Numerical modeling of drop coalescence in the presence of soluble surfactants
Numerical modeling of drop coalescence in the presence of soluble surfactants
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DOI：
10.1016/j.cam.2015.04.013
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
I. Bazhlekov;D. Vasileva
中科院分区：
文献类型：
--
作者：
I. Bazhlekov;D. Vasileva
本文提出了一种数值方法来模拟可溶性表面活性剂对液滴聚结的最后阶段(成膜、排水和破裂)的影响。研究了小毛细管数、小雷诺数和小表面活性剂浓度下液滴间的轴对称相互作用。数学模型的流体力学部分包括液滴相的Stokes方程及其在液滴间隙(膜相)的润滑近似，以及界面上的速度和应力边界条件。表面活性剂被认为是可溶于(液滴和膜)两相的，表面活性剂浓度的分布符合对流扩散方程。用对流扩散方程模拟了表面活性剂在界面上的分布。两相中的浓度与界面上的浓度通过吸附等温线和界面与主体相之间的流量相耦合。数学模型的流体动力学部分和浓度部分通过表面活性剂在液体相中和界面上的平流联系在一起。另一方面，界面上表面活性剂浓度的不均匀会导致界面张力的梯度，进而导致界面上的附加切向应力(Marangoni效应)。对于液滴中的流动，采用了一种简化的边界积分法。用有限差分方法计算了缝隙内的流动、界面的位置和界面上以及流体相中表面活性物质的浓度分布。数值算法的优化采用了不同的方法：(r和z)方向空间离散的非均匀网格；具有自动自适应时间步长的显式和隐式一阶和二阶时间积分格式；在不损失精度的情况下显著减少计算时间的多时间步长积分格式。为了考察不同数值格式的精度和稳定性，进行了试验和比较。
The paper presents a numerical method for simulation of the effect of a soluble surfactant on the last stage of the drop coalescence (film formation, drainage and rupture). An axisymmetric interaction between drops is studied at small capillary and Reynolds numbers and small surfactant concentrations. The hydrodynamic part of the mathematical model includes the Stokes equations in the drop phase and their lubrication approximation in the gap between the drops (film phase), coupled with velocity and stress boundary conditions at the interfaces. The surfactant is considered soluble in both (drop and film) phases and the distribution of the surfactant concentration is governed by a convection–diffusion equation. A convection–diffusion equation is also used to model the distribution of the surfactant on the interfaces. The concentration in both phases is coupled with that on the interfaces via the adsorption isotherm and the fluxes between the interface and the bulk phases. The hydrodynamic and concentration parts of the mathematical model are related via the advection of the surfactant in the fluid phases and on the interfaces. On the other hand, a non-uniform surfactant concentration on the interfaces leads to a gradient of the interfacial tension which in turn leads to an additional tangential stress on the interfaces (Marangoni effects). For the flow in the drops a simplified version of Boundary integral method is used. Finite difference method is used for the flow in the gap, the position of the interfaces and the distribution of surfactant concentration on the interfaces, as well as in the fluid phases. Different approaches are used for an optimization of the numerical algorithm: Non-uniform meshes for space discretization in both (r and z) directions; Explicit and implicit first and second order time integration schemes with automatically adaptive time steps; A multiple time step integration scheme that can decrease significantly the computational time without loss of accuracy. Tests and comparisons are performed in order to investigate the accuracy and stability of the different numerical schemes.