抄録
In the present work, the effect of a fluid’s yield stress is investigated on the hydroelastic instability in pressure-driven flow through a two-dimensional channel lined with a highly-compliant polymeric gel. Having assumed that the fluid obeys the Herschel-Bulkley model with the gel obeying the two-parameter Mooney-Rivlin model, analytical basic solutions were obtained for the fluid and solid sides at vanishingly-small Reynolds numbers. The stability of the basic solutions so-obtained was then investigated when subjected to infinitesimally-small, normal-mode perturbations. Having dropped all nonlinear perturbation terms, an eigenvalue problem was obtained which was numerically solved using the shooting method. The effect of the fluid’s yield stress was then examined on the growth rate of the most unstable modes. Based on the numerical results obtained in this work, it is concluded that the yield stress has a destabilizing effect on pressure-driven flows of Bingham fluids in two-dimensional channels lined with compliant gels. For Herschel-Bulkley fluids, the effect of yield stress can be stabilizing or destabilizing depending on the power-law exponent (i.e., the degree of the fluid’s shear-thinning).
