The University of Illinois at Chicago
Chicago, Illinois, U. S. A.
This talk will address the computation of inertial drift forces experienced by rigid particles near pore entrances as the result zero-mean oscillatory flow. Applied to axisymmetric geometries involving (i) cylindrical pores of finite length with rounded mouths, and (ii) spherical and spheroidal particles, the general asymptotic-numerical approach of Hinch and Nitsche [{\em J.\ Fluid Mech.,} {\bf 256}, 343-401, (1993)] for small Reynolds number and amplitude is extended to this more complex case to obtain the dimensionless drift force over a spectrum of dimensionless frequencies, corresponding to the ultrasonic regime. At zeroth order the relevant analog of Brinkman flow is attacked with a least-squares boundary-singularity method using the point-force and point-source solutions as basis functions. The net drift force (at first order in Reynolds number) is obtained by integrating over the fluid domain a quadratic form obtained from the zeroth-order velocity field and adding a finite-amplitude term from the particle surface. For cyclic flow in the axial direction (through the pore), the net effect is to push particles away from the pore mouth. An analysis of the relevant scales shows that inertial drift can be comparable to Brownian motion in the colloidal size regime. Thereby open interesting possibilities for (i) counteracting concentration polarization in ultrafiltration, and (ii) a novel acoustic `diffusion gate' technology for controlling membrane transport. Extensions to cyclic flow parallel to the membrane surface will also be discussed.