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 dominat 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.
Highlights
Micrometric particles can adsorb to fluid–fluid interfaces and impart stability to emulsions and foams (Binks 2002)
We have investigated the dynamic deformation of a gas–liquid interface induced by a micrometric particle adsorbed either on a planar surface or on a bubble, and driven by a periodic force in the direction normal to the surface
A dynamic point force acting on a planar interface generates a capillary wave with the wavenumber set by the dispersion relation for the surface waves of an inviscid fluid
Summary
Micrometric particles can adsorb to fluid–fluid interfaces and impart stability to emulsions and foams (Binks 2002). In the limit of small deformations and in the absence of dynamic effects, lateral capillary interactions between adsorbed particles can be represented in terms of interactions between two-dimensional multipole moments (Danov et al 2005; Danov & Kralchevsky 2010), in analogy with two-dimensional electrostatics (Domínguez, Oettel & Dietrich 2008) In such an analogy, a particle exerting a net force normal to the interface is represented by a capillary ‘monopole’, a particle exerting a torque in the plane of the interface is represented by a capillary ‘dipole’, while higher-order capillary multipoles describe an undulated three-phase contact line. The results have general applicability to different particle forcing mechanisms such as electric, magnetic or acoustic fields
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