A handbook of mathematical discourse

Attraction and Repulsion between Liquid Droplets over a Liquid-Impregnated Surface

“…By equating the capillary pressure change due to the change in curvature with hydrostatic pressure for ridge height, we can obtain the expression for the variation of interface height h ( r ) around the droplets (Supporting Information). From the surface tension force at the deformed interface and the variation in the interface height caused by the individual droplets, we can calculate the energy of interaction between two droplets from which the force of interaction is determined as follows (detailed derivation in the Supporting Information)­ where R is the contact radius, γ l and ρ l are, respectively, the surface tension and density of the impregnating liquid, B = ( R 2 / L cl 2 ) is the Bond number, , , ρ = (ρ d /ρ l ), ρ d is the density of the droplet, K 1 is modified Bessel’s function of the first kind, and δ is the interdistance between the droplets.…”