Practical drying model for horizontal colloidal films in rapid evaporation processes

Abstract

A practical drying model is developed for horizontal colloidal films with the vertical particle distribution in the film determined by the Peclet number (Pe). The Pe is defined as the ratio between the evaporation speed ($v_{ev}$) and the colloidal diffusion ($D_0$) at the initial wet film thickness $H_0$ ($\text{Pe}=v_{ev}{H}_0/D_0$). The model incorporates the effect of Pe on the temporal particle distribution into the collective diffusivity of particles. Two model parameters are newly adopted into the collective diffusivity, the critical volume fraction ${\varphi }_c$ and the degree of volume exclusion $\chi ,$ to efficiently account for the out-of-equilibrium state of dispersed particles due to the fast-moving interface. The results of the proposed two-parameter model are compared to those of previous models and a recently-published lattice Boltzmann (LB) simulation. The two-parameter model is demonstrated to favorably consistent with the LB simulation for a wide range of Pe (Pe = 10 − 1500).

Keywords:

• Colloidal film
• vertical drying
• Peclet number
• collective diffusivity
• two-parameter model

Additional information

Funding

This research was supported by grants from the National Research Foundation of Korea (NRF) (2016R1A5A1009592 and 2017R1E1A1A01075107).