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<p>This study presents a numerical investigation of the dynamic response of a Newtonian fluid interface subjected to mixed oscillatory deformations. A slender cylindrical probe, floating horizontally at a water–air interface and partially submerged by capillary forces, is driven sinusoidally in the direction perpendicular to its axis. The interface exhibits shear, dilatational, and extensional viscosities, and the system is modeled using the finite volume method within the OpenFOAM framework. The governing equations are nondimensionalized and solved for a wide range of Marangoni numbers (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Ma \in [1, 10^5]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>a</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <msup> <mn>10</mn> <mn>5</mn> </msup> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>) and dilatational-to-shear viscosity ratios (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Theta \in [1, 10^5]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Θ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <msup> <mn>10</mn> <mn>5</mn> </msup> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>). The simulations enable the decomposition of the total interfacial force into its constituent components, revealing distinct regimes dominated by Marangoni, dilatational, or extensional stresses. The results demonstrate the feasibility of isolating these contributions under specific conditions, offering insights into the design and interpretation of interfacial rheometry experiments. The influence of geometric parameters and oscillation characteristics is also explored, confirming the robustness of the observed force dynamics.</p>

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Dynamical response of a Newtonian fluid interface to mixed oscillatory deformations

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  • 发表日期：

    2025年10月21日

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  • Adrián García-Gutiérrez,
  • Fernando Parra,
  • José Antonio Mayo,
  • Carlos Rubio

摘要

This study presents a numerical investigation of the dynamic response of a Newtonian fluid interface subjected to mixed oscillatory deformations. A slender cylindrical probe, floating horizontally at a water–air interface and partially submerged by capillary forces, is driven sinusoidally in the direction perpendicular to its axis. The interface exhibits shear, dilatational, and extensional viscosities, and the system is modeled using the finite volume method within the OpenFOAM framework. The governing equations are nondimensionalized and solved for a wide range of Marangoni numbers ( \(Ma \in [1, 10^5]\) M a ∈ [ 1 , 10 5 ] ) and dilatational-to-shear viscosity ratios ( \(\Theta \in [1, 10^5]\) Θ ∈ [ 1 , 10 5 ] ). The simulations enable the decomposition of the total interfacial force into its constituent components, revealing distinct regimes dominated by Marangoni, dilatational, or extensional stresses. The results demonstrate the feasibility of isolating these contributions under specific conditions, offering insights into the design and interpretation of interfacial rheometry experiments. The influence of geometric parameters and oscillation characteristics is also explored, confirming the robustness of the observed force dynamics.