A theory of withdrawal of cylinders from liquid baths

A theory of the amount of liquid entrained by cylinders upon withdrawal from liquid baths is derived for a wide range of cylinder radii. The theory is based on matching curvatures for static and dynamic menisci. Predicted values are expressed as the effect of the dimensionless wire radius (Goucher number) and dimensionless withdrawal speed (capillary number) on the dimensionless flux. The theory was verified experimentally for all wire radii by removing short cylinders from oily fluids and with other information. The fluids used included kerosene, mineral oil, motor oil, and glycerine, with viscosities from 2 to 500 centipoise; Goucher numbers ranged from 0.05 to 1.2. Deviations, which were noted at high capillary numbers where velocity gradients become appreciable, indicated that the theory is a plug flow or low speed theory. Also discussed are differences found with water and the conditions under which films coalesced into droplets.