The Model Coupling Liquid Bridge Between Ellipsoidal Grains

Abstract

Granular materials are the subject of scientific studies due to their unusual physical properties which differ significantly from solid and liquid states of matter. In this paper we are interested in the role played by humidity on static and dynamic properties of systems consisting of non-spherical grains. The addition of a liquid to the material adds an attractive force to the system and then, increased its stability. Quantitative description of wetting thermodynamics is sensitive not only to the contact angle between solid and the liquid but also to the to the shape of grains and thus we analyze ellipsoidal grains and we assume that liquid spreads uniformly over the whole grain’s surface. We consider a model grain’s surface consisting of asperities of equal size uniformly distributed over the grain’s surface. We also suppose that each asperity may be either totally filled with liquid or stay empty. Thus, in our approach we consider two regimes of the inter-grain adhesive force versus volume of the wetting layer. For very small amount of liquid, the capillary force comes from the fluid accumulated around a small number of asperities at which two neighbouring grains are in contact. If the fluid wets the surface of the grains then all asperities are filled and inter-grain adhesive energy is determined mainly by the macroscopic curvature of the grain, and the surface roughness does not play a crucial role. In this case, the distribution of values of inter-grain energies is determined only by macroscopic quantities, i.e. the geometry of grains and material characteristics. Using toroidal approximation for the shape of liquid bridges and some simple probabilistic arguments we analyze the influence of amount of liquid on mutual grain - grain orientation. We found two energetically favorable orientations: one with mutually parallel and second with perpendicular axes of contacted grains.