Taylor Instability of a Liquid Film Around a Long, Horizontal, Circular Cylindrical Body in Still Air

Abstract

A combined theoretical and experimental investigation is made of the instability of a liquid film around a long, horizontal, circular cylindrical body in still air. In the theoretical investigation, a modified Taylor-type analysis is applied to a simplified physical model. Due to the curvilinear nature of the liquid-air interface, the surface tension as well as the radius of the cylinder are found to play important roles in the establishment of a criterion of instability of the problem. A critical wave length along the length of the cylinder is also found for which the instability will be amplified most rapidly. Such a critical wave length, then, naturally suggests the critical interval distance at which droplets formed as a direct consequence of the instability will break away from the liquid film. In the experimental investigation, measurements were made of a visually observable critical distance of the liquid film around each of several cylinders of different sizes. For two liquids of considerably different surface tension, the results in all cases agree closely with the suggestions made by the theoretical critical wave length.