“Dip coating process with both soluble and insoluble surfactant. Flow pattern transition and inertial effects”.

D.M. CAMPANA, M. D. GIAVEDONI, F. A. SAITA

Praga

Congreso; 19th International Congress of Chemical and Process Engineering (CHISA 2010).; 2010

            Dip coating has been one of the extensively studied coating processes since the pioneering work carried out by Landau and Levich (1942). This process deposits a thin uniform film on a solid by withdrawing it at a constant speed from a bath containing the liquid to be coated. Landau and Levich obtained an analytical expression predicting the thickness of the film formed at very small substrate speeds; i.e. when viscous and capillary forces balance each other. Since then, numerous works has been performed to assess the influence on the film thickness of forces that are usually present, but were not consider by Landau and Levich (viz. gravity, inertia, elastic forces originated by surface active agents, etc.).             The effects produced by the presence of surfactants, particularly on the thickness of the film coated, have been plentifully analyzed during the last two decades. Experimental works carried out on fibers (Ramdane and Quéré, 1997, Shen et al., 2002) as well as those carried out on flat plates (Krechetnikov and Homsy, 2005) indicate that thicker coating films are obtained due to their presence. Theoretical asymptotic analysis (Park, 1991) and numerical solutions of 2-D governing equations (Campana et al., 2009) also indicate that the thickening factor ratio (i.e. the ratio between the predicted film thickness and the Landau-Levich result for a uniformly distributed surfactant) is always larger than one. An exception is the numerical work of Krechetnikov and Homsy (2006); these authors found, in contradiction with their own experiments, thickening factors smaller than one. They assume that their numerical results are correct and explain the discrepancy stating that pure hydrodynamic models are not enough to describe the dip coating process when elastic forces are present.             In this work we present film thickness predictions when dip coating is implemented on a flat substrate in the presence of both soluble and insoluble surfactants. Our numerical model solves the governing equations of the 2-D problem simultaneously, i.e. velocities, pressures, surfactant concentrations and the spatial location of the points representing the discrete version of the free surface are all determined at once. This is a key difference regarding the technique employed by Krechetnikov and Homsy that uses an iterative procedure to update the shape and location of the free surface. Our model was validated with the asymptotic results obtained by Park (1991) and also with the experiments performed by Krechetnikov and Homsy (2005).             Results obtained show a wealth of information: they depict how the flow patterns change when the surfactant solubility diminishes. For highly soluble surfactants the streamlines present the usual single stagnation point located on the free surface and close to the dynamic meniscus. As the solubility decreases the stagnation point moves along the free surface and away from the dynamic meniscus; at the same time a second stagnation point arises in the bulk near the dynamic meniscus together with a swirl located between the free surface and the streamline that ends at the free surface. Finally, when the solubility becomes zero the stagnation point at the free surface disappears; at this instant the flow pattern shows the motion of two separated liquid streams (one moving with the substrate and the other one with the free surface) enclosing a recirculation-flow region. The two streams merge at the stagnation point constituting the final film to be deposited on the substrate.             We also analyzed the influence of inertia on film thickness. Park (1991) already showed that viscous forces prevail over the elastic ones when Capillary number is increased (i.e. when the coating speed is increased); thus, the thickening factor ratio decreases until the Landau and Levich solution is recovered. Our predictions indicate that inertia plays a role similar to viscous forces; however, since inertia forces vary with speed in a quadratic way, the Landau and Levich solution is reached much faster.             The foregoing results indicate that a pure hydrodynamic model correctly reproduces the features observed in conventional deep coating; therefore, the present analysis is now being extended to fiber coating.             References             L. Landau and B. Levich, “Dragging of a liquid by a moving plate,” Acta Physicochim. URSS 17, 42 (1942).   R. Krechetnikov and G. M. Homsy, “Experimental study of substrate roughness and surfactant effects on the Landau-Levich law,” Phys. Fluids 17, 102108-1 – 102108-16 (2005).   R. Krechetnikov and G. M. Homsy, “Surfactant effects in the Landau-Levich problem,” J. Fluid Mech. 559, 429-450 (2006).   C- W. Park, “Effects of insoluble surfactants on dip coating,” J. Coll. Interface Sci. 146, 382-394 (1991).   O. O. Ramdane and D. Quéré, “Thickening factor in Marangoni coating,” Langmuir 13, 2911-2916 (1997).   D. M. Campana, S. Ubal, M. D. Giavedoni and F. A. Saita, “Numerical prediction of the film thickening due to surfactants in the Landau-Levich problem,” submitted to Physics of Fluids (2009).