Peristaltic Transport

Abstract

Peristaltic pumping (viscous fluid flow induced by a sinusoidal traveling wave motion of the walls of a tube) at moderate amplitudes of motion is analyzed in the two-dimensional case. The nonlinear convective acceleration is considered and the nonslip condition is applied on the wavy wall (rather than on the mean position) in order to account for the mean flow induced by the wall motion. In the case in which there is no other cause of flow, the mean flow induced by the peristaltic motion of the wall is proportional to the square of the amplitude ratio (wave amplitude/half width of channel). The velocity profile depends on the mean pressure gradient. In this paper only those cases in which the pressure gradient will produce a flow of the same order of magnitude as that induced by the peristaltic motion are considered. If the pressure gradient is positive and equal to a certain critical value, then the velocity is zero on the center line. Pumping against a positive pressure gradient greater than the critical value would induce a backward flow (reflux) in the core region of the stream. There will be no reflux if the pressure gradient is smaller than the critical value. The velocity profile and the value of the critical pressure gradient are presented in this paper.

Transverse magnetic field driven modification in unsteady peristaltic transport with electrical double layer effects

“…In the context of theoretical and experimental fluid dynamics, it received attention in the mid-1960s onwards, again motivated by the development of efficient pumps for medical and other applications. Important mathematical works in this regard have been communicated by Burns and Parkes [8], Fung and Yih [9], Shapiro et al [10], Jaffrin and Shapiro [11], Shukla et al [12], Takabatake, and Ayukawa [13], Pozrikidis [14] and Li and Brasseur [15]. More recent studies which have extended the purely Newtonian fluid models described in [8]- [15] include Tripathi and Bég [16] who examined viscoelastic peristaltic propulsion, Tripathi and Bég [17] who studied peristaltic flows of magnetized couple stress fluids, Blanchette [18] who considered the influence of suspended drops on peristaltic pumping, Ellahi et al [19] who computed heat transfer in peristaltic flow.…”

Peristaltically induced motion in a closed cavity with two vibrating walls

“…In contrast to the above-cited investigations, Fung and Yih 9 and Yin and Fung 10 studied peristaltic pumping at arbitrary Reynolds numbers and at small wall deformations. Our study is an a͒ Author to whom correspondence should be addressed; electronic mail: bau@seas.upenn.edu extension of these works 9,10 to the case of a closed cavity.…”

“…In this paper, similarly to Fung and Yih, 9 Yin and Fung, 10 and Selverov and Stone, 11 we use a regular perturbation expansion in the wave amplitude ͑⑀͒ to analyze peristaltic flow in a closed cavity. It turns out that in the closedcavity case, the first-order solution consists of two terms: one identical to the expression for the open cavity 9,10 and the other resulting from the pressure oscillations induced by the presence of sidewalls.…”

Effects of Poiseuille flow on peristaltic transport

“…Since then, several investigators have contributed to the study of peristaltic action in both mechanical and physiological situations, such as Burns et al [3], Hanin [8], Barton et al [1], Fung et al [7], Shapiro et al [16], Yih et al [19], Chow [4], Jaffrin et al [9], and Mittra [13].…”