Modelling of driven free surface liquid films

In several types of coating processes a solid substrate is removed at a controlled velocity U from a liquid bath. The shape of the liquid meniscus and the thickness of the coating layer depend on U. These dependencies have to be understood in detail for non-volatile liquids to control the deposition of such a liquid and to lay the basis for the control in more complicated cases (volatile pure liquid, solution with volatile solvent). We study the case of non-volatile liquids employing a precursor film model that describes partial wettability with a Derjaguin (or disjoining) pressure. In particular, we focus on the relation of the deposition of (i) an ultrathin precursor film at small velocities and (ii) a macroscopic film of thickness h ∝ U^(2/3) (corresponding to the classical Landau Levich film). Depending on the plate inclination, four regimes are found for the change from case (i) to (ii). The different regimes and the transitions between them are analysed employing numerical continuation of steady states and saddle-node bifurcations and simulations in time. We discuss the relation of our results to results obtained with a slip model. In connection with evaporative processes, we will study the pinning of a droplet due to a sharp corner. The approach employs an evolution equation for the height profile of an evaporating thin film (small contact angle droplet) on a substrate with a rounded edge, and enables one to predict the dependence of the apparent contact angle on the position of the contact line. The calculations confirm experimental observations, namely that there exists a dynamically produced critical angle for depinning that increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs criterion for pinning that accounts for the non-equilibrium effect of evaporation

Dynamic unbinding transitions and deposition patterns in dragged meniscus problems

We sketch main results of our recent work on the transfer of a thin liquid film onto a flat plate that is extracted from a bath of pure non-volatile liquid. Employing a long-wave hydrodynamic model, that incorporates wettability via a Derjaguin (disjoining) pressure, we analyse steady-state meniscus profiles as the plate velocity is changed. We identify four qualitatively different dynamic transitions between microscopic and macroscopic coatings that are out-of-equilibrium equivalents of equilibrium unbinding transitions. The conclusion briefly discusses how the gradient dynamics formulation of the problem allows one to systematically extend the employed one-component model into thermodynamically consistent two-component models as used to describe, e.g., the formation of line patterns during the Langmuir-Blodgett transfer of a surfactant layer