Shear‐induced alignment of nonspherical Brownian particles near walls

Abstract

AbstractA theoretical investigation is presented of the convection‐diffusion of model nonspherical solutes in shear flow over a plane wall. The analysis proceeds by formulating the underlying configuration‐space Brownian transport equation for the distribution over accessible positions and orientations. Geometrical constraints are imposed via boundary conditions preventing wall penetration, and some of the calculations incorporate hydrodynamic interactions with the wall. The analysis is brought to fruition by regular perturbation expansion in the rotary Péclet number, and solution of the resultant boundary‐value problems by a Galerkin technique. Three specific mechanistic conclusions result from the analysis. First, steric constraints imposed by the wall impedes the shear‐induced solute alignment (producing a more nearly uniform distribution over orientations relative to the unbounded‐fluid case) near the wall. Second, although the first effect of flow is to counteract the equilibrium depletion of solute centers near the wall, flow reinforces this depletion at higher order in the shear rate. Third, solute‐wall hydrodynamic interactions act to strengthen the shear‐induced solute alignment near the wall. This last phenomenon occurs because hydrodynamic wall effects significantly decrease the rotary diffusivity, but have little effect on the angular velocity, thereby locally increasing the effective rotary Péclet number (the effective flow strength). Correspondingly, solute‐wall hydrodynamic interactions reinforce the flow effects on the near‐wall depletion just noted. Steric and hydrodynamic wall effects typically are of order 15–20% near the wall.