Cabrerizo-Vilchez M A, Fernández J R, Fernández-Rodríguez M A, García-Río L, Muñiz M C, Núñez Cristina
Biocolloid and Fluid Physics Group, Applied Physics Department, Faculty of Sciences, University of Granada Avda. de la Fuente Nueva s/n E-18071 Granada Spain.
Department of Applied Mathematics I, University of Vigo Campus Universitario As Lagoas Marcosende s/n E-36310 Vigo Spain.
RSC Adv. 2019 May 23;9(28):16187-16194. doi: 10.1039/c9ra00940j. eCollection 2019 May 20.
This paper introduces a new mathematical model that is used to compute either the interfacial tension of quiescent axisymmetric pendant/sessile drops and pendant/captive bubbles. This model consists of the Young-Laplace equation, that describes interface shape, together with suitable boundary conditions that guarantee a prescribed volume of drops/bubbles and a fixed position in the capillary. In order to solve the problem numerically, the Young-Laplace equation is discretized by using numerical differentiation and the numerical solutions are obtained applying the well-know Newton method. The paper contains a validation of the new methodology presented for what theoretical bubble/drops are used. Finally, some numerical results are presented for both drops and bubbles of water as well as several surfactant solutions to demonstrate the applicability, versatility and reproducibility of the proposed methodology.
本文介绍了一种新的数学模型，该模型用于计算静态轴对称悬垂/ sessile液滴以及悬垂/俘获气泡的界面张力。该模型由描述界面形状的杨-拉普拉斯方程以及合适的边界条件组成，这些边界条件可确保液滴/气泡的规定体积以及在毛细管中的固定位置。为了对该问题进行数值求解，通过数值微分对杨-拉普拉斯方程进行离散化，并应用著名的牛顿法获得数值解。本文针对所使用的理论气泡/液滴对提出的新方法进行了验证。最后，给出了水以及几种表面活性剂溶液的液滴和气泡的一些数值结果，以证明所提出方法的适用性、通用性和可重复性。
