Pressure-driven flows of Quemada fluids in a channel lined with a poroelastic layer: A linear stability analysis

Abstract

Laminar flow of a thixotropic fluid obeying the Quemada model is numerically investigated in a channel lined with a poroelastic layer saturated with a Newtonian fluid. Having assumed that the solid matrix in the poroelastic layer obeys the linear elastic model, basic flow/deformation were obtained in the main channel and also in the poroelastic layer using the biphasic mixture theory. The basic state was then subjected to infinitesimally-small, normal-mode perturbations and their vulnerability to poroelastic instability was studied based on the linear, temporal stability analysis. The eigenvalue problem so obtained was then solved numerically using the spectral collocation method. The main objective of the work was to investigate the role played by the pororelastic layer's parameters (i.e., porosity, flexibility, permeability, density, and thickness) on the stability picture. The roles played by the rheological behavior of the core fluid and the fluid flowing through the poroelastic layer were also investigated. Numerical results were obtained at low-permeability limit, typical of physiological systems, demonstrating that the effect of the layer's properties can be stabilizing or destabilizing depending on the rheological properties of the two fluids involved in the problem. In general, thixotropy was found to have a stabilizing effect on the core flow. The same was found to be true as to the effect of a fluid's shear-thinning. The analysis also served to show that the effect of a fluid's yield stress might also be stabilizing.

Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

“…In the context of the present work, related studies have been performed on particular sub-systems such as decoupled elasticity and diffusion [14]. More recent works tend to integrate further complexity by adding multi-layered coupled systems [15], incorporating domain or mechanical growth [16], the coupling between elasticity-diffusion [17], poroelasticity [18,19], and also porelasticity-diffusion [11], which resembles more the idea we advocate in this work. The key contributions of this paper include a new three-dimensional model for the two-way coupling between poroelasticity and reaction-diffusion, the derivation and discussion of dispersion relations that indicate that the mechano-chemical feedback onsets Turing instabilities (with non-trivial wavenumber) for a range of coupling parameters, the formulation and numerical realisation of a locking-free finite element method, and a sample of numerical results including applications in brain injuries poromechanics.…”

An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid

“…In most such applications, the gel-fluid interface is either immobile or has simple and easily computable displacements so as not to require the coupled solution of the fluid flow and elastic deformation of the solid skeleton. These include 1D shear flow past a layer of poroelastic material [31,32], 1D compression of a poroelastic layer [28], flow in a wavy channel coated with a thin poroelastic layer [33], and linear stability analysis of shear flow past a poroelastic layer [34,35,36]. Recently, poroelastic modeling has been used to explain the dynamics of the actomyosin gel inside biological cells [37,38].…”