Scaling Relations of Viscous Fingers in Anisotropic Hele-Shaw Cells

TL;DR

This paper investigates the scaling relations of viscous fingers in anisotropic Hele-Shaw cells through numerical simulations, comparing them with dendritic growth and providing theoretical evaluations of power-law exponents.

Contribution

It introduces numerical analysis of viscous finger scaling relations in anisotropic Hele-Shaw cells and compares them with dendritic growth, including theoretical evaluation of power-law exponents.

Findings

Identified power-law relations between finger velocity, radius, and pressure gradient.

Compared viscous finger scaling with dendritic growth patterns.

Provided theoretical estimates for the exponents of these relations.

Abstract

Viscous fingers in a channel with surface tension anisotropy are numerically studied. Scaling relations between the tip velocity v, the tip radius and the pressure gradient are investigated for two kinds of boundary conditions of pressure, when v is sufficiently large. The power-law relations for the anisotropic viscous fingers are compared with two-dimensional dendritic growth. The exponents of the power-law relations are theoretically evaluated.