While the rapidly-growing microfluidics technology has already permeated through many aspects of the molecular and biological sciences and enabled a wide variety of low-cost and point-of-care biomedical applications, deformable microfluidics, in which microchannel possesses at least one flexible sidewall, may offer some unique advantages. The recyclability of such platforms is improved and their lifetime is extended thanks to the minimal channel clogging. The difficulties associated with the deviation of device performance from an optimal point can also be alleviated to some extent by tuning the device. Furthermore, deformable microfluidic devices may be adjusted to have more than one optimal operating points. For example, a single deformable microfluidic filter is capable of isolating target cells with multiple sizes or deformability levels as opposed to a rigid counterpart that has only one cutoff size for filtering. In typical deformable microfluidic settings, the deformable part of microchannel is actuated via external pneumatic sources, making it difficult to fabricate and operate such devices. The main objectives of this work are 1) to develop a new class of deformable microfluidics without the need to pneumatic actuation, and 2) to develop analytical tools for studying flows of Newtonian fluids in deformable microchannels. Pressure distribution within a deformable microchannel dictates the membrane deformation, while the membrane deformation governs the hydrodynamic resistance and consequently the pressure distribution within the channel. Deformable microfluidics, therefore, gives rise to a coupled fluid-solid interaction problem. Compressibility of the working fluid and variations of the channel's width are two other factors that can potentially make the problem even more complicated. In this work, an analytical model, with no fitting parameters, is derived simultaneously taking microchannel deformability, fluid compressibility, and microchannel's width profile into account, which makes it a universal tool for studying low-Reynolds-number flows of Newtonian liquids and gases in microscale. A new technique is also developed for fabrication of shallow (few microns in height) rigid/flexible microchannels with either small (tens of microns) or large (several millimeters) width. We show theoretically and experimentally that structural-fluid characteristics are solely dictated by dimensionless fluid compressibility and a lumped dimensionless parameter, called flexibility parameter. A master curve is obtained for fluid flow through any arbitrary shallow and long deformable microchannel presenting the dimensionless flow rate as functions of flexibility parameter and dimensionless fluid compressibility. The experimental and analytical investigations reveal various distinct fluid-structural characteristic behaviors under different fluid compressibility and flexibility parameter regimes. We have also demonstrated that passive rectification of compressible and incompressible flows of Newtonian fluids (liquids and gases) under the Stokes flow regime (Re << 1) is feasible by introducing the non-linear and direction-dependent terms to the otherwise linear equations of motion. Finally, a new class of deformable microfluidics is developed for passively-tunable particle trapping and isolation without the need to the pneumatic actuation. Filtration, isolation, and retrieval of particles are successfully demonstrated.
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