The peristaltic motion of a fluid in which are distributed uniform rigid particles through an axisymmetric tube of arbitrary wave shape is considered for low Reynolds numbers. Solutions for the stream functions and vorticity functions are obtained in the form of asymptotic expansions regarding the ratio (ε) of the tube radius to the wavelength of the peristaltic wave to be small. We have assumed the velocity equilibration length of particulate phase to be equal to the wavelength of the peristalsis. Expressions for mean pressure gradient and shear stress are obtained. Also we have discussed phenomena like “reflux” and “trapping”. The study is particularly helpful in engineering applications such as pumping of solid-fluid mixtures by peristalsis.
Mathematical modelling of two-fluid electro-osmotic peristaltic pumping of an Ellis fluid in an axisymmetric tube