On the shape of a lightweight drop on a horizontal plane

TL;DR

This paper develops an analytical model for the shape of a lightweight droplet on a horizontal surface, incorporating first-order weight corrections and extending the solution to the entire drop surface, validated against experiments.

Contribution

It introduces a new polar coordinate system and a perturbative method to analytically describe the entire shape of a droplet including concave and convex regions.

Findings

Analytical expressions match experimental data.

The model accurately predicts the droplet shape with weight corrections.

Extension of the solution to the entire surface improves understanding of droplet morphology.

Abstract

The shape of drop on a flat horizontal plane is obtained by including the first order of correction by the weight. The sphere solution of the weightless drop is used to introduce a new polar coordinate by which the perturbative expression for a region of a drop can be extended analytically to the entire surface of a drop having both the concave and the convex parts. Comparison with experimental data are presented.