Implications of inertia for hydroelastic instability of Herschel-Bulkley fluids in plane Poiseuille flow
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Department of Mechanical Engineering, Ardabil Branch, Islamic Azad University, Ardabil, Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran
Publication date: 2018-10-20
Journal of Theoretical and Applied Mechanics 2018;56(4):1205–1216
This study investigates the effects of inertia on the hydroelastic instability of a pressure- -driven Herschel-Bulkley fluid passing through a two-dimensional channel lined with a po- lymeric coating. The no-viscous hyperelastic polymeric coating is assumed to follow the two-constant Mooney-Rivlin model. In this work, analytical basic solutions are determined for both the polymeric gel and the fluid at very low Reynolds numbers. Next, the basic so- lutions are subjected to infinitesimally-small, normal-mode perturbations. After eliminating the nonlinear terms, two 4-th order differential equations are obtained. The equations with appropriate boundary conditions are then numerically solved using the shooting method. The results of the solution show that the inertia terms in the perturbed equations destabili- ze the pressure-driven Herschel-Bulkley fluid flow. The investigation reveals that the elastic parameter has a stabilizing effect on the flow. Also, based on the obtained results, the yield stress, depending on the power-law index, has a stabilizing or destabilizing effect on the flow. Since in this work the inertia terms are included in the pertinent governing equations, therefore, the results of this study are much more realistic and reliable than previous works in which inertia terms were absent. In addition, unlike the previous works, the present study considers both the shear-thinning and shear-thickening types of fluids. Hence, the results of this work embrace all the fluids which obey the Herschel-Bulkley model.