Influence of different waveforms on peristaltic flows: a qualitative investigation

Abstract

In this paper, we investigate the qualitative flow features of a peristaltic flow, in a planar channel, resulting by the action of sinusoidal, multisinusoidal, triangular, trapezoidal, and square waveforms. The results show that the vertical velocities are higher for the waveforms with sharp curvatures in the wave interface, e.g. the square waveform and the multisinusoidal (n = 3) waveform. The dynamical system analysis show the presence of centers, under the crest, and saddles near the trough region. It is observed that for waveforms in which wave trough forms a plateau, the saddles are formed at the end of the plateau where the wave interface begins to rise. We identify two critical values of the flux parameter, i.e. ( and ) around which the behavior of the equilibrium point changes. We show that these critical flux values depend, linearly, on the amplitude parameter ϕ and numerically compute the curves and . The critical values are the same for all of the waveforms except the triangular waveform.