Electro-kinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: Mathematical modeling

Abstract

Analytical solutions are developed for the electro-kinetic flow of a viscoelastic biological liquid in a finite length cylindrical capillary geometry under peristaltic waves. The Jefferys’ non-Newtonian constitutive model is employed to characterize rheological properties of the fluid. The unsteady conservation equations for mass and momentum with electro-kinetic and Darcian porous medium drag force terms are reduced to a system of steady linearized conservation equations in an axisymmetric coordinate system. The long wavelength, creeping (low Reynolds number) and Debye–Hückel linearization approximations are utilized. The resulting boundary value problem is shown to be controlled by a number of parameters including the electro-osmotic parameter, Helmholtz–Smoluchowski velocity (maximum electro-osmotic velocity), and Jefferys’ first parameter (ratio of relaxation and retardation time), wave amplitude. The influence of these parameters and also time on axial velocity, pressure difference, maximum volumetric flow rate and streamline distributions (for elucidating trapping phenomena) is visualized graphically and interpreted in detail. Pressure difference magnitudes are enhanced consistently with both increasing electro-osmotic parameter and Helmholtz–Smoluchowski velocity, whereas they are only elevated with increasing Jefferys’ first parameter for positive volumetric flow rates. Maximum time averaged flow rate is enhanced with increasing electro-osmotic parameter, Helmholtz–Smoluchowski velocity and Jefferys’ first parameter. Axial flow is accelerated in the core (plug) region of the conduit with greater values of electro-osmotic parameter and Helmholtz–Smoluchowski velocity whereas it is significantly decelerated with increasing Jefferys’ first parameter. The simulations find applications in electro-osmotic (EO) transport processes in capillary physiology and also bio-inspired EO pump devices in chemical and aerospace engineering.