Thickness of Thin-Layer Liquid Film on a Rotating Roll and its Measurement by the X-Ray Backscattering Technique

A mathematical model is provided to describe the thin-layer liquid film thickness on the surface of a rotating roll which is partially immersed in a liquid bath. The equation expresses the initial film thickness in terms of roll speed and immersion depth as well as liquid viscosity, surface tension, and density. The roll speed and liquid viscosity are the two dominant parameters affecting the film thickness. An x-ray backscattering technique was used to measure the film thickness. An important feature of this technique is that it permits the measurements to be carried out under a steady-state condition without disturbing the liquid film and the roll. The principle of a portable instrument and the technique involved in the measurements are described. Within the scope of the present investigation with Newtonian liquid and laminar flow, the experimental values of film thickness determined by the x-ray backscattering technique agreed very well with the theoretical values predicted by the mathematical model.