Generalization of the Kelvin equation for arbitrarily curved surfaces

Abstract

Capillary condensation, which takes place in confined geometries, is the first-order vapor-toliquid phase transition and is explained by the Kelvin equation, but the equations applicability for arbitrarily curved surface has been long debated and is a sever problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to static shapes and modelling the pressure at the interface nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.

Scalable Solution-Processed Fabrication Approach for High-Performance Silver Nanowire/MXene Hybrid Transparent Conductive Films

“…Additionally, the inset graph showed the welding effect at the junctions, which could be explained by the capillary force effect during solvent evaporation [ 33 ]. As predicted by Kelvin’s equation, the solvent water prefers to condense at these nanogaps, which formed positions with large mean curvature [ 34 , 35 ]. The strong capillary force was generated at junctions, and the wire junctions were welded during subsequent water evaporation [ 33 ].…”

Influence of ion structure and solvent electric dipole on ultrananoporous supercapacitor: a lattice model study

“…Although development of computer simulation technique greatly promotes our ability in treating liquid-related problems [11][12][13][14][15][16][17][18][19][20], there are still some problems such as large computing consumption and convergence particularly for strong electrostatic coupling systems such as the low r e value system, like ultrananoporous EDL, ionic liquids, melting salt, etc. Liquid state theories [21][22][23][24][25][26][27][28][29][30][31][32] have experienced remarkable development during the past several decades. For liquid interface problems, one of the most effective theoretical tools is classical density functional theory (CDFT) [33,34], which is widely applied in broad areas like phase transitions occurring in confined fluid systems [35][36][37][38][39][40], surface and interface structures of neutral systems [41][42][43][44] and charged systems like the EDL systems [5,41,[45][46][47][48][49][50][51]…”