Capillary interactions between dynamically forced particles adsorbed at a planar interface and on a bubble

Abstract

We investigate the dynamic interfacial deformation induced by micrometric particles exerting a periodic force on a planar interface or on a bubble, and the resulting lateral capillary interactions. Assuming that the deformation of the interface is small, neglecting the effect of viscosity and assuming point particles, we derive analytical formulas for the dynamic deformation of the interface. For the case of a planar interface the dynamic point force simply generates capillary waves, while for the case of a bubble it excites shape oscillations, with a dominant deformation mode that depends on the bubble radius for a given forcing frequency. We evaluate the lateral capillary force acting between two particles, by superimposing the deformations induced by two point forces. We find that the lateral capillary forces experienced by dynamically forced particles are non-monotonic and can be repulsive. The results are applicable to micrometric particles driven by different dynamic forcing mechanisms such as magnetic, electric or acoustic fields.

Capillary surfers: wave-driven particles at a vibrating fluid interface

“…We let zj = −g − ζ j ω 2 cos ωt, where ζ j is the oscillation amplitude of particle j. By generalizing the derivation presented by De Corato & Garbin [30] to account for the static (non-oscillatory) deformation of the interface, we find that the solution to Eq. ( 8) is…”

“…The masses are assumed to oscillate vertically at the forcing frequency ω and amplitude γ/ω 2 of the bath, and thus generate capillary waves of wavelength λ = 2π/k given by the dispersion relation in the deep-water limit, ω 2 = σk 3 /ρ. Since the waves are of small amplitude, γ/ω 2 λ, their form may be deduced by solving the linearized hydrodynamic problem of a periodically oscillating point force acting on a fluid interface [30] (see Methods). Each surfer is a pair of capillary wave sources, which mediate the interaction between surfers.…”

“…2b. Both the surfers and capillary waves oscillate at the forcing frequency ω, and the capillary interaction force is nonzero when time-averaged over the forcing period [30] (see Methods).…”

Pairwise hydrodynamic interactions of spherical colloids at a gas-liquid interface

“…For shear flow imposed across the interface, Vidal & Botto (2017) examined theoretically the Stokes drag on a planar array of immobile colloids straddling a gas/liquid interface () by placing the array, fully immersed, at the midplane of a channel with a shear flow and using the symmetry of the configuration to find the drag on the particles at the gas/liquid interface as 1/2 the fully immersed drag. De Corato & Garbin (2018) and Huerre, De Corato & Garbin (2018) examined microstructure development for particles attached to a planar or spherical gas/liquid interface under rapid surface expansion, and the related capillary attraction between these particles under normal rapid periodic forcing in the inviscid rather than the Stokes limit.…”

The effective shear and dilatational viscosities of a particle-laden interface in the dilute limit

“…Interfacial particles mechanically stabilize droplets (e.g. Binks 2002; Aveyard, Binks & Clint 2003; Dickinson 2010; Wu & Ma 2016; De Corato & Garbin 2018). These composite structures are often referred to as liquid marbles (Aussillous & Quéré 2001).…”