Numerical simulation of dip-coating in the evaporative regime

Abstract

A hydrodynamic model is used for numerical simulations of a polymer solution in a dip-coating-like experiment. We focus on the regime of small capillary numbers where the liquid flow is driven by evaporation, in contrast to the well-known Landau-Levich regime dominated by viscous forces. Lubrication approximation is used to describe the flow in the liquid phase. Evaporation in stagnant air is considered (diffusion-limited evaporation), which results in a coupling between liquid and gas phases. Self-patterning due to the solutal Marangoni effect is observed for some ranges of the control parameters. We first investigate the effect of evaporation rate on the deposit morphology. Then the role of the spatial variations in the evaporative flux on the wavelength and mean thickness of the dried deposit is ascertained, by comparing the 2D and 1D diffusion models for the gas phase. Finally, for the very low substrate velocities, we discuss the relative importance of diffusive and advective components of the polymer flux, and consequences on the choice of the boundary conditions.

Connecting Monotonic and Oscillatory Motions of the Meniscus of a Volatile Polymer Solution to the Transport of Polymer Coils and Deposit Morphology

“…Here we have determined pattern types and discussed their main features but have not given any further quantitative measures. In contrast, some theoretical works, based on time simulations, have analyzed the dependency of properties of line patterns on control parameters. , In particular, the onset of pattern formation is of interest. Hypotheses regarding the underlying bifurcations are formulated elsewhere based on time simulations, while another study was able to employ continuation techniques to determine the full bifurcation diagram for line deposition in Langmuir–Blodgett transfer.…”

Paper and Other Fibrous Materials—A Complete Platform for Biosensing Applications

“…Although the formation of the film is seemingly simple, complex physical and chemical variables are involved. The thickness and morphology of the deposited thin films are governed by parameters such as immersion time, dip coating cycles, withdrawal speed, density, surface tension, viscosity, substrate surface, conditions of evaporation, among others [ 209 ].…”

Pattern Formation in Slot-Die Coating

“…However, besides plenty of experimental results, for these systems modelling of pattern formation is also quite advanced. Thin-film models, i.e., hydrodynamic long-wave models and amended Cahn-Hilliard models, are used to analyse the bifurcation behaviour of pattern formation processes in evaporative dewetting [20], dip coating [21][22][23] and Langmuir-Blodgett transfer [24,25]. Normally, this is done for one-dimensional substrates, but first bifurcation results also exist in the two-dimensional case (see [26] and section 8.2 of [27]).…”