A SIMPLE THEORY FOR THE ENTRAINED FILM THICKNESS DURING MENISCUS COATING

An analysis is presented of the fluid dynamics of meniscus coating, in which a horizontal substrate contacts the top surface of a liquid film flowing down an inclined plane, forming a meniscus. The substrate is then moved and a film is entrained on it. The analysis shows the dependence of the entrained film thickness on the substrate translation rate, suspension viscosity, geometry and failing film flowrate. An idealized geometry is assumed which retains the physics of the coating process but which allows a leading-order analytic solution by requiring continuity of the meniscus curvature across three regions: an entrained film flow region near the substrate, static meniscus region and a falling film region down the inclined plane. It is shown that, except for a small term associated with the falling film flow, the film thickness equation is identical to the leading order result for the familiar dip-coating problem. Results of the model agree very well with optical film thickness measurements for films deposited from a Newtonian suspension, and departures from the theory due to non-Newtonian rheology are discussed.