Dynamical response of a Newtonian fluid interface to mixed oscillatory deformations

Abstract 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 ( $$Ma \in [1, 10^5]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mi>a</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> ) and dilatational-to-shear viscosity ratios ( $$\Theta \in [1, 10^5]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Θ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> ). 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.