Marangoni Interfacial Instability Induced by Solute Transfer Across Liquid-Liquid Interfaces

TL;DR

This paper investigates how solute transfer influences Marangoni interfacial instability in two-liquid systems, revealing distinct behaviors driven by diffusivity and viscosity ratios through analytical and numerical methods.

Contribution

It develops a validated phase-field numerical model to analyze nonlinear dynamics and interfacial deformation effects in Marangoni instability with solute transfer.

Findings

Short-wave instability triggered by solute transfer from less diffusive layer.

Long-wave instability induced by solute transfer into less viscous layer.

Distinct nonlinear flow behaviors depending on diffusivity and viscosity ratios.

Abstract

This study presents analytical and numerical investigations of Marangoni interfacial instability in a two-liquid-layer system with constant solute transfer across the interface. While previous research has established that both diffusivity and viscosity ratios affect hydrodynamic stability via the Marangoni effect, the specific nonlinear dynamics and the role of interfacial deformation remain fully unclear. To address this, we developed a phase-field-based numerical model, validated against linear stability analysis and existing theories. The validated parameter space includes Schmidt number, Marangoni number, Capillary number, and the diffusivity and viscosity ratio between the two layers. Our finding shows that solute transfer from a less diffusive layer triggers short-wave instability, governed by the critical Marangoni number, while solute transfer into a less viscous layer induces long-wave instability, controlled by the critical Capillary number. Nonlinear simulations reveal distinct field coupling behaviors: in the diffusivity-ratio-driven instability, the spatially averaged flow intensity remains symmetric about a flat interface, while solute gradient is uneven. In contrast, in viscosity-ratio-driven instability, a deforming interface separates the two layers, with a uniform solute gradient but asymmetric spatially averaged flow intensity. These results highlight the crucial role of diffusivity and viscosity in shaping Marangoni flows and enhance our understanding of interfacial instability dynamics.