Particles with an Undulated Contact Line at a Fluid Interface: Interaction between Capillary Quadrupoles and Rheology of Particulate Monolayers

Abstract

We consider solid particles attached to a liquid−fluid interface. If the solid−liquid−fluid contact line (at the particle surface) is undulated, the convex and concave local deviations of the meniscus shape from planarity can be treated as positive and negative capillary charges, which form capillary multipoles. Correspondingly, the meniscus shape can be expressed as a multipole expansion. The leading terms of the capillary multipole expansion turn out to be the charges and quadrupoles. In the present article, we derive theoretical expressions, which enable one to calculate the energy and force of interaction between two capillary quadrupoles for arbitrary interparticle distance. Depending on the amplitudes of the contact-line undulations, and on the particle mutual orientations, the interaction is either monotonic attraction or attraction at long distances but repulsion at short distances. As a rule, the interaction energy is much larger than the thermal energy kT, even for undulations of nanometer ampli...