Peristaltic Pumping of a Newtonian Fluid With Particles Suspended in It at Low Reynolds Number Under Long Wavelength Approximations

Abstract

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.

Peristaltic Pumping of a Conducting Sisko Fluid through Porous Medium with Heat and Mass Transfer

“…where, 1 T and 1 C are the temperature and the concentration of the fluid at the lower wall of the channel, 2 T and 2 C are the temperature and the concentration of the fluid at the upper wall of the channel. Substituting (30) into Equations (21)-(29) we obtain the following non-dimensional equations after dropping the star mark: 2 2 2 2 2 2 2 2 2 2 1 , …”

“…Shapiro et al [1] explained the basic principles and brought out clearly the significances of the various parameters governing the flow. The non-Newtonian effects in peristaltic motion were included in Kaimal [2]. Later several mathematical and experimental models have been developed to understand the fluid mechanical aspects of peristaltic motion.…”

Numerical study of particulate suspension flow through wavy-walled channels

“…The peristaltic motion of a mixture of uid and solid particles has also been theoretically examined, e.g. by Hung and Brown [10] and Kaimal [11], Srivastava and Srivastava [12] and Misra and Pandey [13]. These studies on peristaltic ows of particulate suspension or two-phase model have either neglected inertia or assumed very slow motion, low frequency and small amplitudes.…”

Fluid transport with suspended particles by means of dilating peristaltic waves

“…In order to obtain qualitative and quantitative insight of the motion of suspended solid and rigid particles distributed uniformly in a homogeneous medium due to the passage of discrete peristaltic waves, Hung and Brown [1] employed a two-dimensional experimental model to investigate various geometries and dynamic effects on peristaltic transport. It was followed by Kaimal [2] who investigated peristaltic pumping of a Newtonian fluid with rigid solid particles suspended in it at low Reynolds number using long wavelength approximations. He discussed reflux and trapping but noted that the presence of the suspended particles does not lead to any significant disturbance to the flow field of the fluid.…”