A single dumbbell falling under gravity in a cellular flow field

Abstract

We study the motion of a single polymer chain settling under gravity in an ensemble of periodic, cellular flow fields, which are steady in time. The molecule is an elastic dumbbell composed of two beads connected by a nonbendable Hookean spring. Each bead is subject to a Stokes drag and a Brownian force from the flow. In the absence of particle inertia, the molecule settles out at a rate which depends on three parameters: the particle velocity in a fluid at rest, Vg, the spring constant, B, and the diffusion coefficient, D. We investigate the dependence of the molecule settling velocity on B, for fixed Vg and D. It is found that this velocity strongly depends on B and it has a minimum value less than Vg. We also find that the molecule is temporarily trapped at fixed points for certain values of the parameters. We analyse one fixed point in detail and conclude that its stability is the main factor which contributes to slowing down the settling process.