Analysis of peristaltic two-phase flow with application to ureteral biomechanics

Abstract

Fluid flow in the ureter is sometimes accompanied by solid particles that are produced in the kidneys or result from the breakup of larger kidney stones; ureteral peristalsis is affected by the presence of these solids. Peristaltic flow is analyzed for a solitary traveling wave in an axisymmetric tube with an incompressible, Newtonian fluid in which identical, solid spherical particles are distributed. A two-phase flow model is used in conjunction with a perturbation method based on a small radius to length ratio of the wave to obtain a closed-form solution of the flow and particle velocities. The phenomenon of trapping in which closed fluid recirculation streamlines in a moving coordinate frame occurs is discussed. Peristaltic pumping is affected as particle volume fraction is increased. The pressure drop diminishes as the amplitude ratio (wave amplitude/wave radius) decreases. The pressure in the contracted part of the ureter increases as the particle volume fraction is increased. It is suggested that certain pathological and physiological manifestations on the ureter can be related to these findings. The results may also be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.