Drag on a spheroidal particle at clean and surfactant-laden interfaces: effects of particle aspect ratio, contact angle and surface viscosities

Abstract

Translation of a non-spherical particle trapped at a membrane or at a complex interface between fluids is a relevant situation occurring in biological, technological and everyday life systems. Here, we consider prolate spheroidal particles, translating at a clean or (insoluble) surfactant-laden planar interface located between a viscous fluid and air, protruding into the surrounding subphase. Both the subphase and monolayer contribute to the total resistance experienced by the particle, which in turn is a function of interface and bulk viscosities, particle size and aspect ratio as well as the immersion depth of the particle. We explore how the drag on a spheroidal particle at a viscous interface can both rise or decrease with particle size depending on the dimensionless Boussinesq and Marangoni numbers. For a surfactant-laden interface, the surfactant distribution in the vicinity of the moving spheroid is significantly affected by the particle's immersion depth. When a particle sinks more in the viscous fluid, as determined by the involved surface tensions, the difference in surfactant concentration between front and rear of the particle decreases. For the drag coefficient of a spherical particle at an incompressible interface at low shear Boussinesq numbers, we propose a correction to previously reported analytic expressions. We probe both parallel and perpendicular friction coefficients as they are significantly different depending on particle shape, qualitatively different depending on surface shear viscosity, and we resolve the full three-dimensional distortion of the flow field around the moving particle.