A Diffuse-Interface Marangoni Instability

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, $δ_\mathrm{cr} \sim Ma^{-1}$, 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 $Ma^δ$, independent of capillary number and interfacial mobility. A critical crossover at $Ma^δ\approx 590$ 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.

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