Wolfson Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa, Israel 32000.
Soft Matter. 2016 Jun 29;12(26):5693-707. doi: 10.1039/c6sm00579a.
We propose a model for the pattern deposition of the solute from an evaporating drop of a dilute solution on a horizontal substrate. In the model we take into account the three-phase contact angle hysteresis and the deposition of the solute whenever its concentration exceeds the solubility limit. The evaporating drop is governed by a film equation. We show that unless for a very small three-phase contact angle or a very rapid evaporation rate the film adopts a quasi-steady geometry, satisfying the Young-Laplace equation to leading order. The concentration profile is assumed to satisfy an advection diffusion equation subject to the standard Fick's law for the diffusive flux. We further use an integral boundary condition to describe the dynamics of the concentration in the vicinity of the three-phase contact line; we replace an exact geometric description of the vicinity of the contact line, which is usually assumed such that mathematical singularities are avoided, with general insights about the concentration and its flux. We use our model to explore the relationships between a variety of deposition patterns and the governing parameters, show that the model repeats previous findings, and suggest further insights.
我们提出了一个模型，用于描述稀溶液蒸发液滴在水平基底上的溶质图案沉积。在该模型中，我们考虑了三相接触角滞后以及溶质浓度超过溶解度极限时的沉积。蒸发液滴受膜方程控制。我们表明，除非三相接触角非常小或蒸发速率非常快，否则膜会采用准稳态几何形状，满足主导阶的 Young-Laplace 方程。浓度分布被假设满足对流扩散方程，并服从扩散通量的标准 Fick 定律。我们进一步使用积分边界条件来描述三相接触线附近浓度的动力学；我们用关于浓度及其通量的一般见解来代替接触线附近的精确几何描述，这通常假设为避免数学奇点。我们使用我们的模型来探索各种沉积图案与控制参数之间的关系，表明模型重复了先前的发现，并提出了进一步的见解。
