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.

Electro-magneto-hydrodynamic peristaltic pumping of couple stress biofluids through a complex wavy micro-channel

“…This is the focus of the present investigation. It extends the existing work in the field which has previously been confined to electrofluid thermal viscoelastic dielectric peristalsis [49], electrokinetic Jefferys (viscoelastic) peristaltic pumping [50] and electro-osmotic power-law peristaltic pumping [51]. The present work is relevant to simulation of real working fluids in electromagnetic biomimetic microscale pumps utilizing the peristaltic propulsion mechanism [52].…”

Study of microvascular non-Newtonian blood flow modulated by electroosmosis

“…This highly efficient and adaptive mechanism of internal fluid propulsion arises in embryology, intestinal pumping, vaso-motion in small blood vessels, swallowing, lymph dynamics, water transport in botany etc. A classical investigation of the pumping characteristics in peristalsis was presented many decades ago by Shapiro et al [27] [39] who used the Jefferys viscoelastic model, Shit et al [40] who employed a powerlaw model and also considered heat transfer and Joule dissipation effects and very recently…”

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

“…This model however constitutes a relatively simple formulation for analyzing electro-peristaltic transport. In this direction, some more recent investigations [20][21][22][23][24][25] have been reported to analyze the electro-peristaltic transport with channel flow [20], capillary flow [21], power law fluids [22], couple stress fluid [23], magnetohydrodynamics [24], Viscoelastic fluids [25]. They have concluded that peristaltic transport/physiological flow may be controlled by adding and opposing the external electric field.…”