title: Interfacial pattern formation in confined power-law fluids.
abstract: The interfacial pattern formation problem in an injection-driven radial Hele-Shaw flow is studied for the situation in which a Newtonian fluid of negligible viscosity displaces a viscous non-Newtonian power-law fluid. By utilizing a Darcy-law-like formulation, we tackle the fluid-fluid interface evolution problem perturbatively, and we derive second-order mode-coupling equations that describe the time evolution of the perturbation amplitudes. This allows us to investigate analytically how the non-Newtonian nature of the dislocated fluid determines the morphology of the emerging interfacial patterns. If the pushed fluid is shear-thinning, our results indicate the development of side-branching structures. On the other hand, if the displaced fluid is shear-thickening, one detects the formation of petal-like shapes, markedly characterized by strong tip-splitting events. Finally, a time-dependent injection protocol is presented that is able to restrain finger proliferation via side-branching and tip-splitting. This permits the emergence of symmetric n-fold interfacial shapes for which the number of fingers remains fixed as time progresses. This procedure generalizes existing controlling strategies for purely Newtonian flow circumstances to the case of a non-Newtonian, displaced power-law fluid.
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
authors.forename: Rodolfo
authors.initials: R
authors.lastname: Brandão
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
authors.forename: João V
authors.initials: JV
authors.lastname: Fontana
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: D057446:Hydrodynamics; D017711:Nonlinear Dynamics; D012212:Rheology; D014783:Viscosity