1. Surprising consequences of ion conservation in electro-osmosis [1]: A variety of microfluidic technologies utilize electrokinetic transport over surfaces with rapid variations in charge. Here, as a paradigmatic model system for such scenarios, we consider electro-osmosis over a flat wall possessing a sudden jump in surface charge. The requirement of ion conservation at the jump gives rise to gradients in the bulk electric field and fluid flow (i.e. outside of the nanometer sized screening cloud adjacent to the wall). Remarkably, we show that these bulk variations may persist over length scales much greater than the screening-cloud thickness, with the implication that they may be readily observed in microfluidic channels.
2. Active and nonlinear microrheology [2]: Microrheology aims to infer the rheological properties of complex, microstructured materials from the motion of embedded colloidal probes. In passive microrheology, the probe motion is driven by thermal (Brownian) fluctuations, and the linear viscoelastic response (moduli) of a sample is measured via a generalized Stokes-Einstein relation. In contrast, in active or nonlinear microrheology, one actively forces a probe through a material (via e.g. optical tweezers) with the aim of inferring nonlinear rheological properties (e.g. shear thinning, normal stress differences). As a theoretical model for nonlinear microrheology, we investigate the actively driven motion of a probe particle immersed in a colloidal dispersion. A major goal is to establish under what conditions the computed microrheological properties are in agreement with those from macroscopic rheometry.
3. Hydrodynamics of Janus particles [3]: The last several years have witnessed significant progress in the design of nanometer sized "Janus" particles, possessing patterned surface properties. Here, we propose and investigate a hydrodynamically Janus particle: the "slip-stick" sphere, whose surface is partitioned into two regions. On one region fluid sticks to the particle, whereas on the other fluid slips past it. The Janus nature of a slip-stick sphere leads to a number of interesting findings. In particular, when placed in a shear flow, a slip-stick sphere undergoes either periodic translational motion or a net displacement along the flow direction. Moreover, the rheology of a dilute suspension of Janus spheres is non-Newtonian to even first order in particle volume fraction.
4. Electrophoretic mobility of a colloidal particle redux : The calculation of the electrophoretic mobility of a spherical particle is a fundamental problem in colloid science, with practical relevance in separation of macro- and bio-molecules. We report on ongoing work aimed at extending the standard model for computing the mobility (O'Brien and White, J. Chem. Soc. Faraday Trans. II 74.) to capture the effects of fluid slip and finite ion size.
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References:
[1] A. S. Khair and T. M. Squires, "Surprising consequences of ion conservation in electro-osmosis over a surface charge discontinuity," J. Fluid Mech. (In press).
[2] A. S. Khair and J. F. Brady, "Single particle motion in colloidal dispersions: a simple model for active and nonlinear microrheology," J. Fluid Mech. 557, 73 (2006).
[3] A. Ramachandran and A. S. Khair, "The dynamics and rheology of a dilute suspension of hydrodynamically Janus spheres in a linear flow," J. Fluid Mech. (Submitted)