Capillary-lubrication force exerted on a 2D particle moving towards a fluid interface

TL;DR

This paper investigates the capillary-lubrication force on a 2D particle moving towards a fluid interface, revealing velocity and acceleration-dependent forces with implications for colloid mobility and microbiological motility.

Contribution

It introduces a combined analytical and numerical analysis of capillary-lubrication forces, highlighting two main force contributions in a novel fluid interface context.

Findings

Identified a velocity-dependent adhesion-like force.

Discovered an acceleration-dependent inertial-like force.

Characterized force dependencies on interfacial tension and viscosities.

Abstract

A rigid object moving in a viscous fluid and in close proximity with an elastic wall experiences self-generated elastohydrodynamic interactions. This has been the subject of an intense research activity, with a recent and growing attention given to the particular case of elastomeric and gel-like substrates. Here, we address the situation where the elastic wall is replaced by a capillary surface. Specifically, we analyze the lubrication flow generated by the prescribed normal motion of a rigid infinite cylinder near the deformable interface separating two immiscible and incompressible viscous fluids. Using a combination of analytical and numerical treatments, we compute the emergent capillary-lubrication force at leading order in compliance, and characterize its dependencies with the interfacial tension, viscosities of the fluids, and length scales of the problem. Interestingly, we identify two main contributions: i) a velocity-dependent adhesion-like force ; ii) an acceleration-dependant inertial-like force. Our results may have implications for the mobility of colloids near complex interfaces and for the motility of confined microbiological entities.