Molecular dynamics of the surface tension of a drop

The curvature dependence of the liquid–vapor surface tension is described in the limit of small curvatures by Tolman’s length. Measurements of it, either experimentally or in a simulation, have not yet given a clear idea of its magnitude, even its sign is being debated. Previous attempts to relate Tolman’s length to a pressure tensor have led to ill-defined expressions. From an analysis of the pressure difference over the interface of a liquid drop, a pressure tensor expression is obtained for Tolman’s length that does not suffer from the previously encountered inconsistencies. This pressure difference is studied in a simulation of liquid drops, leading to an estimate of Tolman’s length. It appears to be small and bounds are given on it.