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We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations which relate the pressure and the stream function, respectively, to gradients in the zeta potential distribution parallel and perpendicular to the applied electric field. We solve the governing equations for the fundamental case of a disk with uniform zeta potential and show that the flow-field in the outer region takes the form of a pure dipole. We illustrate the ability to generate complex flow-fields around smooth convex regions by superposition of such disks with uniform zeta potential and a uniform pressure driven flow. This method may be useful for future on-chip devices, allowing flow control without the need for mechanical components.
We adopt a boundary integral method to study the dynamics of a translating droplet confined in a Hele-Shaw cell in the Stokes regime. The droplet is driven by the motion of the ambient fluid with the same viscosity. We characterize the three-dimensio
We study the spreading and leveling of a gravity current in a Hele-Shaw cell with flow-wise width variations as an analog for flow {in fractures and horizontally heterogeneous aquifers}. Using phase-plane analysis, we obtain second-kind self-similar
We study microfluidic self digitization in Hele-Shaw cells using pancake droplets anchored to surface tension traps. We show that above a critical flow rate, large anchored droplets break up to form two daughter droplets, one of which remains in the
Micro and nanodroplets have many important applications such as in drug delivery, liquid-liquid extraction, nanomaterial synthesis and cosmetics. A commonly used method to generate a large number of micro or nanodroplets in one simple step is solvent
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior more viscous