x 0.39 = 2.43 x 1012 e

1 u.A.-sec.

0.39 u.A.-sec.
This indicates that 2.43 x 1012 positive charges should pass
through the cellulose pad each second, when the flow rate was
106 x 10"3 cm/sec. However, the actual number Of positive charges
which passed per second was:

0.29 p.A.-sec. = 0.6 242 x 1013 x 0.29 = 1.81 x 1012 positive

charges/sec
For each positive charge passed through the pad, one electron
was expelled to the cellulose pad. The constant reading Of the
voltage means that there existed an equilibrium condition in
which the electrons expelled to the cellulose were balanced by
some electrons discharged from the cellulose.
Water has 10..7 of its molecules dissociated in (H+) and

(H0-) ions. The (H+) ions, being attracted toward the negatively

90

charged cellulose surfaces, discharged some of the accumulated
electrons, then were dragged with the flow without causing any
current.

The number of (H+) ions which passed through the pad per
second were calculated as follows:

mass flow rate/sec.= 0.1067:x .99737 = 0.10642 gm/sec

Number of H20 molecules/sec = 0.10642 x (6.023 x 1023)
18

= 3.56 x 1021 molecules/sec

Where the Avocadro Number = 6.023 x 1023 molecules/mole

 

Number of (H+) ions/sec = 3.56 x 1021 x 10.7 = 3.56 x 1014
(H+) ions/sec

Ratio of §H+l = 3.56 x 1014 = 1.97 x 102 z 200
e 1.81 x 1012

This ratio indicates that the number of (H+) ions which passed
through the pad per second, was 200 times the number of the
positive charges which passed through the pad per second. This
great number of (H+) ions should discharge all the accumulated
electrons on the cellulose surfaces.

However, no electron could be discharged unless there was
an (H+) ion passing adjacent to the negatively charged walls of
water inlets of the pad. The number of these (H+) ions, which
were moving along with the water molecule layer adjacent to the
inner walls of the passages, was estimated as follows:

If the inlet diameter is 6, and water molecule diameter is

91

6w, the ratio between the number of water molecules which pass,
to the number of the molecules which pass adjacent to the inner

walls will be:

H 52/4 5

n 62/4 - N (§ __§)2 4 6w (1-6w )
w

2 5

 

 

This ratio increases as the diameter of the inlet in-

 

 

 

creases.

0

Assuming 6 = 0.6 micron and 5w = 1.5 A

5 = 4000 5w
The ratio 6 will be 4000 6w z 1000
4 6 (1- 6w ) 6w
w "E 4 6w (1- ' gr )
4000 w

Therefore, the number of (H+) ions which could discharge the

electrons from inner wall surfaces, was computed as

3.56 x 1014 x 1 = 3.56 x 1011
1000
, + _ 11 1
The ratio (H 1 - 3.56 x 10 - 0.20
e 1.81 x 1012

This ratio means that the (H+) ions, which discharged some
electrons from the cellulose, were about 20 per cent of the
positive charges which were moving along with the flow.

Each (H+) ion discharged one electron, passed with the flow
as a neutral (H). At the same time, there was an (H0-) ion
passing also with the flow. These (HO') ions created a current

in Opposite direction, which when superimposed on the real current,

92

decreased the reading. The number of these (H0-) ions, like
the (H+) ions, was also about 20 per cent of the number of the
positive charge which were moving with the flow.

Therefore the real current of positive charges can be
computed to be:

the actual current of positive charges x 120
100

12 12

x 120 = 2.172 x 10 e
100

1.81 x 10

This number is closer to the number of positive charges which
was computed from the tangent of the current curve, and which
was = 2.43 x 1012 e.

From these calculations, it can be concluded that the non-
linearity of the current curve was due to:

1) the repulsive effect of the accumulated electrons

on cellulose surfaces.
2) the superimposed reverse current.

A calculation was made to examine the effect of the smaller

diameters of the gaps between cellulose macrofibrils in the

 

 

cell wall.
0 O

5 = 100 A and 5w = 1.5 A

5 = 60 5w
The ratio 5 = 60 5w = 15

5 - 5
4 w (1 .E) 4 6w (1- £53'—--———-)
5 6O 5

W

+
The number of (H ) ions which could discharge the electrons will

93

 

be
1
3.56 x 1014 x 1/15 = 2.37 x 10 3 (H+) ions/sec
The ratio (n+1 = 2.37 x 1013 = 10
e 1.81 x 1012

This large ratio indicates that all the accumulated electrons on
cellulose surfaces should be discharged by these (H+) ions.

This calculation also indicates that the diameters of flow
passages limits the ability of the existing positive ions in any
solution to discharge the accumulating electrons.

Similar calculations were done for the (0.005 M) KCl
solution. Table A.4 shows that at a flow rate of 0.1175 cm/sec.,
the voltage was 2.32 millivolts and the current was 1.7 microamperes.
The current reading was converted to a number of positive charges,
as follows:

1.7LhA./S€C = 0.6242 x 1013 x 1.7 = 1.0611 x 1013 e

The number of (Hi) ions and (K+) ions which were moving

adjacent to the inner wall, were computed as follows:

mass flow of water/sec. = .1175 x .99737 .11719 gm./sec.

2
Number of H20 molecules/sec. = .11719 x 6.023 x 1023 = 3.92 x 10 1
18 molecules/sec.

21

3.92 x 1014 (11+)
ions/sec.

Number of (H+) ions/sec. = 3.92 x 10 x 10-7

2
Number of KCl molecules/liter = 1 x 6.023 x 10 3 3.0125 x 1021

200 molecules/liter

94

21 -3

Number of KCl molecules/sec. = 3.0125 x 10 x 10 x .1175 = 3.54 x 1017

molecules/sec.

17

+ +
Number of (K ) ions/sec. = 3.54 x 10 (K ) ions/sec.

+ +
Since (H+) ions are l of (K ) ions, the (H ) ions can be
1000

neglected.

+
By considering the inlet diameter 5 and (K ) diameter 5k

 

 

6 = 0.6 u and 6k = 3 X
5 = 2000 5k
The ratio 5 = 2000 5k a 500
5
4 k (1- £5.) 4 5k (1- 6k )
5 2000 5k

+
The number of (K ) ions which passed adjacent to the walls will

 

be = 3.54 x 1017 x l = 7.08 x 1014 (K+) ions/sec.
500
The ratio (K+) = 7.08 x 1014 z 60
8 1.0611 x 1013

Therefore, the number of (K+) ions which had the ability to
discharge the accumulated electrons, was 60 times the calculated
positive charges which caused the current. However, the voltage
remained constant with a reading greater than zero. This means
that these (Ki) cations did not discharge all the accumulated
electrons. This indicates also that the number of the expelled
electrons was greater than the number of (K+) cations which were

moving adjacent to the cellulose surfaces.

95

Each (Ki) cation discharged one electron. At the same time
there was an (01-) anion also moving with the flow, since the
diameters of the passages were big enough for (01-) anion to
pass through. This created a current in the Opposite direction.
Therefore the real number of the positive charges which were
moving per second were greater than the actually measured ones.

This real number can be estimated as

14

7.08 x 1014 + .106 x 10 = 7.2 x 1014 e

14

This number means that 7.2 x 10 positive charges were passing

per second with the flow, and the number of electrons expelled

per second also was 7.2 x 1014. This is 300 times greater than

12 electrons/sec.

that calculated for pure water, which was 2.17 x 10

This comparison shows that when the repulse effect of the
accumulated electrons was cancelled by their discharge, the water
molecules could expel 300 times as many electrons.

If the flow passage diameters were small enough to prevent
(Cl-) anion to pass, the cellulose pad will be charged as follows.
The upstream side will be negatively charged with both the
accumulated electrons and (Cl-) anions. The downstream side will
be positively charged with the water molecules which have lost
their electrons.

Other calculations were done for the glass fiber pad.

Table A.7 shows that at a flow rate of 0.2356 cm/sec., the

voltage was 4200 millivolts, and the current was 6.5 microamperes.

96

The current reading was converted to a number of positive
charges, as follows:
_ 13 _ 13
6.5 pA/sec - 0.6242 x 10 x 6.5 - 4.0573 x 10 e
The number of (H+) ions of water which passed through the pad
per second were calculated as follows:
mass flow rate/sec = 0.2356 x .99764 = .2350 gm/sec

Number of H20 molecules/sec ¢ .235 (g 023 x 1023)

7.86 X 1021 molecules/sec

Number of (H+) ions/sec. 7.86 X 1021x10-7 = 7.86 x 1014

(H+) ions/sec.

Considering the inlet diameter of glass fiber pores to be 0.8

 

micron: 0 1' 5400 (S
W
The ratio 5 = 5,005“ e 1400
4 6w(1-5w ) 4 5w (1-_ 6w )
5 5400 5W

The number of (H+) ions which passed adjacent to the inner walls

of the pores was computed as:

 

ll
7.86x 1014x 1 = 5.613 10 (11+) ions/sec
1400
. + _ 11
The ratio (H 1 — 5.61x 10 = 0.013
e

4.057 x 1013

+ . . .
This ratio means that the (H ) ions, which discharged some elec-
trons from glass fiber surfaces were only about 1 per cent of the
positive charges which were moving along with the flow. Both the
low rate of electron discharge and the high rate of electron accumu-
lation, resulting from a high rate of energy dissipation, may

have caused the high voltage reading of 4.2 volts.

97

V B-3. The Role of Electric Energy in Plant:

The role of electric energy in plant can be seen if the flow
pattern of xylem sap is examined.

To simplify the discussion, it is better to start the study
of the flow pattern when water potential in both the xylem and
the surrounding tissues is nearly in an equilibrium condition.

Equilibrium conditions do not exist in the living plant.
Since the water potential is nearly at equilibrium early in the
morning, it is convenient to start the study at that time of the
day.

During night, water stresses inside xylem vessels decrease,
because transpiration drops to its minimum value. Due to the
osmotic pressure of cell sap in the surrounding tissues, and the
low water stresses inside the vessels, the diffusion pressure
deficit of the surrounding cells will be greater than that of the
vessels. Therefore, water flows from the inside of the vessels
towards those surrounding cells. As this flow continues during
the night, the diffusion pressure deficit of the surrounding cells
decreases, till it reaches its minimum value about dawn. There-
fore, the rate of sap flow to the surrounding tissue reaches
its minimum value or may stop completely at dawn. Figure 36.A
expresses this schematically.

With the first light of the morning, photosynthesis and
tranSpiration start once again. The rate of these two pro-
cesses increases as the day advances. The increase of the rate

of transpiration affect the stress condition of water inside

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EBou

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98

 

 

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r U-.. Ltuhurhlfrk.

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region

 

 

 

 

‘IY‘

 

 

 

 

(BI DURING DAY LIGHT

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AT

(A)

 

 

 

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gr... ..... .-CLLLLLVCFHu.

 

 

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(C) AT THE END OF THE. DAY

 

 

ID) DURING NIGHT

DURING THE 24 HOURS OF THE DAY

FLOW PATTERN

FIG. 36 -

99

xylem vessels. When the rate of transpiration becomes greater

than the rate of root absorption, the potential of xylem sap

drOps and its diffusion pressure deficit increases. This

disturbs the balance between the potential of xylem sap and that of
the surrounding cell sap. The result is the changing of the
direction of flow, towards the inside of xylem vessels.

The rate of sap flow in that direction is greater near the
lower part of the vessels, because the surrounding tissues of
this part are closer to the higher water potential of the root,
and further away from the region of higher concentration of
sucrose. Figure 36-B shows this flow pattern schematically.

At the end of the day, both photosynthesis and tranSpiration
rates decrease. The sucrose concentration will be greater in
the upper part of the stem near the leaf. This keeps water
potential of the surrounding tissues of the upper part, at a
lower level than that of the tissues near the bottom of the
stem. At the same time, the potential of the sap inside xylem
vessels increases, due to the continuation of root absorption and
the cesseation of water losses by tranSpiration. Therefore, the
flow of water reverses once again, from inside the vessels towards
the surrounding tissues. The rate of this flow will be higher
in the upper part of the stem near the leaf, than in the lower
part near the root-hair zone. This difference in the flow rate,
may be the cause of the mass flow which occurs in the phloem in

the direction of the roots. Figure 36-C shows this schematically.

100

As the night advances, the flow pattern approaches a
condition more close to equilibrium, Figure 36-D.

According to the results of the experiments performed,
whenever flow of water occurs through porous media, electric
energy is generated. In the case where electrolytes or carbon
dioxide are present, which is the case inside the plant, and in
the case where water passage are narrow, this electric energy
is utilized in moving an extra number of cations with the flow.
The cations are first attracted towards the negatively charged
inlets, they discharge the electrons, then are dragged off with
the flow. The pattern of flow of these cations depends on their
concentration, the flow rate, and the diameter of the flow
inlets.

The solutes move from the soil to the endodermis, with the
absorbed water via the apoplast. Because the passage diameters
are big in the apoplast, the cations discharge some of the
accumulated electrons, and the greatest portion of the anions move
also with the flow. The outer surfaces of root-hairs become
negatively charged, which may have a great effect in attracting
more cations.

In the endodermis, the narrow gaps of the casparian strip
play another role in absorption of ions. A greater number of
cations are attracted toward the negatively charged inlets, they
discharge the electrons and then pass on with the flow. The

anions, cause a negatively charged surge in the central portion

101

of the passage, due to their attraction toward the positively
charged water molecules which have lost their electrons. This
may be the reason why solutes sometimes move inside the root
with velocity greater than the velocity of water molecules.

There is also a selective absorption of some of the solutes
as a result of an active transport by the cytoplasm. This
process is considered to be a biological one. Whenever active
tranSport occurs, the role of the electric energy which is
generated from the dynamics of the flow, is to help this biological
transport, by accumulating the selected cations close to the
cytoplasm.

Refering to water flow pattern, Figure 36, water potential
was considered nearly at an equilibrium condition, early in the
morning. At that time, the cations which have entered the xylem
vessels, are transported next toward the surrounding tissues
following the flow pattern of water, Figure 36-A. The trans-
portation of the existing anions outwards depends on the flow
passage diameters, and the magnitude of the negative charge
inside the cells of the surrounding tissues.

During the high rate of tranSpiration and photosynthesis,
some cations are forced to move with water flow, from the surrounding
tissues towards the inside xylem vessels. Since the rate of
respiration is high in some of the surrounding tissues, especially

cambium cells and the companion cells of phloem tissue, the

 

 

 

Ill- lll} It i] I. {I .11Il1

102

hydronium ions_(H30+) move toward xylem vessels, leaving (H003)
ions inside these cells, which increase the negativity of these
cells. Refering to Figure 36-B, water flow from the surrounding
tissues at the lower part of vessels is greater than the flow
from the surrounding tissues at the upper part of the vessels.
Therefore, the surrounding tissues of the lower part of vessels
will be more negatively charges than those of the upper part.

When xylem sap, with the cations in it, reaches the leaf,

 

the generated electric energy helps, once again, in the active
transport of these cations by the cytoplasm. Once these cations
enter the cytOplasm, they can move via the symplast. Because
of their positive charges, they are attracted towards the
negatively charged cytoplasm of the companion cells. This
helps in moving sugars and assimilates towards the sieve tubes.
This movement of sugars and assimilates continues downwards,
due to the more negativity of the cytoplasm of the sieve tubes
at the lower part of the stem and the root.

Refering to Figure 36-C, the high flow rate of both water
and cations in the direction of the surrounding tissue in the
upper part of the stem, causes the high rate of downward flow
in phloem. It also causes the distribution of sugar and
assimilates to regions of their consumption, since these regions
are known to be more negatively charged because of their high

rate of respiration.

103

From the previous discussion, it can be concluded that the
existence of the electric energy is a product of the flow process.
This means that ”Electro-osmosis", according to its definition,
does not play a role in the flow process in xylem tissue.

It can also be concluded that "Electro-osmosis" does not
affect fluid flow in phloem sieve tubes, since the downward surge
of cations, which are accompanied by the sugars and assimilates,
is due to a process similar to the "Donnan equilibrium" rather

than "Electro-osmosis".

V C. The Role of Xylem Vessel Wall Structure in Plant:
The structure of the walls of xylem vessels plays three

important functions in plants. These functions are:

V C-l. The Generation offglectric Energy:

As discussed in sections V.A. and V.B., the porousity of
the structure of wall material, provides the means for generating
the electric energy. The magnitude of this electric energy
depends on the rate of water flow.

This electric energy helps in moving extra cations in the
direction of flow. Sometimes, it causes a surge of anions,
whose velocity may be faster than that of the water molecules.

In the active transport of ions, the electric energy helps
the cytoplasm by accumulating these ions close to the action of

this biological process.

104

V C-2. The Existence of High Tensile Stresses in Xylem Sap:

The second function, is that this structure, which consists
of layers of cellulose microfibrils and macrofibrils, is the only
guarantee for the existence of high tensile stresses in xylem
sap, without permitting evaporation to occur.

When water pressure decreases until it reaches a value equal
or less than the vapor pressure at the existence temperature,
evaporation occurs.

At 700F., vapor pressure of water is 0.3631 psi

0.3631 psi = 2.503 x 104 dyne/om2

At this temperature, negative pressure exists in the xylem
tissue of, not only tall trees, but also many of the annual
plants like corn. A negative pressure of 10 atm. in xylem sap

was estimated in corn plant.

1 atm. = 1.013 x 106 dyne/cm2
Evaporation cannot occur at any point located inside a
liquid. In the absence of any gas bubble, vapor bubbles are
unstable and collapse.
There are two forces acting on these vapor bubbles:

l) The surface tension force = 2nro

where r bubble radius
0 = surface tension of the liquid

This surface tension acts to collapse the bubble,

Figure 37-A.

 

105

2) The force of vapor pressure = nr2 (pv - pw)
where (pV-pw) = the difference between water pressure
and vapor pressure at the existing
temperature.
This force acts in the direction of increasing the
size of the bubble, if (pv - pw) is a positive quantity.

At equilibrium

 

(P-P)=Ap=2"nro =2_g_

This means that in the absence of other gas bubbles, Ap must
be greater than _2g_ for any vapor bubble to form and grow.

For water r

O = .005 lbf/ft = 72.9695 dyne/cm = 73 dyne/cm

The maximum distance between water molecules is 5 X. By
assuming that one molecule is evaporated, the radius of the

o -
starting bubble will be 5 A = 5 x 10 8 cm.

At equilibrium:

 

2
Ap = 20 = 2 x 73 = 2.92 x 109 dyne/cm
r 5 x 10’
= 2.92 x 109 e 2000 atm.
1.013 x 106

This figure means that 4p must be greater than 2000 atm. for
evaporation to occur inside water. That is the reason that
evaporation always starts at the interface between the water

and the container. The reasons for that are:

106

l. The roughness of the container wall traps gas. This
gas becomes under high pressure because of the adherent
force between water and the material of the container
walls, Figure 37-B.

2. The surface of container wall is sometimes contaminated
with some material having little or no adherence to
water, Figure 37-C.

Both cases, allow the radius of the first bubble of vapor

to be big enough for its growth.

Applying these principals to xylem vessels, explains the
ability of vessel structure of maintaining the high tensile
stresses which occur in xylem sap. The cellulose has great
affinity for water, and water adheres to it very strongly.
Cellulose in cell walls and xylem vessel walls, does not have
any contaminates to let water separate from the cellulose macro-
fibrils.

The distance between cellulose macrofibrils is of the
order of 100 X. For any gas or water vapor bubble to pass

through this wall structure, Ap must be greater than:

 

 

Ap > 2Q = 2 x 73 = 2.92 x 108 dyne/om2
r 50 x 10‘8
= 2.92 x 108 = 200 atm.
1.013 x 106

Xylem vessels have pits in their walls. Gas and water vapor

bubbles may pass through these pits. The pit diameters are

 

107

of higher order than the distance between cellulose macrofibrils.
If the diameters of the pits were about 0.2 micron, the difference
in pressure (pv - pw) which is needed for vapor bubbles to pass

through it, must be greater than

 

7 2
AP = (pv - Pw) > 2g = 2 x 73 + 1.43 x 10 dyne/cm
r 0.1 x 10'4
= 1.43 x 107 e 10 atm.
1.013 x 106

This order of magnitude of 4p can be found inside xylem
vessels. This means that gas and vapor bubbles can move from
the intercellural spaces, in which air and gases are found, towards
the inside of the vessels through these pits. However, this
does not happen. The reasons of that is that xylem vessles are
surrounded with living cells, which have no intercellural spaces
between them and these vessels. For any gas or vapor bubble to
enter any vessel, it must pass through the gaps between cellulose
macrofibrils of the walls of these cells.

To investigate this role of the cellulose wall structure, an
experiment was carried on, to examine the possibility of the
existence of tensile stresses in water, without evaporation or
separation in water column.

A steel cylinder, 0.635 cm inside diameter, "Diesel fuel
pump cylinder”, with two lapped pistons, were used in this

experiment. The parts were cleaned and dried. In order to get

108

rid of gas molecules which were adhered to metal surface, these
parts were heated to about 2000c under vacuum. The heating was
done to increase the kinetic energy of the adhered gases, to
enable the vacuum to remove nearly all these gas molecules.
After heating for 15 minutes, the parts were cooled under vacuum
to room temperature.

Distilled water was boiled and cooled under vacuum. This
cold water was introduced to the steel part until the water
covered them completely. The vacuum then was released.

The two pistons were inserted in the cylinder, one in each
end, while all parts were under water.

A tensil test was carried on the assembly, by applying a
tensile force on the two piston while the assembly was under
water, Figure 38. The maximum tensile stress which was reached
before a separation in the water column occured, was 2.5 atm.

This experiment was performed to examine the possibility
of the existence of tensile stresses in water column. However,
this experiment must be performed with more sensitive measuring
instrumentation, in order to measure the maximum tensile stress

of water, which can be reached in cell wall structure.

V C-3. The Existence of a Communication System in Plants:
The third function of the structure of xylem vessel walls,
is to provide the plant with a communication system. In this

system, the sap inside the vessels acts as a communicating cord

 

I09

1
:43: ___ t[

2
/nr (pl-pw)

 
  

 

/W

,ZTrrO‘ scale

 

 

 

 

HO
2

 

 

fl

 

(A) forces acting on
vapor bubbles

 

 

Ho"
.2

_\\
trapped
air

 

 

(B) the roughness of container walls

 

piston

r
I
l

l

(C) the contaminates on container walls J T J
l “”2 __

 

 

 

    

contaminates

 

 

 

 

 

 

FIG. 37 —- VAPOR BUBBLE FORMATION FIG. 38 - THE APPARATUS
USED IN TESTING THE EXISTANCE
OF TENSILE STRESS IN WATER

\llll‘ll‘lli‘lv‘i‘e‘llli‘l‘ul'l'!‘ll}ll“lll‘ll|l‘ll.ll,'

 

110

along the whole height of the plant, analogous to the nerve system
in the higher classes of animals.

This function, in fact, is a result of the first two
functions of vessel wall structure.

The structure of vessel wall permits theexistence of high
tensile stresses in xylem sap. The state of stress in xylem sap
affect the surrounding tissues, as was mentioned in sections V.B.
According to the state of stress in xylem sap, water flow through
vessel walls and the surrounding tissues in one direction or
another, Figure 36. The result is the generation of electric
energy which in turn affect ion movements,and subsequently, some
of the biological activities of the surrounding tissues.

The tensile stress which occurs in the xylem sap can reach
very high values, not only in high trees, but also in many of
the annual plants. The differences in water pressure, which are
due to the elevation along the height of xylem vessels, are
considered negligable when compared to the high tensile stress
in xylem sap. Therefore, water column inside xylem vessels,
act as a metal cord subjected to a tensile stress. If the state
of stress is forced to change at a location = Z along water
column, at time = t, the change in the state of stress will be
transmitted immediately to all locations = Z i A2, at time =
t + At, where At is the very short time-interval which is needed

to transmit stresses along any elastic cord. As a result, all

111

the surrounding tissue at all locations along the height of the
plant, will find a new state of stress, and will react according
to it. This reaction will be, not only hydraulic, but also
electric. The magnitude of the electrical reaction will depend
on the magnitude of water potential change, the change in flow

pattern, and the size of pores in the vessels and cell walls.

112

VI SUMMARY AND CONCLUSIONS

VIA- Sew

The concept of electro-osmotic flow in plants has been the
interest of many scientists. ’Some investigators related the
natural electric potential in plants to the translocation of sap
and assimilates. Others considered the translocation of fluid
a result of electro-osmosis. Therefore, this study was intended
to investigate the engineering bases of fluid flow inside xylem
vessels and the nature and role of the electric phenomenon in
plants.

A review of the fundamental bases of plant anatomy and
physiology was done to examine the limits imposed by them on
the vascular tissues and the whole intact plant , The limits
imposed by the physical laws were also considered.

The finding of many of the earlier and latest eXperiments
in the area of electro-osmosis were examined, some of these
findings disagree with some others. However, the explaination
of the results of many experiments were based on the zeta
potential concept. This concept assumes that the surfaces of
any wetted porous material aquire two layers of opposite elec-
trical charges at the solid-liquid interface. The potential
difference between these two layers is called the zeta potential.

To study the engineering bases of fluid flow process inside

xylem tissue, a model represents xylem vessels was deve10ped.

113

The flow of energy through this model was examined and analyzed
mathematically. The energy balance equation for this model was
solved for the dissipated energy, which was considered the only
possible source for the generated electric energy.

To investigate the relationship between the dissipated
energy and the electric energy, experiments were performed on
a model represents the material of vessel walls. This model
consisted of .9 cm cellulose pad constructed of 50 sheets of
filter paper ”Whatman No: 1". Water was forced to pass through
the cellulose pad by applying an external pressure. Voltage
and current across the pad, was measured by means of two silver-
silver chloride electrodes. Different water heads were applied,
and voltage, current, flow rate were measured and recorded.
Five fluids were used. They were: distilled deionized water

at 23.8Oc, water at 30.00c, CO -saturated water, (0.005M),

2
KCl solution, and (0.01M) KCl solution. Another matrix was
tested also. This matrix was constructed of 20 sheets of
glass fiber filter papers.

The data were analyzed and the nature and the role of

the electric energy in plants were discussed. The role of the

anatomy of vessel walls to plants was also discussed.

VI B. Conclusion:
1. Electro-osmosis, according to its definition, does

not play a role in sap movement in xylem vessels.

l l ' II II III‘ ‘Iltl I'I' IIII,IIII III. II' III III I II (II ‘5. all! 4‘ III .IIIIII I! ll l.l .] I I III I III 1" Jf‘II '1' ...-I l all! '5 III .IId .

 

114

The dissipated flow energy and the generated electric
energy during water movement through a porous pad

are related. Both are parabolic functions of Ap.

The source of the electric energy in a system of
cellulose and water, may not be an "intrinsic constant
quantity" of the solid material and the liquid, such
as the zeta potential. The electric energy may result
from energy dissipation during the flow process itself
due to the sliding of water layers over each other,
causing wate to expel electrons to the cellulose
surfaces. A greater accumulation of expelled elec-
trons on the upstream side, creates an electric
potential difference across the pad.

Based on the observations of the reduction in the
electrical potential and the increase in current

when an electrolete was added to water, it is con-
cluded that the generated electric energy is utilized
in moving an additional number of cations more than
that which would normally be carried with the flow.

An extrapolation of the previous conclusions to water
flow in plant is that the flow of water from the

soil to the cortex in the root, may cause the outer
surfaces of the root hairs to be negatively charged.
The final equations (equations 24 and 25) of the
mathematical analysis can be solved for the pattern

of ion movement in plant, by using numerical techniques.

 

115

RECOMMENDATIONS FOR FURTHER STUDY

The relationship between the dissipated energy and the gen-

erated energy which are resulted from flow of water through

porous material, can be studied further, by using improved

equipment and techniques. Such improvements are:

3.

Performing the experiments under adiabatic conditions

to relate the exact magnitude of heat energy to the
generated electric energy.

Performing the experiments on other fluids having
different Dielectric constants, and on different porous
materials to examine the effects of the electric con-
ductivity of the fluid used, and the effects of the dia-
meters of the pores on the movement of the cations and
anions.

Provide means to measure voltage, current, conductivity,
and pH at different locations inside the porous material

pad and in the upstream and downstream sides.

After part one, above, is studied, experiments can be per-

formed on plant. Such experiments are:

8.

Using microtechniques to measure the electric potential
difference across one of xylem vessel walls.

Study the response of xylem sap to the applied external
electric effects.

Study the relationship between both transpiration and

photosynthesis rates and the electric potential and current

116

generated in xylem vessels.

d. Study the relationship between tranSpiration and photo-
synthesis rates and the movement of asshnilates and
sugar in phloem tissues, in order to relate this move-
ment to the generated electric energy.

3. After the studies of parts one and two are done, the effects
of the application of external electric voltage and current

can be determined experimentally for the whole plant.

‘.l“|‘ll‘l.‘l(ill1l‘.lll‘ljiI'll[‘1'7',15..I'I

 

117

Selected References

Berry, L. J. and Hoyt, R. C. (1943), Simulation of the onion root
by alternating current, Plant Physiol., 18 (570-587).

Blackman, V. H. (1924), Field experiments in electro-culture,
Journal of Agricultural Science, 14 (240-267).

Blackman, V. H. and Legg, A. T. (1924b), Pot-culture experiments
with an electric discharge, Journal of Agricultural Science,
14 (268-286).

Breazeale, E. L., McGeorge, W. T. and Breazeale, J. F. (1951),
Nutrition of plants considered as an electrical phenomenon -
A new approach, Soil Science, 71 (371-375).

Breazeale, E. L. and McGeorge, W. T. (1953), Cation uptake by
plants as affected by the applied potential, Soil Science,
75 (443-448).

 

Burr, H. S. (1942), Electrical correlates of growth in corn
roots, Yale Journal of Biology and Medicine, 14 (581-588).

Burr, H. S. and Sinnott, E. W. (1944), Electrical correlates of
form in cucurbit fruit, Am. Journal of Botany, 31, 5, (249-

253) C

Burr, H. S. (1945), Diurnal potentials in the Maple tree, Yale
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Burr, H. S. (1947), Tree potentials, Yale Journal of Biology and
Medicine, 19 (311-318).

Clark, W. G. (1938), Electric polarity and auxin transport, Plant
Ph siol, 13 (529-552).

Collins, G. M., Flint, L. H. and McLane, J. W. (1929), Electric
stimulation of plant growth, Journal of Agric. Res., 38
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Collins, R. E. (1961), Flow of Fluid Through Porous Materials,
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Crafts, A. S. (1961), Movement of water, salts and assimilates,
Translocation In Plants, Holt, Rinehart, and Winston, Inc.,
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Dainty, J., Croghan, P. C. and Fensom, D. S. (1963), Electro-
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118

Esau, K. (1965), Plant Anatomy, John Wiley and Sons, Inc., New
York.

Fensom, D. S. (1957), The bio-electric potentials of plants and
their functional significance, I: An electrokinetic theory
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Fensom, D. S. (1958), The bioelectric potentials of plants and
their functional significance, II: The patterns of bio-
electric potentials and exudation rate in excised sunflower
roots and stems, Can. J. Bot., 36 (367-383).

Fensom, D. S. (1959), The bio-electric potentials of plants and
their functional significance, III: The production of con-
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APPENDICES

123

TABLE A l

The Effect of Flow of Deionized Distilled Water
Through Cellulose Pad (23.8°c)

 

 

 

A1) Flow Rate Potential Volt- Cur- Electric
Energy age rent Energy
in Hg 103 ml/min 10'3 105 erg +m.V. +pA. 10"2 erg
dyne/cm2 cm/sec

0.2 6.7 0.22 0.6 0.004 25 .078 1.95
0.5 16.8 1.00 2.6 0.04 35 .089 3.12
1.0 33.6 2.00 5.2 0.17 46 .090 4.14
2.0 67.3 4.00 10.3 0.69 61 .099 6.04
3.0 100.9 6.10 15.8 1.59 75 .116 8.70
4.0 134.5 8.25 21.3 2.87 88 .129 11.35
5.0 168.2 10.25 26.5 4.45 100 .124 14.20
6.0 201.8 12.25 31.7 6.39 103 .155 15.97
7.0 235.4 14.27 36.8 8.67 115 .165 18.98
8.0 269.0 17.00 43.9 11.82 124 .178 22.07
9.0 302.7 18.25 47.2 14.27 135 .189 25.52
10.0 336.3 20.25 52.4 17.59 145 .198 28.71
11.0 369.9 22.00 56.9 21.02 153 .207 31.67
12.0 403.6 24.50 63.4 25.54 164 .216 35.42
14.0 470.8 28.00 72.4 34.06 180 .235 42.30
16.0 538.1 32.50 84.0 45.18 198 .250 49.50
18.0 605.4 37.00 95.7 57.86 216 .272 58.75
20.0 672.6 41.25 106.7 71.66 235 .290 68.15

 

IIIIIIIIIIIIIIIIlli'Illlllllili-llllllll -

124

TABLE A 2

The Effect of Flow of Warm Deionized Distilled
Water Through Cellulose Pady130.0°c)

 

 

 

Ap Flow Rate Potential Volt-.Cur- Electric
_. Energy age rent Energy,
in Hg 103 m1/min 10'37 103erg +m.V. +uA. 10:2erg
.1 dyne/cm2 cm/sec
0.5 16.8 1.10 2.8 0.05 31 .086 2.67
1.0 33.6 2.25 5.8 0.20 40 .105 4.20
2.0 67.2 4.50 11.6 0.78 '55 .126 6.93
3.0 100.8 6.75 17.5 1.76 71 .145 10.30
4.0 134o4 9.25 23.9 3.21 86 .165 14.19
5.0 168.0 11.50 29.7 4.99 98 .184 18.03
6.0 201.5 14.25 36.8 7.42 110 .202 22.22
7.0 235.2 16.50 42.7 10.02 122 .220 26.84
8.0 268.8 19.50 50.4 13.53 133 .243 32.32
9.0 302.4 22.00 56.9 17.17 143 .258 36.89
10.0 336.0 24.75 64.0 21.47 154 .280 43.12
11.0 370.0 27.00 69.8 25.76 162 .295 47.79
12.0 403.2 30.00 77.6 31.22 172 .315 54.18
14.0 470.4 35.00 90.5 42.50 182 .330 60.06
16.0 537.6 40.25 104.0 55.85 208 .345 71.76
18.0 604.8 45.00 116.5 70.25 228 .360 82.08
20.0 672.0 51.25 132.5 88.90 246 .375 92.25

 

 

125

TABLE A 3

The Effect of Flow of CO2 Saturated Water

Through Cellulose Pad (23.40c)

 

 

 

 

AP Flow Rate Potential Volt- Cur- Electric

Energy age rent Energy

in Hg 103 ml/min 10'3 163 erg +m.V. +11A. 10-Yerg

dyne/cm2 cm/sec

1.0 33.6 2.00 5.2 0.17 2.60 0.15 0.390
2.0 67.3 4.00 10.3 0.70 2.80 0.17 0.406
3.0 100.9 6.40 16.5 1.67 2.80 0.16 0.448
4.0 134.5 9.20 23.8 3.20 3.10 0.19 0.589
5.0 168.2 11.75 30.4 5.10 3.80 0.23 0.874
6.0 201.8 14.75 38.1 7.69 4.40 0.27 1.188
7.0 235.4 17.50 45.3 10.64 5.05 0.32 1.616
8.0 269.0 20.50 53.0 14.25 5.55 0.35 1.943
9.0 302.7 24.50 63.3 19.16 6.10 0.40 2.440
10.0 336.3 27.00 69.8 23.46 6.45 0.43 2.774
12.0 403.6 33.00 85.4 34.41 7.45 0.52 3.874
14.0 470.8 39.00 100.9 47.44 8.50 0.60 5.100
16.05 539.8 45.5 117.5 63.45 9.50 0.69 6.555
18.0 605.4 51.0 131.8 79.76 11.00 0.77 8.470
20.0 672.6 57.0 147.4 99.05 11.80 0.85 10.030

 

I'l-xlllll‘lllllll‘lllllll' III-ll" Illillllll‘li I!" I It! '- .‘fll

126

TABLE A 4

The Effect of Flow ofy(.005M ) KCl Solution
Through Cellulose Pad (23.8°c)

 

 

 

Ap Flow Rate Potential Volt- Cur- Electric

Energy age rent Energy

in Hg 105 ml/min 10"3 103 erg +m.V. +pA. 10'Zerg

dynelcm cm/sec

0.5 16.8 1.30 3.4 0.06 0.60 0.21 0.126
1.0 33.6 2.25 5.8 0.20 0.44 0.22 0.097
2.0 67.3 4.75 12.3 0.83 0.52 0.26 0.135
3.0 100.9 7.00 18.1 1.82 0.61 0.31 0.189
4.0 134.5 9.25 23.9 3.21 0.70 0.35 0.245
5.0 168.2 11.50 29.5 5.00 0.79 0.40 0.316
6.0 201.8 13.75 35.5 7.17 0.88 0.44 0.387
7.0 235.4 16.00 41.4 9.73 0.98 0.49 0.480
8.0 269.0 18.25 47.2 12.68 1.10 0.51 0.561
9.0 302.7 20.50 53.0 16.03 1.20 0.56 0.672
10.0 336.3 22.75 58.8 19.77 1.28 0.60 0.768
11.0 369.9 25.00 64.7 23.89 1.40 0.67 0.938
12.0 403.6 27.00 69.8 28.15 1.50 0.71 1.065
14.0 470.8 32.00 82.7 38.92 1.70 0.81 1.377
16.0 538.1 35.50 91.8 49.35 1.90 0.94 1.786
18.0 605.4 40.00 103.3 62.55 2.10 1.50 3.150
20.0 672.6 45.50 117.5 79.06 2.32 1.70 3.944

 

127

TABLE A 5

The Effect of Flow of (.01 M) KCl Solution
Through Cellulose Pad (23.8UQ),

 

 

 

Ap Flow Rate Potential Volt- Cur- Electric

Energy age rent Energy

in Hg 103 ml/min 10-5 103 erg +m.V. +~uA. 10-2 erg

dyne/cm2 cm/sec .

0.25 8.4 0.20 0.5 0.004 0.16 0.10 0.016
0.50 16.8 1.25 3.2 0.05 0.17 0.11 0.018
1.05 35.3 2.50 6.5 0.23 0.19 0.12 0.023
2.10 70.6 4.75 12.3 0.87 0.21 0.15 0.032
3.00 100.9 7.00 18.1 1.82 0.32 0.20 0.064
4.00 134.5 9.00 23.3 3.13 0.39 0.25 0.098
5.05 169.8 11.50 29.5 5.05 0.47 0.29 0.136
6.00 201.8 13.75 35.6 7.17 0.52 0.32 0.166
7.05 237.1 16.00 41.4 9.80 0.58 0.36 0.209
8.00 269.0 18.25 47.2 12.68 0.63 0.39 0.246
9.00 302.7 20.75 53.6 16.22 0.68 0.43 0.292
10.00 336.3 22.75 58.8 19.77 0.72 0.45 0.324
12.00 403.6 27.50 71.2 28.67 0.82 0.51 0.418
14.00 470.8 32.00 82.7 38.92 0.91 0.56 0.510
16.00 538.1 36.00 93.2 50.04 1.02 0.59 0.602
18.05 607.0 40.50 104.7 63.51 1.12 0.65 0.728
20.05 674.3 45.00 78.39 1.22 0.69 0.842

116.3

 

 

_. .l it'll" [Ill‘lll'lilllllllllll Illlllll'll

128

TABLE A 6

The Effect of the Distance of Down Stream Electrode
From the Pad

 

 

 

 

 

 

Distance Pure Water C02 Saturated Water
From Voltage Current Resistance Voltage Current Resistance
Cellulose m.V. uA K9 m.V. uA K0

cm

0.0 57.0 .100 559 1.72 0.15 11.47
0.1 62.0 .096 646 --- --- ---
0.2 68.0 .088 773 2.52 0.20 12.60
0.4 74.5 .066 1128 2.75 0.20 13.75
0.6 73.5 .052 1413 2.70 0.19 14.21
0.8 73.5 .044 1670 2.68 0.18 14.89
1.0 73.0 .040 1825 2.68 0.17 15.76
2.0 72.5 .028 2589 2.68 0.15 17.87
3-0 72.0 .022 3273 --- --- ---
Distance (3005M) KCl Solution (,01M) KCl Solution
From Voltage Current Resistance Voltage Current Resistance
Cellulose m.V. HA K9 m.V. uA K0
0.0 0.33 0.16 2.06 0.47 0.29 1.62
0.2 0.38 0.18 2.11 0.47 0.29 1.62
0.4 --- --- --- 0.47 0.29 1.62
0.6 0.44 0.20 2.20 0.48 0.29 1.66
0.8 0.47 0.22 2.14 0.50 0.29 1.72
1.0 0.51 0.23 2.22 0.49 0.28 1.75
1.5 0.55 0.24 2.29 --- --- ---
2.0 0.56 0.23 2.43 0.49 0.27 1.82

 

itllllllillllil'l‘lll I
lifill I‘llllllll'l ill:
. I‘ll t.
if

TABLE A 7

129

The Effect of Flow of Deionized Distilled Water
Through Glass Fiber Pad (22.60c)

 

 

 

 

AP Flow Rate Potential Volt- Cur- Electric
Energy age rent Energy
in H8 103 m1/min 10'3 I03 erg +m.V. +p.A. 10"2 erg
dyne/cm cmLsec
0.25 8.4 0.40 4.3 0.036 47. 0.12 0.056
0.50 16.8 0.85 9.2 0.155 114 0.28 0.319
1.05 35.3 1.60 17.3 0.612 238 0.48 1.142
2.05 69.0 3.15 34.1 2.35 480 0.87 4.176
3.00 100.9 4.60 49.8 5.03 694 1.20 8.328
4.0 134.6 6.00 65.0 8.75 900 1.50 13.50
5.0 168.2 7.40 80.2 13.49 1128 1.80 20.30
6.0 201.9 8.75 94.8 19.13 1350 2.20 29.70
7.0 235.5 10.00 108.3 25.51 1576 2.50 39.40
8.0 269.2 11.00 119.2 32.07 1805 2.80 50.54
9.0 302.8 12.00 130.0 39.36 2030 3.20 64.96
10.0 336.5 13.25 143.5 48.29 2260 3.50 79.10
11.0 370.1 14.25 154.4 57.13 2475 3.90 96.53
12.0 403.8 14.75 159.8 64.51 2664 4.20 111.89
14.0 471.1 16.75 181.4 85.47 3095 4.80 148.56
16.0 538.4 18.75 203.1 109.34 3490 5.40 188.46
18.0 605.6 20.25 219.4 132.85 3840 5.90 226.56
20.0 672.9 21.75 235.6 158.55 4200 6.50 273.00
Note: The inlet of the flow was 1.4 cm only.

MICHIGAN STATE UNIVERSITY LIBRARIES
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