Non-Newtonian Rheology in a Capillary Tube with Varying Radius

Abstract Fluid blobs in an immiscible Newtonian fluid flowing a capillary tube with varying radius show highly nonlinear behavior. We consider here generalization of previously obtained results to non-Newtonian fluids. compute the yield pressure drop and mean flow rate two cases: (i) When single blob is injected, (ii) many are randomly injected into tube. find that effects emerge from non-uniformity contribute threshold for occur. Furthermore, presence value depends on number their relative distances which distributed. For fiber bundle identical parallel tubes, we calculate probability distribution rate. geometries: tubes sinusoidal shape, derive explicit expressions, triangular-shaped essential singularities developed. perform numerical simulations confirming our analytical results.