A Diffuse-Interface Marangoni Instability
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917200736026624 |
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| author | Li, Xiangwei Wan, Dongdong Hao, Haohao Diddens, Christian Zhang, Mengqi Tan, Huanshu |
| author_facet | Li, Xiangwei Wan, Dongdong Hao, Haohao Diddens, Christian Zhang, Mengqi Tan, Huanshu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_09945 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Diffuse-Interface Marangoni Instability Li, Xiangwei Wan, Dongdong Hao, Haohao Diddens, Christian Zhang, Mengqi Tan, Huanshu Fluid Dynamics Mesoscale and Nanoscale Physics Soft Condensed Matter 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. |
| title | A Diffuse-Interface Marangoni Instability |
| topic | Fluid Dynamics Mesoscale and Nanoscale Physics Soft Condensed Matter |
| url | https://arxiv.org/abs/2506.09945 |