Dynamics of viscous flow induced in a linearly viscoelastic channel by peristaltic forcing

A mathematical model is developed to investigate the effect of wall viscoelasticity on the flow induced by peristaltic forcing in a viscous fluid occupying a two-dimensional channel. The main objective of the work is to investigate the role played by viscous damping of the channel wall on the net flow rate. To that end, the resistance of the walls to deformation is modeled using a Kramer-type linearly viscoelastic model. Numerical results are presented for periodic waves in wave frame at arbitrary wavelengths and amplitudes of the peristaltic forcing for parameter values typical of the human digestion system. The viscous behavior of the channel wall is predicted to reduce the flow rate. It also gives rise to a phase lag between the applied force and the wall deformation, with its severity depending on the wave parameters and fluid/solid properties. The peristaltic forcing mechanism is predicted to be better suited for long waves, but it is shown that beyond a threshold amplitude, the effect of wavelength saturates when trapping occurs. For highly viscous fluids such as chyme flowing in human colon, the viscous normal stress exerted by the fluid on the inner side of the wall is shown to play a key role in the deformation of the walls and thereby the flow rate. It is predicted that competition between the fluid internal forces and the external peristaltic forcing causes the flow rate to initially decrease with the Reynolds number before starting to increase beyond a threshold.