On the effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel

Abstract

The effect of variable viscosity on the peristaltic flow of a Newtonian fluid in an asymmetric channel was studied by Hayet and Ali using a viscosity function that takes two different values for any two symmetrical points with respect to the channel axis. This contrasts with the natural phenomena in many situations, such as the motion of chyme within the small intestines and the blood in the arteries where the spatial variation of viscosity is axisymmetric from the axis or walls. Thus, the viscosities at any two symmetrical points should be equal. To achieve this condition, the viscosity function is modified in the present work and the peristaltic flow of a Newtonian fluid in an asymmetric channel is restudied. The effect of the new viscosity function is symmetric about the channel axis and it is decreasing in the direction of the upper and lower walls. The expressions for the pressure gradient per wavelength are obtained and the pumping characteristics are discussed. We present a detailed analysis of the effects of the variation of viscosity, upper wave amplitude, lower wave amplitude, channel width, and phase difference on the pressure rise, the friction force, the pumping, and co-pumping regions. The study also shows that, in addition to the mean flow parameter, the wave amplitude, and the phase difference, the viscosity parameter also affects the pressure rise, the friction force, and the pumping region. Therefore, the interval for the flow rate where the pressure rise was positive and the interval for flow rate in which frictional forces have direction opposite to the wave velocity increase when the viscosity parameter rises. Moreover, the pressure rise and the frictional forces decrease by increasing viscosity, which is quite the opposite of the case of dissymmetric viscosity.