Passive tracer transport in peristaltic pumping of non-Newtonian blood flow: A mathematical model

Abstract

The large time behavior of passive contaminant in non-Newtonian peristaltic blood flow in a two-dimensional (2D) channel (capillary) has been examined in this paper. The power-law model is employed in order to highlight the non-Newtonian blood characteristic. The study was conducted using the Reynolds decomposition technique, which converts a 2D transport problem into a 1D transport model in which species concentration can be decomposed into sectional average concentration and variation from its mean value. For flow velocity, the same decomposition method is used. This allows the derivation of the dispersion coefficient and convection coefficient. Using Fick’s law, the advection–diffusion equation is modified by replacing these coefficients by their corresponding average values and analytical solutions for the mean concentration are derived. In the absence of peristalsis effects ([Formula: see text]), i.e., for the straight rigid channel, the dispersion coefficient is invariant along the channel length. With increasing modulation (peristaltic wave) parameter, [Formula: see text], there is a strong elevation in advection coefficient in the initial half of the channel with a subsequent suppression in the second half of the channel, indicating that the location in the channel strongly influences advection characteristics. Advection coefficient is significantly elevated with increment in power-law rheological index (for shear-thinning fluids, [Formula: see text]) across the channel length and exhibits an oscillatory nature due to the peristaltic waves. In the shear-thickening range ([Formula: see text]), with progressive increase in n, an increment in peristaltic modulation parameter, [Formula: see text], induces a marked reduction in the axially average relative advection coefficient. Dispersion coefficient is initially boosted along the early section of the channel with increment in modulation parameter whereas further long the channel this trend is reversed. Increasing aspect ratio and Péclet number consistently boost dispersion coefficient along the entire channel length. The study provides a solid benchmark for further generalized simulations with computational fluid dynamics.