The motion of solid objects at complex planar Newtonian gas-liquid interfaces: Influence of gas phase drag

Micro- and macro-interfacial rheology techniques involve the motion of solid probes at complex gas-liquid interfaces. Understanding the flow dynamics in such situations requires the separation of dilatation, shear, Marangoni, and bulk phase effects on probe motion. The effect of air phase drag is usually neglected, although it is relevant for low-viscosity interfaces. We present a numerical study using a three-dimensional model that assumes the interface is planar and Newtonian, the surfactant is insoluble, the bulk fluid phases are incompressible, and the problem is isothermal. The model includes the Navier-Stokes equations for the flow in the liquid and gas phases, the transport equation for the interfacial surfactant concentration, and the interfacial stress balance equation. Our package iRheoFoam uses finite volume and finite area discretization methods for the bulk fluid phases and the interface, respectively, and a one-fluid formulation with jump conditions at the interface. We show a detailed study of all the components of the drag on the probes, including the gas phase drag, as a function of the Marangoni number and the dilatational and shear Boussinesq numbers.