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润滑理论中接触线运动的数学模型与无网格数值方法

A mathematical model and mesh-free numerical method for contact-line motion in lubrication theory.

作者信息

Pang Khang Ee, Ó Náraigh Lennon

机构信息

School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.

出版信息

Environ Fluid Mech (Dordr). 2022;22(2-3):301-336. doi: 10.1007/s10652-021-09827-0. Epub 2022 Jan 19.

DOI:10.1007/s10652-021-09827-0
PMID:35664689
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9156478/
Abstract

ABSTRACT

We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving, spreading droplet. The model describes well the physics of droplet spreading-including Tanner's Law for the evolution of the contact line. The model can be configured to describe complete wetting or partial wetting, and we explore both cases numerically. In the case of partial wetting, the model also admits analytical solutions for the droplet profile, which we present here.

ARTICLE HIGHLIGHTS

We formulate a mathematical model to regularize the contact-line singularity for droplet spreading.The model can be solved using a fast, accurate mesh-free numerical method.Numerical simulations confirm that the model describes the quantitative aspects of droplet spreading well.

摘要

摘要

我们引入了一个具有无网格数值方法的数学模型，以描述润滑理论中的接触线运动。我们展示了该模型如何解决接触线处的奇异性问题，并为不断演化、扩散的液滴生成平滑轮廓。该模型很好地描述了液滴扩散的物理过程，包括接触线演化的坦纳定律。该模型可以配置为描述完全润湿或部分润湿情况，我们对这两种情况都进行了数值研究。在部分润湿的情况下，该模型还允许对液滴轮廓进行解析求解，我们在此给出这些解。

文章亮点

我们制定了一个数学模型来正则化液滴扩散的接触线奇异性。该模型可以使用快速、准确的无网格数值方法求解。数值模拟证实该模型能很好地描述液滴扩散的定量方面。

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