# On a type of non-classical boundary condition of Lagrangian field

## TL;DR

This paper introduces a novel non-classical boundary condition in Lagrangian field theory linked to boundary surface curvature, simplifying to Tolman's formula under specific conditions, highlighting size effects of surface tension.

## Contribution

It derives a new boundary condition related to mean curvature in Lagrangian field theory, connecting geometric properties with physical surface tension effects.

## Key findings

- New boundary condition linked to boundary curvature
- Simplification to Tolman's formula under isotropy
- Size effects of surface tension are characterized

## Abstract

In the framework of the Lagrangian field theory, we derive a type of new non-classical natural boundary condition to be correlated with the mean curvature of boundary surface. Under the condition of homogeneity and isotropy, this type of boundary condition can be simplified into the Tolman's formula in which the size effect of surface tension is prescribed.