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The Tolman length δ {\displaystyle \delta } measures the extent by which the surface tension of a small liquid drop deviates from its planar value. It is conveniently defined in terms of an expansion in 1 / R {\displaystyle 1/R} , with R = R e {\displaystyle R=R_{e}} the equimolar radius of the liquid drop, of the pressure difference across the droplet's surface:
In this expression, Δ p = p l − p v {\displaystyle \Delta p=p_{l}-p_{v}} is the pressure difference between the pressure of the liquid inside and the pressure of the vapour outside, and σ {\displaystyle \sigma } is the surface tension of the planar interface, i.e. the interface with zero curvature R = ∞ {\displaystyle R=\infty }. The Tolman length δ {\displaystyle \delta } is thus defined as the leading order correction in an expansion in 1 / R {\displaystyle 1/R}.
The equimolar radius is defined so that the superficial density is zero, i.e., it is defined by imagining a sharp mathematical dividing surface with a uniform internal and external density, but where the total mass of the pure fluid is exactly equal to the real situation. At the atomic scale in a real drop, the surface is not sharp, rather the density gradually drops to zero, and the Tolman length captures the fact that the idealized equimolar surface does not necessarily coincide with the idealized tension surface.
Another way to define the Tolman length is to consider the radius dependence of the surface tension, σ {\displaystyle \sigma }. To leading order in 1 / R {\displaystyle 1/R} one has: