Diffusion-driven transition between two regimes of viscous fingering

Abstract

Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable. For miscible fluids the situation is more complicated due to the formation of interfacial structure in the thin dimension spanning the gap. Here we study the effect of the inherent diffusion between the two miscible fluids on this structure and on the viscous fingering patterns that emerge. We discover an unexpected transition separating two distinct regimes where the pattern morphologies and mode of onset are different. This transition is marked by a regime of transient stability as the structure of the fingers evolves from having three-dimensional structure to being quasi-two dimensional. The presence of diffusion allows an instability to form where it was otherwise forbidden.

17 pages, 10 figures; have added additional experimental data with a new setup and conducted additional analysis, this has resulted in added figures and additional description in the text; have merged the supplemental section into appendices

References in corpus (2)

• Fingering versus stability in the limit of zero interfacial tension
• Singular limit of Hele-Shaw flow and dispersive regularization of shock waves

Cited by in corpus (8)

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• Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments
• Determining the refractive index, absolute thickness and local slope of a thin transparent film using multi-wavelength and multi-incident-angle interference
• Measurement of Pressure Gradients near the Interface in the Viscous Fingering Instability
• Fingering instability of self-similar radial flow of miscible fluids in a Hele-Shaw cell
• Flow birefringence measurement in a radial Hele-Shaw cell considering three-dimensional effects