A Diffuse-Interface Marangoni Instability

TL;DR

This paper reveals a new Marangoni instability unique to diffuse fluid interfaces, showing how finite interfacial thickness influences flow stability through solute transport and surface tension effects.

Contribution

It introduces a phase-field model to analyze diffuse-interface Marangoni instability and identifies universal scaling laws and critical parameters for stability.

Findings

Critical interfacial thickness scales inversely with Marangoni number.

Finite interface thickness causes asymmetric solute distribution and flow destabilization.

A universal power-law scaling with a modified Marangoni number determines stability.

Abstract

We investigate a novel Marangoni-induced instability that arises exclusively in diffuse fluid interfaces, absent in classical sharp-interface models. Using a validated phase-field Navier-Stokes-Allen-Cahn framework, we linearize the governing equations to analyze the onset and development of interfacial instability driven by solute-induced surface tension gradients. A critical interfacial thickness scaling inversely with the Marangoni number, $\delta_\mathrm{cr} \sim Ma^{-1}$, emerges from the balance between advective and diffusive transport. Unlike sharp-interface scenarios where matched viscosity and diffusivity stabilize the interface, finite thickness induces asymmetric solute distributions and tangential velocity shifts that destabilize the system. We identify universal power-law scalings of velocity and concentration offsets with a modified Marangoni number $Ma^\delta$, independent of capillary number and interfacial mobility. A critical crossover at $Ma^\delta \approx 590$ distinguishes diffusion-dominated stabilization from advection-driven destabilization. These findings highlight the importance of diffuse-interface effects in multiphase flows, with implications for miscible fluids, soft matter, and microfluidics where interfacial thickness and coupled transport phenomena are non-negligible.