Role of long-range forces in heterogeneous nucleation

Abstract

We analyzed the structure of the contact line between a van der Waals fluid and a flat solid, in the regime where the contact angle θ is small—which allows for a continuum theory of the long-range forces. We computed the size ( χ m) of the perturbed region near the line: χ m ∼ a/ θ 2 (where a is a molecular length), and the line energy τ. We then discussed the structure of the droplets which occur in heterogeneous nucleation, with special emphasis on the case of relatively large sursaturations Δ, where the droplets are small. We found, surprisingly, that an approach based on a constant τ remains qualitatively valid even for drops smaller than the line core size χ m: τ is only logarithmically sensitive to the overall size. We also extended these results to long-range forces other than those of van der Waals, leading to disjoining pressures Π d vs thickness e of the form Π d ∼ e − n with an arbitrary exponent n.