Wavelength selection in Hele-Shaw flows: a maximum-amplitude criterion

Area of Science:

• Fluid Dynamics
• Interfacial Phenomena
• Nonlinear Dynamics

Background:

• Viscous fingering instability is a common phenomenon in interfacial flows, particularly in Hele-Shaw cells.
• Standard theoretical models often rely on maximizing the linear growth rate for wavelength selection.
• Existing experimental data show discrepancies with predictions based on the standard growth rate maximization criterion.

Purpose of the Study:

• To investigate the viscous fingering instability in radial Hele-Shaw flow.
• To account for the combined effects of viscous normal stresses and wetting phenomena.
• To introduce and validate an alternative wavelength selection criterion.

Main Methods:

• Linear stability analysis of the radial Hele-Shaw flow system.
• Inclusion of viscous normal stresses and wetting effects in the theoretical model.
• Development and application of a new selection criterion based on maximum interfacial perturbation amplitude.

Main Results:

• The standard criterion of maximizing linear growth rate leads to discrepancies with experimental results.
• The proposed alternative criterion, maximizing interfacial perturbation amplitude, resolves these discrepancies.
• Significantly improved agreement between theoretical predictions and experimental data is achieved.

Conclusions:

• The maximum interfacial perturbation amplitude criterion offers a more accurate prediction for wavelength selection in viscous fingering.
• Considering viscous normal stresses and wetting effects is crucial for accurate modeling of Hele-Shaw flows.
• This work reconciles theoretical predictions with experimental observations in viscous fingering instabilities.