Dip-coating with prestructured substrates: transfer of simple liquids and Langmuir–Blodgett monolayers

Abstract

When a plate is withdrawn from a liquid bath, either a static meniscus forms in the transition region between the bath and the substrate or a liquid film of finite thickness (a Landau-Levich film) is transferred onto the moving substrate. If the substrate is inhomogeneous, e.g. has a prestructure consisting of stripes of different wettabilities, the meniscus can be deformed or show a complex dynamic behavior. Here we study the free surface shape and dynamics of a dragged meniscus occurring for striped prestructures with two orientations, parallel and perpendicular to the transfer direction. A thin film model is employed that accounts for capillarity through a Laplace pressure and for the spatially varying wettability through a Derjaguin (or disjoining) pressure. Numerical continuation is used to obtain steady free surface profiles and corresponding bifurcation diagrams in the case of substrates with different homogeneous wettabilities. Direct numerical simulations are employed in the case of the various striped prestructures. The final part illustrates the importance of our findings for particular applications that involve complex liquids by modeling a Langmuir-Blodgett transfer experiment. There, one transfers a monolayer of an insoluble surfactant that covers the surface of the bath onto the moving substrate. The resulting pattern formation phenomena can be crucially influenced by the hydrodynamics of the liquid meniscus that itself depends on the prestructure on the substrate. In particular, we show how prestructure stripes parallel to the transfer direction lead to the formation of bent stripes in the surfactant coverage after transfer and present similar experimental results.

Self-organized dip-coating patterns of simple, partially wetting, nonvolatile liquids

“…We model the evolution of the local height h(r, t), r = (x, y) of the film of simple, nonvolatile liquid in the laboratory frame for the dip-coating geometry shown in Fig. 1 with the well-established long-wave, thin-film or lubrication equation [41,42] in its nondimensional form, including a Derjaguin (or disjoining) pressure accounting for partial wettability [43,44], gravitational contributions and an advection term accounting for the withdrawal of the substrate [13,28]:…”

“…1). The boundary conditions, which are also employed in [28], read h = h l , ∇h = (−α, 0) T , n · ∇∆h = 0 at x = 0 (4) n · ∇h = 0, n · ∇∆h = 0 at x = L x , n = (1, 0) T (5) h(x, y = 0) = h(x, y = L y ).…”

“…They are implemented using the open-source framework DUNE-PDELab [55][56][57]. For further implementation details, see also [28], where a similar numerical approach is employed. One-dimensional simulations are performed on a domain Ω 1D = [0, 400] discretised on 400 elements, while two dimensional simulations are performed on Ω 2D = [0, 600] × [0, 300] discretised on 300 × 150 elements.…”

“…The implied continuous character of the film surface profile across the contact-line region allows for detailed bifurcation studies and the identification of a variety of transition scenarios [13,14,28].…”

Modelling of surfactant-driven front instabilities in spreading bacterial colonies

“…To that end, we use the software package AUTO-07p [45] which has previously been successfully employed for thin-film models, e.g. for dewetting simple and complex liquids [51], pattern formation in dip-coating [52] or osmotically spreading biofilms. [5,33] We impose that far away from the colony, the surfactant concentration is fixed to a small but finite value.…”