Eur. Phys. J. Plus (2011) 126: 94
https://doi.org/10.1140/epjp/i2011-11094-8

Regular Article

Exploring topological singularities with phase-field methods

Centrifugal viscous fingering as a case study

Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona, Spain

^* e-mail: jaume.casademunt@ub.edu

Received: 20 April 2011
Revised: 9 May 2011
Published online: 18 October 2011

Abstract

We discuss the use of phase-field methods in problems of interface dynamics where topological singularities are relevant. We illustrate our discussion on the case study of centrifugally driven Hele-Shaw flows, where the proposed analysis has been recently tested. We argue that the phase-field formulation of a given sharp-interface model is not only suitable in order to regularize topological singularities, but it may be instrumental to explore to what extent the occurrence of finite-time singularities is inherent to the sharp-interface model at hand, or from external origin. The question is relevant to assess whether singularities are potentially controllable or avoidable in experiments by modifying the conditions governing the pinch-off. In the case of centrifugal viscous fingering, from the study of the dependence of the pinch-off time on the phase-field interface thickness, we show that for low viscosity contrast, finite-time pinch-off is intrinsic within the two-dimensional Hele-Shaw dynamics. On the contrary, in the high viscosity contrast limit, the dependence of pinch-off time on the interface thickness shows that the singularities are typically spurious.