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A diffuse-interface Marangoni instability
Published online by Cambridge University Press: 04 December 2025
Abstract
We investigate a novel Marangoni-induced instability that arises exclusively in diffuse fluid interfaces, that is absent in classical sharp-interface models. Using a validated phase-field Navier–Stokes–Allen–Cahn framework, we linearise the governing equations to analyse the onset and development of interfacial instability driven by solute-induced surface tension gradients. A critical interfacial thickness scaling inversely with the Marangoni number, 
$\delta _{\textit{cr}} \sim \textit{Ma}^{-1}$, emerges from the balance between advective and diffusive transport. Unlike sharp-interface scenarios where matched viscosity and diffusivity stabilise the interface, finite thickness induces asymmetric solute distributions and tangential velocity shifts that destabilise the system. We identify universal power-law scalings of velocity and concentration offsets with a modified Marangoni number 
$\textit{Ma}_\delta$, independent of capillary number and interfacial mobility. A critical crossover at 
$ \textit{Ma}_\delta \approx 590$ distinguishes diffusion-dominated stabilisation from advection-driven destabilisation. 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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Li et al. supplementary movie 1
Direct numerical simulations of system dynamics with parameters Sc = 103, Ca = 0.01, α = 1.5 (Pe φ ∼ δ −α ), Ma = 104, and δ = 0.05, corresponding to Fig. 3c in the main text. Panels show: (a) temporal evolution of kinetic energy ( $${E_k} = \sqrt {\boldsymbol{u \cdot u}} $$ ); (b) kinetic energy contours; (c) solute concentration field c; (d) phase-field distribution φ s; (e) velocity profile u along y at the x-location of |u|max; (f) solute perturbation profile c ′ = c − C b along y at the x-location of |u|min.
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Li et al. supplementary movie 2
Same setup as Movie 1, but with δ = 0.8, corresponding to Fig. 3d in the main text. Panel descriptions are identical to those in Movie S1.
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Li et al. supplementary material 3
Li et al. supplementary material
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