title: Mode-coupling approach to non-Newtonian Hele-Shaw flow.
abstract: The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. Owing to vorticity arising from our modified Darcy's law, we introduce a vector potential for the velocity in contrast to the conventional scalar potential. Our analytical results address how mode-coupling dynamics relates to tip splitting and sidebranching in both shear-thinning and shear-thickening cases. The development of non-Newtonian interfacial patterns in rectangular Hele-Shaw cells is also analyzed.
authors.affiliation: Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
authors.forename: Magdalena
authors.initials: M
authors.lastname: Constantin
authors.forename: Michael
authors.initials: M
authors.lastname: Widom
authors.forename: José A
authors.initials: JA
authors.lastname: Miranda