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

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(d) 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-ev 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(d) similar to 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 hd 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-ev is independent of the evaporation rate amplitude, and roughly independent of its spatial distribution. Conversely, hd 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.