Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption—Deviation from the Gaussianity

Abstract

Unsteady solute dispersion in a pulsatile Herschel–Bulkley fluid flow in a tube is reinvestigated to examine the significance of the skewness and kurtosis on the concentration distribution using Aris' method of moments considering Hermite polynomials. This study is also an initiation in the direction of solute dispersion in a pulsatile non-Newtonian flow considering the first five moments. This investigation not only brings in the accuracy in the estimation but also measures the deflection and decrease in the axial mean concentration distribution of a solute in a tube. Significant variations in the skewness and kurtosis coefficients against various values of the flow governing parameters, such as the yield stress τy, the wall absorption parameter β, the power law index a, the Womersley frequency parameter α, and the amplitude of fluctuating pressure component e, are presented graphically along with the variations in the mean concentration distribution of the solute in the tube. For larger values of the Womersley frequency parameter, the occurrence of double frequency period for the convection and dispersion coefficients is noticed, which has significant influence on the skewness and kurtosis coefficients. The results for solute dispersion in Newtonian fluid, Bingham fluid, and power law fluid flows are also reported as special cases of this analysis.

Significance of skewness and kurtosis on the solute dispersion in pulsatile Carreau–Yasuda fluid flow in a tube with wall absorption

“…For small in figure 4, there is no significant change in , but for higher values of , the magnitude of decreases with increasing , and eventually it reaches the steady state as seen in figure 4. This was noticed in Sankarasubramanian & Gill (1973), Singh & Murthy (2022 a , b ) and Rana & Murthy (2016 a , b , c ). Also, (t) is unaffected by the pulsatility and the type of the fluid, whether it is a Newtonian or non-Newtonian fluid.…”

“…(1978), Yasuda, Armstrong & Cohen (1981), Bird et al. (1987), Cho & Kensey (1991), Gijsen, van de Vosse & Janssen (1999), Abraham, Behr & Heinkenschloss (2005), Chandran, Rittgers & Yoganathan (2012), Rana & Murthy (2016 a ), Rana & Murthy (2016 c ), Singh & Murthy (2022 a ) and Singh & Murthy (2022 b ), and these are listed in table 1. By following integrals that are seen in convection , dispersion , skewness , kurtosis , expressions are evaluated using Simpson's 1/3 rule using MATLAB (2019).…”

“…Much discussion on , is seen even for various non-Newtonian fluids such as the yield stress Casson, H–B, K–L and non-yield stress C–Y fluids in the literature (Rana & Murthy 2016 a , b , c , 2017; Singh & Murthy 2022 a , b ). What follows is a brief discussion on these coefficients with the parameters due to the pulsatile fluid nature.…”

“…Furthermore, the drift, dispersivity and skewness were studied. Unsteady solute dispersion in a pulsatile H–B fluid flow in a tube has been reinvestigated by Singh & Murthy (2022 a ) to examine the skewness and kurtosis on the concentration distribution using Aris’ method of moments considering Hermite polynomials. Yet another yield stress model, the Kuang and Luo (K–L) model, was also addressed very recently by Singh & Murthy (2022 b ).…”

Transient solute dispersion in electro‐osmotic viscoplastic flow in a microchannel

“…[12], Debnath et al. [13, 14], Singh and Murthy [15], etc.). These studies have continuously refined the original Taylor model to compute with increasing accuracy a variety of different transport coefficients.…”