液滴形貌方程的能量描述  

Energy Formulation of the Morphological Equation of a Droplet

作　　者：秦剑锋[1] 姜礼鑫[2,3] 

机构地区：[1]青岛广播电视大学,山东青岛266012 [2]中国石油大学(华东)工程力学系,山东青岛266555 [3]青岛开发区职业中专,山东青岛266500

出　　处：《鲁东大学学报（自然科学版）》2011年第3期232-235,共4页Journal of Ludong University:Natural Science Edition

基　　金：山东省自然科学基金(2009ZRA05008)

摘　　要：基于可动边界条件下的能量变分法,本文给出了一种关于任意液滴形貌的新的分析方法,推导出了液滴形貌的控制方程(Laplace方程)以及相应的横截性条件(Young方程).当液滴的尺寸远小于毛细长度时,这些方程退化为球缺形液滴的控制方程.通过求解液滴的形貌方程,发现液滴的形貌具有很强的尺寸效应,即液滴的体积越小,其形状越接近于球缺;体积越大则其形状越来越远离于球缺.这些分析结果对于微型传感器、超疏水表面、微流体器件等工业应用具有一定的参考价值,同时也可以对于我们加深可动边界条件以及液滴表面浸润性质的进一步理解.Based upon the variation of the energy functional with moving boundary condition,a new analysis method to investigate the morphology of an arbitrary droplet is presented,and the governing equation,i.e.the Laplace equation,and the transversality conditiion,i.e.the Young＇s equation are derived.When the size of the droplet is much smaller than the capillary length,these equations are reduced for the droplet of a spherical cap shape.it is found that the droplet is strongly size-dependent through solving the morphological equation of the droplet.When its volume becomes smaller,its shape is more similar to the spherical cap,and vice visa,it will be faraway from the spherical cap.These analyses may be beneficial to micro-sensors,superhydrophobic surfaces and micro-fluidics,and then bring us more deep understanding of the moving boundary condition and surface wetting of droplets.

关 键 词：能量泛函 可动边界条件 液滴形貌 横截条件 控制方程 

分 类 号：O647[理学—物理化学]