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We present an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compare our results with experimental measurements. The film thickness is, to a good approximation, uniform above the point where the film is withdrawn from the fluid bath, and depends on the rotation rate, the fluid properties and the substrate geometry. Theoretical predictions of the film thickness for a number of dierent sub- strate geometries (an inclined plate, roller and fiber) are presented, and are compared with experimental measurements in a single roller geometry. Results are obtained for two dierent limits of the Criminale-Ericksen-Filbey constitutive equation in which the fluid rheology is either weakly elastic and dominated by shear-thinning, or strongly elastic and dominated by elastic stresses. A lubrication analysis yields a thin-film equation which characterizes the film thickness as a function of spatial position. The rheological properties of the test fluids are measured independently using steady and oscillatory shearing deformations. The viscometric parameters are then used, in conjunction with the governing thin-film equation, which is solved using matched asymptotics, to give a quantitative prediction of the thickness of the fluid coating. The onset of an instability which causes the film thickness to vary with axial position along the roller is also observed experimentally.

Coating flows of non-Newtonian fluids: weakly and strongly elastic limits