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.