title: Radial viscous fingering in yield stress fluids: onset of pattern formation.
abstract: We report analytical results for the development of interfacial instabilities in a radial Hele-Shaw cell in which a yield stress fluid is pushed by a Newtonian fluid of negligible viscosity. By dealing with a gap averaging of the Navier-Stokes equation, we derive a Darcy-law-like equation for the problem, valid in the regime of high viscosity compared to yield stress effects. A mode-coupling approach is executed to examine the morphological features of the fluid-fluid interface at the onset of nonlinearity. Within this context, mechanisms for explaining the rising of tip-splitting and side-branching events are proposed.
authors: Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil.
authors: João V
authors: JV
authors: Fontana
authors: Sérgio A
authors: SA
authors: Lira
authors: José A
authors: JA
authors: Miranda
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*