https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03859808Lanza, FedericoFedericoLanzaLPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueRosso, AlbertoAlbertoRossoLPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueTalon, LaurentLaurentTalonFAST - Fluides, automatique, systèmes thermiques - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueHansen, AlexAlexHansenPhysics NTNU - Department of Physics [Trondheim] - NTNU - Norwegian University of Science and Technology [Trondheim] - NTNU - Norwegian University of Science and TechnologyNon-Newtonian rheology in a capillary tube with varying radiusHAL CCSD2022Non-Newtonian fluidsImmiscible two-phase flowCapillary tubeCapillary fiber bundle model[PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]Talon, Laurent2022-11-18 13:24:062023-02-08 17:11:262022-11-25 10:24:46enJournal articleshttps://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03859808/document10.1007/s11242-022-01848-7application/pdf1Fluid blobs in an immiscible Newtonian fluid flowing in a capillary tube with varying radius show highly non-linear behaviour. 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 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.