Computational and experimental investigations of two-dimensional nonlinear peristaltic flows

Abstract

An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[sdot ]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).

A model experiment to understand the oral phase of swallowing of Newtonian liquids

“…Brown and Hung (1977) claimed also that this trend reverses for finite amplitude to wavelength ratios, Finally, our experimental results suggest also a weak dependence of oral residues on bolus volume. Splitting a bolus in several smaller volumes could therefore increase the cumulated residual mass.…”

“…Another mechanism that could explain the residue increase when high viscosity liquids are swallowed, is a reduced effectiveness of the peristaltic flow. Brown and Hung (1977) considered the steady viscous flow induced by a peristaltic wave in a bi-dimensional channel.…”

In vivo observations and in vitro experiments on the oral phase of swallowing of Newtonian and shear-thinning liquids

“…In the case of a very flexible membrane, such as the one considered in this study, the drag force has been shown in Takagi and Balmforth (2011) to be provided purely by the fluid pressure and determined by the flow within the bolus. While Hayoun et al (2015) have considered a linear dependency of F d in ω, other studies (Brown and Hung, 1977;Takabatake and Ayukawa, 1982) have shown that this is valid only at low Reynolds numbers Re. At higher Re (typically reached for lower viscosity liquids), it becomes necessary to account for inertial effects in the fluid.…”

Simulations of peristaltic slip-flow of hydromagnetic bio-fluid in a curved channel

“…Later studies on the subject extended the previous ones to include inertial effects, 5,6 high Reynolds number effects, 7,8 creeping flow condition, 9 effects of peripheral layers 10 etc. The non-Newtonian nature of biological and industrial fluids is also incorporated in the studies on peristaltic transport.…”