Diffusion, sedimentation, and Taylor dispersion of a Brownian cluster subjected to a timehyphen;periodic external force: A micromodel of ac electrophoretic phenomena

摘要

A generalized formulation of the Fokkerndash;Planck equation is utilized to calculate the mean velocity and dispersivity of a flexible Brownian cluster of rigid particles which is acted upon by a timehyphen;periodic external force. It is shown that if the force consists of a nonzero mean part and a lsquo;lsquo;fluctuatingrsquo;rsquo; (i.e., zero mean) part, their effects are decoupled. Similarly, if a Fourier expansion of the force is carried out, the effect of each term of the expansion can be treated independently of the others. A representative force term of the formFnthinsp;exp(iohgr;nt) +Fcirc;nthinsp;exp(minus;iohgr;nt) was selected to act upon a flexible dumbbell composed of two identical tethered spheres of radiia, with the inextensible tether acting as an lsquo;lsquo;attractiversquo;rsquo; internal potential. The dispersion tensor is found to consist of a lsquo;lsquo;parallelrsquo;rsquo; contribution (directed alongFnFcirc;n+Fcirc;nFn) and a lsquo;lsquo;hydrostaticrsquo;rsquo; contribution. This dispersion tensor depends linearly upon the scalar (Fnsdot;Fcirc;n)a/24pgr;mgr;kT(mgr;=viscosity), approaches a constant asymptotic value for small nondimensional frequencies OHgr;n=12pgr;mgr;a3ohgr;n/kT, and decreases asymptotically to zero for very large frequencies.