Laminar dispersion at low and high Peclet numbers in a sinusoidal microtube: Point-size versus finite-size particles

Abstract

This paper adopts Brenner’s homogenization theory to investigate dispersion properties, over a wide range of Peclet values, of point-size and finite-size particles in sinusoidal cylindrical microchannels in the presence of a pressure-driven Stokes flow field. The periodic alternation of entropic barriers/traps can unexpectedly increase the effective finite-size particle velocity as well as decrease the effective dispersion coefficient for both point-size and finite-size particles, for large values of the radial Peclet number. While this phenomenon has a simple explanation for tracer particles, its understanding for finite-size particles is not trivial and goes through the analysis of the localization feature of the equilibrium unit-cell particle density w0(x) and how this spatial nonuniformity impacts upon the effective particle velocity and on the solution of the so-called b field, controlling the large scale axial dispersion coefficient. Unfortunately, dispersion reduction cannot be exploited for the sake of the separation of particles having different radii because the separation performance of a hydrodynamic sinusoidal column turns out to be worse than that of a standard straight column for experimentally feasible Peclet values. Interesting analytical results for long-wavelength sinusoidal channels are obtained by a long-wave asymptotic expansion. Both zero-order and first-order terms for the asymptotic expansion of the w0(x) measure and of the b field are obtained, thus exploring a wide range of Peclet values and deriving an analytical expression for the Taylor dispersion coefficient.