Abstract:In the present work, the effect of inertial terms is numerically investigated on the hydroelastic stability of shearthinning fluids in pressure-driven flow between two parallel plates lined with a Mooney-Rivlin hyperelastic polymeric gel. Having obtained the basic flow for the fluid and the basic deformation for the solid, the vulnerability of the basic solutions are examined when subjected to infinitesimally-small, normal-mode perturbations. By dropping all nonlinear perturbation terms, an eigenvalue problem … Show more
“…(We have decided to go for the hardest scenario simply because in our recent publication dealing with compliant layers [20] we have already shown that the creeping-flow scenario may give rise to unrealistic behavior in the neutral stability curve.) We have reached to the following main conclusions:…”
Section: Discussionmentioning
confidence: 99%
“…25, we start with Eqs. [16][17][18][19][20]. At the basic state, poroelastic region consists of fluid and solid phases both under steady conditions.…”
Section: Appendix A: the Shear-thinning Aspect Of The Moore Modelmentioning
confidence: 99%
“…It was shown that for this particular solid model a depth-dependent first normal-stress-difference arises in the base state (even under creeping-flow conditions) leading to a shortwave instability. In a more recent work, Pourjafar and Sadeghy [20] resorted to the Mooney-Rivlin model and reached to the conclusion that a negative second normal-stress-difference has a stabilizing effect on the flow. They also showed that, in order to avoid discontinuity in the neutral stability curve, inertial terms should always be included in the analysis no matter how small the Reynolds number might be.…”
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.
“…(We have decided to go for the hardest scenario simply because in our recent publication dealing with compliant layers [20] we have already shown that the creeping-flow scenario may give rise to unrealistic behavior in the neutral stability curve.) We have reached to the following main conclusions:…”
Section: Discussionmentioning
confidence: 99%
“…25, we start with Eqs. [16][17][18][19][20]. At the basic state, poroelastic region consists of fluid and solid phases both under steady conditions.…”
Section: Appendix A: the Shear-thinning Aspect Of The Moore Modelmentioning
confidence: 99%
“…It was shown that for this particular solid model a depth-dependent first normal-stress-difference arises in the base state (even under creeping-flow conditions) leading to a shortwave instability. In a more recent work, Pourjafar and Sadeghy [20] resorted to the Mooney-Rivlin model and reached to the conclusion that a negative second normal-stress-difference has a stabilizing effect on the flow. They also showed that, in order to avoid discontinuity in the neutral stability curve, inertial terms should always be included in the analysis no matter how small the Reynolds number might be.…”
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.
“…It is assumed that the pressure difference causes the fluid to flow with no gravity influence and both the fluid and solid are of the same density and are incompressible. 51,52 Figure 1.Schematic of laminar flow in a two-dimensional channel with a compliant soft coating.…”
Section: Geometry Description and Governing Equationsmentioning
confidence: 99%
“…[38][39][40][41][42][43][44][45][46][47][48][49][50] A variety of solid and fluid models have been used in previous studies when tackling this formidable fluid-solid interaction (FSI) problem. In a recent paper by Pourjafar et al, 51 the effect of inertia terms on the linear stability of shear-thinning fluids was investigated.…”
In this paper, the effect of inertial terms on hydroelastic stability of a pressure-driven flow of a viscoplastic fluid flowing through a channel lined with a highly compliant polymeric gel is investigated. It is assumed that the fluid obeys the Bingham constuitive equation and the polymeric gel follows a two-constant Mooney–Rivlin material, which is used for modeling a nonviscous hyperelastic polymeric coating. A base-state solution is obtained for the fluid motion and solid deformation, simultaneously. Next, some infinitesimally small two-dimensional disturbances are imposed on the base-state solution. Dropping out all nonlinear perturbation terms, the modal linear stability analysis of the channel flow is conducted. The effects of the Bingham number and material constants are then examined on the critical Reynolds number. It is found that the yield stress has a stabilizing effect while the Mooney–Rivlin parameters have destabilizing effects on the pressure-driven flow of Bingham fluids.
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