Fluid blobs in an immiscible Newtonian fluid flowing in a capillary tube with varying radius show highly nonlinear behavior. We consider here a generalization of previously obtained results to blobs of non-Newtonian fluids. We compute here the yield pressure drop and the mean flow rate in two cases: (i) When a single blob is injected, (ii) When many blobs are randomly injected into the tube. We find that the capillary effects emerge from the non-uniformity of the tube radius and contribute to the threshold pressure for flow to occur. Furthermore, in the presence of many blobs the threshold value depends on the number of blobs and their relative distances which are randomly distributed. For a capillary fiber bundle of identical parallel tubes, we calculate the probability distribution of the threshold pressure and the mean flow rate. We consider two geometries: tubes of sinusoidal shape, for which we derive explicit expressions, and triangular-shaped tubes, for which we find that essential singularities are developed. We perform numerical simulations confirming our analytical results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.