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A rigid object moving in a viscous fluid and in close proximity with anelastic wall experiences self-generated elastohydrodynamic interactions. Thishas been the subject of an intense research activity, with a recent and growingattention given to the particular case of elastomeric and gel-like substrates.Here, we address the situation where the elastic wall is replaced by acapillary surface. Specifically, we analyze the lubrication flow generated bythe prescribed normal motion of a rigid infinite cylinder near the deformableinterface separating two immiscible and incompressible viscous fluids. Using acombination of analytical and numerical treatments, we compute the emergentcapillary-lubrication force at leading order in compliance, and characterizeits dependencies with the interfacial tension, viscosities of the fluids, andlength scales of the problem. Interestingly, we identify two maincontributions: i) a velocity-dependent adhesion-like force ; ii) anacceleration-dependant inertial-like force. Our results may have implicationsfor the mobility of colloids near complex interfaces and for the motility ofconfined microbiological entities.

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