Continuous dip-coating flow in the presence of a liquid-liquid interface

Dip-coating is a widely utilized industrial process for applying protective coatings over substrates. Landau and Levich's theoretical analysis highlighted the key viscous-capillary interactions. The process becomes complex with liquid-liquid interfaces, as seen in multilayered coatings. This study explores the continuous dip-coating of a wire in a two-immiscible liquid system, focusing on the fluid dynamics at the liquid-liquid interface and the resulting film coating. Both experimental and numerical analysis reveals multiple flow regimes: visco-capillary, visco-inertial, boundary layer-dominated, and visco-gravitational. Our findings extend the Landau-Levich law beyond the classical capillary number values and show a distinct visco-inertial regime with a sharp, delayed transition. At high inertia, boundary layer effects reduce film thickness, while a visco-gravitational regime emerges when inertia is minimal and diminishing capillary suction effectiveness.