Mathematical modelling of peristaltic propulsion of viscoplastic bio-fluids.

This article studies theoretically the transportation of rheological viscoplastic fluids through physiological vessels by continuous muscle contraction and relaxation, that is, peristalsis. Both cases of planar and cylindrical physiological vessels are considered. A mathematical model is developed under long wavelength and low Reynolds number approximations. Expressions for axial velocity in core region, axial velocity in plug flow region, volume flow rate and pressure gradient in non-dimensional form are obtained. A comparative study of velocity profiles, pressure distribution, friction force and mechanical efficiency for different viscoplastic liquids is conducted. The influence of width of plug flow region, shear rate strain index and yield stress index on the pressure distribution, friction force and mechanical efficiency is elaborated. The study is relevant to gastric fluid mechanics and also non-Newtonian biomimetic pump hazardous waste systems exploiting peristaltic mechanisms.

Numerical simulation of Dean number and curvature effects on magneto-biofluid flow through a curved conduit.

A numerical study is performed to investigate the magnetohydrodynamic viscous steady biofluid flow through a curved pipe with circular cross section under various conditions. A spectral method is applied as the principal tool for the numerical simulation with Fourier series, Chebyshev polynomials, collocation methods and an iteration method as secondary tools. The combined effects of Dean number, Dn , magnetic parameter, Mg , and tube curvature, δ, are studied. The flow patterns have been shown graphically for large Dean numbers as well as magnetic parameter and a wide range of curvatures, 0.01 ≤δ≤ 0.2. Two-vortex solutions have been found. Axial velocity has been found to increase with an increase of Dean number, whereas it is suppressed with greater curvature and magnetic parameters. For high magnetic parameter and Dean number and low curvature, almost all the fluid vortex strengths are weak. The study is relevant to magnetohydrodynamic blood flow in the cardiovascular system.