Quantifying particle adhesion to the ureteral walls during peristaltic flow

In this paper, we investigate the motion of particle(s) under the action of peristaltic flow. The particle trajectories are simulated by considering sinusoidal peristaltic waves. The fluid flow is governed by a two-dimensional Navier-Stokes equation, whereas for the particle dynamics we use the Basset-Boussinesq-Oseen (BBO) equation. The particle trajectories computed for different characteristic peristaltic flows, that is, trapping flow, augmented flow, and backward flow, show that the net horizontal particle displacement is largest for the augmented flow case. In general, the particle motion depends on its location in the peristaltic channel because of the wall curvature, which directly affects the flow velocities. The reported results for a cluster of particles show that whilst a fraction of particles form a group and propagate along the wave, some particles are left behind that deposit on the channel wall. In many biological processes it is desirable to know the number of particles that accumulate on the channel walls. In the present work, we propose empirical relations which can be used to calculate particle adhesion as a function of time.