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).

摘要

为水平胶体薄膜开发了一个实用的干燥模型，薄膜中的垂直颗粒分布由佩克莱特数 (Pe) 确定。Pe定义为蒸发速度($v_{ev}$）和胶体扩散（$D_0$) 在初始湿膜厚度$H_0$($\text{佩}=v_{ev}{H}_0/D_0$）。该模型将 Pe 对时间粒子分布的影响纳入粒子的集体扩散率中。两个模型参数新加入集体扩散率，临界体积分数${\phi }_C$和体积排斥的程度$\chi ,$由于快速移动的界面，有效地解释了分散粒子的不平衡状态。所提出的双参数模型的结果与以前的模型和最近发表的格子玻尔兹曼 (LB) 模拟的结果进行了比较。对于大范围的 Pe (Pe = 10 - 1500)，双参数模型被证明与 LB 模拟一致。