Spontaneous Formation of Stable Capillary Bridges for Firming Compact Colloidal Microstructures in Phase Separating Liquids: A Computational Study

Computer modeling and simulations are performed to investigate capillary bridges spontaneously formed between closely packed colloidal particles in phase separating liquids. The simulations reveal a self-stabilization mechanism that operates through diffusive equilibrium of two-phase liquid morphologies. Such mechanism renders desired microstructural stability and uniformity to the capillary bridges that are spontaneously formed during liquid solution phase separation. This self-stabilization behavior is in contrast to conventional coarsening processes during phase separation. The volume fraction limit of the separated liquid phases as well as the adhesion strength and thermodynamic stability of the capillary bridges are discussed. Capillary bridge formations in various compact colloid assemblies are considered. The study sheds light on a promising route to in-situ (in-liquid) firming of fragile colloidal crystals and other compact colloidal microstructures via capillary bridges

Derivative Formula and Applications for Degenerate Diffusion Semigroups

By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.Comment: 18 page