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Dip-coating is a common technique used to cover a solid surface with a thinliquid film, the thickness of which was successfully predicted by the theorydeveloped by Landau & Levich and Derjaguin in the 1940's. In this work, wepresent an extension of their theory to the case where the dipping bathcontains two immiscible liquids, one lighter than the other, resulting in theentrainment of two thin films on the substrate. We report how the thicknessesof the coated films depend on the capillary number, on the ratios of theproperties of the two liquids and on the relative thickness of the upper fluidlayer in the bath. We also show that the liquid/liquid and liquid/gasinterfaces evolve independently from each other as if only one liquid wascoated, except for a very small region where their separation falls quickly toits asymptotic value and the shear stresses at the two interfaces peak.Interestingly, we find that the final coated thicknesses are determined by thevalues of these maximum shear stresses.

Dip-coating flow in the presence of two immiscible liquids