Role of Vapor Mass Transfer in Flow Coating of Colloidal Dispersions in the Evaporative Regime

Abstract

In flow-coating processes at low substrate velocity, solvent evaporation occurs during the film withdrawal and the coating process directly yields a dry deposit. In this regime, often referred to as the evaporative regime, several works performed on blade-coating-like configurations have reported a deposit thickness h proportional to the inverse of the substrate velocity V. Such a scaling can be easily derived from simple mass conservation laws, assuming that evaporation occurs on a constant distance, referred to as the evaporation length, noted L in the present paper and of the order of the meniscus size. However, the case of colloidal dispersions deserves further attention. Indeed, the coating flow leads to a wet film of densely packed colloids before the formation of the dry deposit. This specific feature is related to the porous nature of the dry deposit, which can thus remain wet when capillary forces are strong enough to prevent the receding of the solvent through the pores of the film (the so-called pore-emptying). The length of this wet film may possibly be much larger than the meniscus size, therefore modifying the solvent evaporation rate, as well as the scaling h ∼ 1/V. This result was suggested recently by different groups using basic modeling and assuming for simplicity a uniform evaporation rate over the wet film. In this article, we go a step further and investigate the effect of multidimensional vapor mass transfer in the gas phase on L and h in the specific case of colloidal dispersions. Using simplified models, we first provide analytical expressions in asymptotic cases corresponding to 1D or 2D diffusive vapor transport. These theoretical investigations then led us to show that L is independent of the evaporation rate amplitude, and roughly independent of its spatial distribution. Conversely, h strongly depends on the characteristics of vapor mass transfer in the gas phase, and different scaling laws are obtained for the 1D or the 2D case. These theoretical findings are finally tested by comparison with experimental results supporting our theoretical simplified approach.

Comparison of one-sided and diffusion-limited evaporation models for thin liquid droplets

“…Diffusion-limited evaporation often well-approximates evaporation rates observed in simple drying-droplet experiments, so it has been attractive for both experimental and theoretical studies (usually assuming a spherical-cap droplet) (Poulard, Bénichou & Cazabat 2003;Hu & Larson 2006;Shahidzadeh-Bonn et al 2006;Ristenpart et al 2007;Sefiane, David & Shanahan 2008;Eggers & Pismen 2010;Larson 2014;Tsoumpas et al 2015;Diddens et al 2017a,b;Karpitschka, Liebig & Riegler 2017;Jambon-Puillet et al 2018;Pahlavan et al 2021;Wray et al 2021;Gelderblom, Diddens & Marin 2022;Thayyil Raju et al 2022;Yariv 2023) and has also been used to model drying films (Dey, Doumenc & Guerrier 2016;Loussert et al 2017;Sobac, Colinet & Pauchard 2019;Larsson & Kumar 2022).…”

“…2022; Yariv 2023) and has also been used to model drying films (Dey, Doumenc & Guerrier 2016; Loussert et al. 2017; Sobac, Colinet & Pauchard 2019; Larsson & Kumar 2022).…”

Thin Coatings of Cerium Oxide Nanoparticles with Anti-Reflective Properties

“…In brief, CSA is a modified blade-coating technique where the withdrawing velocity of the substrate on which the coating will be deposited is so small that evaporation competes with the film casting rate, so that the dispersion is pre-concentrated at the level of the deposition meniscus; on top of this, it enhances the structure of the deposit [6][7][8][9].…”

“…Convective self-assembly (CSA) is a modified blade-coating technique where the withdrawing velocity of the substrate on which the coating will be laid ( Figure 8) is so small that evaporation competes advantageously with the film drawing rate: both the meniscus and the wet film (deposited continuously due to the displacement of substrate with good wetting properties) act as suction pumps via evaporation that drag the nanoparticles in this confined zone to eventually build a dense film, which fully dries soon after [7][8][9]. The final thickness h of the film is controllable via the velocity v, the evaporation rate, the bulk volume fraction φ 0 of the dispersion, shape of the meniscus, etc.…”

Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere

“…By following our preceding work [26] devoted to the moving contact line, we consider a partial wetting configuration with a 2D geometry suitable, e.g., for drying of the liquid films deposited on the Wilhelmy plate [27]. We consider a diffusive layer of thickness Λ above the thin liquid wedge-like film.…”