title: Selection of the Taylor-Saffman bubble does not require surface tension.
abstract: A new general class of exact solutions is presented for the time evolution of a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension effects are neglected. These solutions are obtained by conformal mapping the viscous flow domain to an annulus in an auxiliary complex plane. It is then demonstrated that the only stable fixed point (attractor) of the nonsingular bubble dynamics corresponds precisely to the selected pattern. This thus shows that, contrary to the established theory, bubble selection in a Hele-Shaw cell does not require surface tension. The solutions reported here significantly extend previous results for a simply connected geometry (finger) to a doubly connected one (bubble). We conjecture that the same selection rule without surface tension holds for Hele-Shaw flows of arbitrary connectivity.
authors.affiliation: Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife, Brazil.
authors.forename: Giovani L
authors.initials: GL
authors.lastname: Vasconcelos
authors.affiliation: New Mexico Consortium, Los Alamos, New Mexico 87544, USA and International Institute of Physics, Federal University of Rio Grande do Norte, 59078-400 Natal, RN, Brazil.
authors.forename: Mark
authors.initials: M
authors.lastname: Mineev-Weinstein
mesh_terms: D057446:Hydrodynamics; D008962:Models, Theoretical; D013500:Surface Tension; D013995:Time; D014783:Viscosity