Abstract
The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.
Highlights
The laminar, oscillating flow, driven by a harmonic pressure gradient in Newtonian fluids in pipes has been studied theoretically at least since the work by Sexl in 1930 [1], who obtained the classical velocity profile in the radial direction in terms of the Bessel function of the first kind and order 0.In his paper, Sexl analyzed the behavior of the solution for some limit values of the dimensionless √parameter a ω/ν, where a is the radius of the tube, ω the angular frequency of the pressure gradient, and ν the kinematic viscosity of the fluid
Parameter a ω/ν, where a is the radius of the tube, ω the angular frequency of the pressure gradient, and ν the kinematic viscosity of the fluid
Uchida [8] studied the flow of a Newtonian fluid due to pulsatile pressure gradient
Summary
The laminar, oscillating flow, driven by a harmonic pressure gradient in Newtonian fluids in pipes has been studied theoretically at least since the work by Sexl in 1930 [1], who obtained the classical velocity profile in the radial direction in terms of the Bessel function of the first kind and order 0. In addition to the paper by Steller [12], we can mention those by Daprà and Scarpi [24], who got a perturbation solution to the second-order of the pulsatile flow of a pseudoplastic Williamson fluid, and that by Nandakumar et al [25] for a shear-thinning fluid in a two-dimensional stenosed channel. The goal of the present study was to determine analytical solutions for the two-dimensional flow of an Ostwald-de Waele type fluid driven by a pulsating pressure gradient To accomplish this goal, a perturbation method was used to obtain the velocity distribution up to a second-order term, from which the instantaneous discharge, wall shear stress, cycle-average discharge, and dispersion coefficient were analytically obtained and computed. The solution presented in this article includes more details of the algebra than reported previously [15,24]
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