Three-dimensional solutions for coating flow on a rotating horizontal cylinder: Theory and experiment

We present three-dimensional numerical simulations of the flow of a thin liquid coating on a rotating horizontal right circular cylinder. The liquid motion is described using a lubrication model. The model evolution equation is discretized and solved numerically using an alternating-direction implicit algorithm. The cylinder rotates about its axis, carrying liquid around its circumference, resulting in the formation of a relatively thick coating where the cylinder surface moves upward. For coatings which are initially nearly uniform along the cylinder axis, this results in a ridge of liquid aligned with the cylinder axis. Over time, this ridge may break up into one of several possible configurations, including drops near the underside, and rings enveloping the cylinder. Simulations show that on larger cylinders, under certain circumstances this ridge may develop undulations which grow to form long fingers. These fingers drain down the cylinder. The simulation results are compared with a simple laboratory experiment, which exhibits similar fingering. (c) 2005 American Institute of Physics.