On the behavior of liquid drops on a solid surface. 1. The sliding of drops on an inclined surface

TL;DR

This paper analyzes the shape and motion of liquid drops on inclined surfaces using energy principles, deriving differential equations and discussing contact angle hysteresis and detachment limits.

Contribution

It generalizes contact angle concepts and models drop behavior on inclined surfaces, including shape, detachment, and internal liquid motion.

Findings

Derived differential equations for drop shapes on inclined surfaces

Identified the inclination angle limit for drop sliding

Discussed models of drop detachment and internal flow

Abstract

The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations describing the drop shapes are found in both cases. A case of good wetting is considered to determine the profiles of the sessile and inclined drops. The generalization of the boundary conditions for the contact angle hysteresis of the drop on an inclined surface is discussed. The limit of the inclination angle at which the drop begins to run down the inclined plane is found. The models of the drop detachment from the solid and the motion of liquid inside of the drop are discussed. This is not an original text.