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A diffuse-interface Marangoni instability

Published online by Cambridge University Press:  04 December 2025

Xiangwei Li Open the ORCID record for Xiangwei Li [Opens in a new window] ,
Dongdong Wan ,
Haohao Hao ,
Christian Diddens Open the ORCID record for Christian Diddens [Opens in a new window] ,
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window]  and
Huanshu Tan Open the ORCID record for Huanshu Tan [Opens in a new window]
Xiangwei Li
Affiliation:
Multicomponent Fluids Group, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology , Shenzhen, 518055 Guangdong, PR China
Dongdong Wan
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore, Republic of Singapore
Haohao Hao
Affiliation:
Multicomponent Fluids Group, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology , Shenzhen, 518055 Guangdong, PR China
Christian Diddens
Affiliation:
Physics of Fluids Department, Max-Planck Center Twente for Complex Fluid Dynamics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P. O. Box 217, 7500AE Enschede, The Netherlands
Mengqi Zhang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore, Republic of Singapore
Huanshu Tan*
Affiliation:
Multicomponent Fluids Group, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology , Shenzhen, 518055 Guangdong, PR China
*
Corresponding author: Huanshu Tan, tanhs@sustech.edu.cn
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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.

JFM classification

Convection: Marangoni convection Interfacial Flows (free surface): Interfacial Flows (free surface) Instability: Instability

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1024 , 10 December 2025 , A37
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

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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Supplementary material: File

Li et al. supplementary material 3

Li et al. supplementary material
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