Capillary forces quadrupole

The possible relevance of this quadrupole-quadrupole force at colloidal length scales was advanced in references [9,46,47]. As emphasized in reference [9], the natural surface roughness in the nanometer scale of a micrometer-sized spherical particle could conceivably cause a force of this kind. It was also proposed as an explanation of the structures observed experimentally [47] in 2D colloids of nonspherical micrometer particles at a fluid interface. This motivated the theoretical investigation of the anisotropic capillary forces The main difficulty lies in the determination of the capillary charges in terms of given properties of the particles (e.g., wettability and shape). Different simplifications were applied the contact line is approximated by a circle [48-50] or by an expansion in small eccentricity [45] highly elongated shapes are dealt with numerically [51]. 

An original method involves quadrupole oscillations of drops K The drop (a) in a host liquid (P) is acoustically levitated. This can be achieved by creating a standing acoustic wave the time-averaged second order effect of this wave gives rise to an acoustic radiation force. This drives the drop up or down in p, depending on the compressibilities of the two fluids, till gravity and acoustic forces balance. From then onwards the free droplet is, also acoustically, driven into quadrupole shape oscillations that are opposed by the capillary pressure. From the resonance frequency the interfacial tension can be computed. The authors describe the instrumentation and present some results for a number of oil-water interfaces. 

The forces and torques we have just discussed are additional to and compete with the quadru-pole-quadrupole capillary interaction in the presence of more than one particle. This could conceivably lead to an interesting phenomenology and also help control the assembling of structures in 2D colloids at curved interfaces, as exemplified experimentally in reference [72]. 

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