Department of Chemical Engineering and Materials Science, University of Minnesota , Minneapolis, Minnesota 55455, United States.
Langmuir. 2017 Sep 26;33(38):10061-10076. doi: 10.1021/acs.langmuir.7b02341. Epub 2017 Sep 12.
In many technological applications, excess solvent must be removed from liquid droplets to deposit solutes onto substrates. Often, the substrates on which the droplets rest may possess some roughness, either intended or unintended. Motivated by these observations, we present a lubrication-theory-based model to study the drying of droplets of colloidal suspensions on a substrate containing a topographical defect. The model consists of a system of one-dimensional partial differential equations accounting for the shape of the droplet and depth-averaged concentration of colloidal particles. A precursor film and disjoining pressure are used to describe the contact-line region, and evaporation is included using the well-known one-sided model. Finite-difference solutions reveal that when colloidal particles are absent, the droplet contact line can pin to a defect for a significant portion of the drying time due to a balance between capillary-pressure gradients and disjoining-pressure gradients. The time-evolution of the droplet radius and contact angle exhibits the constant-radius and constant-contact-angle stages that have been observed in prior experiments. When colloidal particles are present and the defect is absent, the model predicts that particles will be deposited near the center of the droplet in a cone-like pattern. However, when a defect is present, pinning of the contact-line accelerates droplet solidification, leading to particle deposition near the droplet edge in a coffee-ring pattern. These predictions are consistent with prior experimental observations, and illustrate the critical role contact-line pinning plays in controlling the dynamics of drying droplets.
在许多技术应用中，必须从液滴中去除多余的溶剂，以便将溶质沉积到基底上。通常，液滴所接触的基底可能具有某种粗糙度，无论是有意还是无意的。受这些观察结果的启发，我们提出了一个基于润滑理论的模型，以研究含有地形缺陷的基底上胶体悬浮液液滴的干燥过程。该模型由一组一维偏微分方程组成，用于描述液滴的形状和胶体颗粒的深度平均浓度。采用前驱膜和非附着力压力来描述接触线区域，并使用著名的单侧模型来包含蒸发。有限差分解表明，当不存在胶体颗粒时，由于毛细压力梯度和非附着力压力梯度之间的平衡，液滴接触线可能会在干燥过程的很大一部分时间内固定在缺陷处。液滴半径和接触角的时间演化表现出先前实验中观察到的恒定半径和恒定接触角阶段。当存在胶体颗粒且不存在缺陷时，模型预测颗粒将以锥形图案沉积在液滴中心附近。然而，当存在缺陷时，接触线的固定会加速液滴的凝固，导致颗粒在液滴边缘附近以咖啡环图案沉积。这些预测与先前的实验观察结果一致，说明了接触线固定在控制干燥液滴动力学方面的关键作用。
