Creeping flow of Herschel-Bulkley fluids in collapsible channels: A numerical study

In this paper, the steady flow of a viscoplastic fluid is modeled in a planar channel equipped with a deformable segment in the middle of an otherwise rigid plate. The fluid is assumed to obey the Herschel-Bulkley model which accounts for both the yield stress and the shear-thinning behavior of physiological fluids such as blood. To accommodate the large deformations of the flexible segment, it is assumed to obey the twoparameter Mooney-Rivlin hyperelastic model. The so-called fluid-structure interaction problem is then solved numerically, under creeping-flow conditions, using the finite element package, COMSOL. It is found that the yield stress leads to a larger wall deformation and a higher pressure drop as compared with Newtonian fluids. This behavior is predicted to intensify if the fluid is shear-thinning. That is, for a given yield stress, the pressure drop and the wall deformation both increase with an increase in the degree of the fluid's shear-thinning behavior.