Calculation of Brownian particle transmission in long, wide channels

The transport of Brownian particles in channels which are long and wide com pared ro their height is addressed The cross-sectional shape of the channel is assumed to be slowly varying, but otherwise arbitrary A solution to the convective-diffusive equation with reaction-rare boundary condition was ob tained by locally incorporating the modified Graetz solution in a flat chan nel. The solution was evaluated asymptotically for the eases of a channel w ith a maximum height occurring at an endpoint and at an interior maximum. T he asymptotic method was applied in two example geometries: the calibration apparatus used to determine reaction-rate constants for virus adsorption t o lares barriers, and overlapping pores in a nucleation-track membrane. The asymptotic expressions compared well with finite-element calculations in t he examples. The utility Of the asymptotic approach lies in rapid estimatio n of particle transmission through a channel us a function of geometric and physical parameters.