title: Elastic fingering in rotating Hele-Shaw flows.
abstract: The centrifugally driven viscous fingering problem arises when two immiscible fluids of different densities flow in a rotating Hele-Shaw cell. In this conventional setting an interplay between capillary and centrifugal forces makes the fluid-fluid interface unstable, leading to the formation of fingered structures that compete dynamically and reach different lengths. In this context, it is known that finger competition is very sensitive to changes in the viscosity contrast between the fluids. We study a variant of such a rotating flow problem where the fluids react and produce a gellike phase at their separating boundary. This interface is assumed to be elastic, presenting a curvature-dependent bending rigidity. A perturbative weakly nonlinear approach is used to investigate how the elastic nature of the interface affects finger competition events. Our results unveil a very different dynamic scenario, in which finger length variability is not regulated by the viscosity contrast, but rather determined by two controlling quantities: a characteristic radius and a rigidity fraction parameter. By properly tuning these quantities one can describe a whole range of finger competition behaviors even if the viscosity contrast is kept unchanged.
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
authors.forename: Gabriel D
authors.initials: GD
authors.lastname: Carvalho
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
authors.forename: Hermes
authors.initials: H
authors.lastname: Gadêlha
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
authors.forename: José A
authors.initials: JA
authors.lastname: Miranda
mesh_terms: D002498:Centrifugation; D003198:Computer Simulation; D055119:Elastic Modulus; D008956:Models, Chemical; D044367:Phase Transition; D012212:Rheology / Q000379:methods*; D012996:Solutions / Q000737:chemistry*; D014783:Viscosity
chemical_list: D012996:Solutions