Abstract

We compute the roughness exponent of the averaged contact line width of a liquid on heterogeneous substrates with randomly distributed dilute defects in statics. We study the case of circular “mesa”-type defects placed on homogeneous base. The shape of the liquid meniscus and the contact line are obtained numerically, using the full capillary model when a vertical solid plate, partially dipped in a tank of liquid, is slowly withdrawing from the liquid. The obtained results imply that the contact line roughness exponent depends on the contact angle \(\theta \), which the liquid meniscus forms with the solid homogeneous base. The roughness exponent grows when \( |\theta - 90^{\circ } |\) decreases, and it changes from 0.5 at \(|\theta - 90^{\circ } |= 70^{\circ }\) to 0.67 at \(|\theta - 90^{\circ } |= 0^{\circ }\). A wide range of contact angles (\(60^{\circ }\)–\(107.5^{\circ }\)) is present, where the roughness exponent is practically constant, equal to previously obtained experimental results on the magnitude of the roughness exponent and its dependence on \(\theta \).

Graphic abstract

中文翻译：

---

接触线粗糙度指数对具有稀台面缺陷的基板上接触角的依赖性：数值研究

摘要

我们计算了异质衬底上液体的平均接触线宽度的粗糙度指数，在静力学中具有随机分布的稀薄缺陷。我们研究了放置在同质基底上的圆形“台面”型缺陷的情况。液体弯月面的形状和接触线是通过数值获得的，使用全毛细管模型，当垂直的固体板部分浸入液体罐中时，慢慢地从液体中抽出。所得结果表明接触线粗糙度指数取决于接触角\(\theta \)，液体弯月面与固体均质基底形成的接触角。当\( |\theta - 90^{\circ } |\)减小时，粗糙度指数增加，并在\(|\theta - 90^{\circ } |= 70^{\circ }\)处从 0.5 变化在\(|\theta - 90^{\circ } |= 0^{\circ }\)处为 0.67 。存在宽范围的接触角 ( \(60^{\circ }\) – \(107.5^{\circ }\) )，其中粗糙度指数实际上是恒定的，等于先前获得的关于粗糙度指数及其对\(\theta \)的依赖性。

图形摘要