dorsal/arxiv
View SchemaInterfacial standing wave-patterns disentangle dilatational and shear surface viscous effects
| Authors | Debashis Panda, Abdullah M. Abdal, Mosayeb Shams, Lyes Kahouadji, Jalel Chergui, Seungwon Shin, Damir Juric, Omar K. Matar |
|---|---|
| Categories | |
| ArXiv ID | 2601.06881vv1 |
| URL | https://arxiv.org/abs/2601.06881 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Dilatational and shear surface viscosities are highly correlated parameters, making their individual contributions difficult to disentangle in Stokes flow, linearised flow models, or two-dimensional flows. We therefore investigate the three-dimensional interfacial standing waves as a means to decouple the influence of dilatational and shear surface viscosities. Two dimensionless controlling parameters are introduced: $Bq$, the total Boussinesq number, which quantifies the the relative importance of surface viscous stresses compared with bulk viscous stresses, and $\tan \chi$, which quantifies the ratio of surface dilatational viscosity to surface shear viscosity. The growth rates and threshold accelerations are independent of $\chi$, consistent with previous theoretical predictions. Nonlinear analyses of square and hexagonal patterns reveal that Fourier decomposition of wave-patterns can effectively decouple the intricate dynamics into axial modes, where the waves are weakly dependent on $\chi$, and oblique modes, where additional damping occurs in the shear surface viscous dominant interface. These results demonstrate that Faraday wave-patterns provide a route for identifying and quantifying the distinct roles of dilatational and shear surface viscosities.
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"abstract": "Dilatational and shear surface viscosities are highly correlated parameters, making their individual contributions difficult to disentangle in Stokes flow, linearised flow models, or two-dimensional flows. We therefore investigate the three-dimensional interfacial standing waves as a means to decouple the influence of dilatational and shear surface viscosities. Two dimensionless controlling parameters are introduced: $Bq$, the total Boussinesq number, which quantifies the the relative importance of surface viscous stresses compared with bulk viscous stresses, and $\\tan \\chi$, which quantifies the ratio of surface dilatational viscosity to surface shear viscosity. The growth rates and threshold accelerations are independent of $\\chi$, consistent with previous theoretical predictions. Nonlinear analyses of square and hexagonal patterns reveal that Fourier decomposition of wave-patterns can effectively decouple the intricate dynamics into axial modes, where the waves are weakly dependent on $\\chi$, and oblique modes, where additional damping occurs in the shear surface viscous dominant interface. These results demonstrate that Faraday wave-patterns provide a route for identifying and quantifying the distinct roles of dilatational and shear surface viscosities.",
"arxiv_id": "2601.06881",
"authors": [
"Debashis Panda",
"Abdullah M. Abdal",
"Mosayeb Shams",
"Lyes Kahouadji",
"Jalel Chergui",
"Seungwon Shin",
"Damir Juric",
"Omar K. Matar"
],
"categories": [
"physics.flu-dyn"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Interfacial standing wave-patterns disentangle dilatational and shear surface viscous effects",
"url": "https://arxiv.org/abs/2601.06881",
"version": "v1"
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