Dip-coating flow in the presence of two immiscible liquids

TL;DR

This paper extends classical dip-coating theory to systems with two immiscible liquids, analyzing how film thicknesses depend on fluid properties and flow conditions, revealing independent interface evolution and shear stress influence.

Contribution

It introduces a theoretical extension for dip-coating with two immiscible liquids, detailing interface behavior and shear stress effects on film thicknesses.

Findings

Film thicknesses depend on capillary number and fluid property ratios.

Interfaces evolve independently except in a small region.

Final thicknesses are determined by maximum shear stresses.

Abstract

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