Computations of viscous fingering in a wedge: selection mechanisms and capillarity-driven ripples in the small surface tension limit
Year: 2025
Type: article
Abstract: We present a numerical scheme that solves for the self-similar viscous fingers that emerge from the Saffman–Taylor instability in a divergent wedge. This is based on the formulation by Ben Amar (1991, Phys. Rev. A, vol. 44, pp. 3673–3685). It is demonstrated that there exists a countably infinite set of selected solutions, each with an associated relative finger angle, and furthermore, solutions can be characterised by the number of ripples located at the tip of their finger profiles. Our numerical scheme allows us to observe these ripples and measure them, demonstrating that the amplitudes are exponentially small in terms of the surface tension; the selection mechanism is driven by these exponentially small contributions. A recently published paper derived the selection mechanism for this problem using exponential asymptotic analytical techniques, and obtained bifurcation diagrams that we compare with our numerical results.
Source: Journal of Fluid Mechanics
Authors: Cecilie Andersen, Philippe H. Trinh, Jean-Marc Vanden-Broeck
Institutions: University of Bath, University College London
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4411328300