# Generalization of the Kelvin Equation for Arbitrarily Curved Surfaces

## TL;DR

This paper extends the Kelvin equation to apply to arbitrarily curved surfaces by using newly proposed dynamic equations for moving surfaces, providing a universal solution across scales and geometries.

## Contribution

It introduces a generalized form of the Kelvin equation valid for any surface curvature using dynamic surface equations.

## Key findings

- The generalized Kelvin equation applies to all surface types.
- It is valid across atomic to macro scales.
- The approach resolves longstanding debates on curvature effects.

## Abstract

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid 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.