基于DUGKS 方法的液滴在剪切流中变形过程的数值研究

NUMERICAL STUDY OF DROPLET DEFORMATION IN SHEAR FLOW USING THE DUGKS APPROACH

苏明宇

11849034

硕士

力学

王连平

2020-05-28

2020-06-07

哈尔滨工业大学

深圳

液滴悬浮在另一种互不相溶的流体中，在剪切力作用下发生变形。当剪切作用大到一定程度时，液滴会变形至破裂，分裂出多个小液滴。液滴在不相溶流体中受剪切作用发生的变形和破裂在工程、生物医药等领域应用广泛，例如微流体技术和乳化液工业。液滴在均匀剪切流中的变形过程可以由剪切力与表面张力之比（毛细管数Ca）、液滴粘度与外部流体粘度之比（粘度比）和流体惯性力与粘性力之比（雷诺数Re）来描述。但是，在工业实际中，比如微流控芯片中，管内流动与液滴形变均受到壁面约束的影响。因此，需要额外考虑壁面约束来描述剪切两相液滴系统。本研究利用基于相场理论的离散统一气体动理学（DUGKS）两相模型，研究初始圆形的二维液滴在壁面相对运动引起的剪切流作用下的变形过程。除了上述物理参数，液滴变形还可能会受到数值方法中二个数值参数的影响：就是佩克莱特数（Pe：对流扩散与相场模型里的数值扩散的比值）和卡恩数（Ch：界面厚度W 与初始液滴半径R 之比）对数值计算精度与数值稳定性的影响。论文重点是分析毛细管数、粘度比、壁面约束以及雷诺数对液滴变形的影响。通过数值实验，发现对于缓慢剪切流动，当液滴半径为界面厚度的10 倍且佩克莱特数小于1 时，数值耗散较大，计算结果会不准确。在给定界面厚度的情况下，卡恩数越高，数值耗散越大。数值模拟结果显示，如果初始液滴半径小于10W 或者卡恩数大于0.1，液滴的变形参数由于数值耗散会无法准确模拟。不考虑流体惯性，液滴在小毛细管数条件下会变形至近似椭圆。毛细管数越大，液滴的变形参数越大，倾斜角越小，与文献结果吻合。考虑壁面效应时，不同粘度比下的剪切流中二维液滴的变形参数和毛细管数仍然近似线性相关，但是比例因子与壁面约束和粘度比有关。壁面约束大于0.4 时，即使液滴依旧变形为近似椭圆状，Taylor 模型不再适用，说明壁面效应不能忽略。较大毛细管数和粘度比下的DUGKS结果与文献三维结果存在偏差，但是与文献中二维变形问题的预测一致，说明了DUGKS两相模型结果可靠，也为二维液滴问题与三维问题存在定量偏差提供了新的数据。研究发现，在有限雷诺数或比较大的毛细管数条件下，液滴的稳态形状明显和椭圆有偏差，并且这种偏差随着壁面约束而增强。本研究证明了结合相场理论的DUGKS 两相模型可以成功应用于液液两相流的研究中。

A droplet suspended in another immiscible fluid can deform when subjected to a ambient flow shear. When the shear rate is large enough, the droplet will have large deformation and even break up into several satellite droplets. Droplet deformation and breakup subjected to a uniform shear in immiscible two-phase fluids are widely encountered in many engineering and biomedical applications such as microfluidic technology and emulsion processing. The deformation of an isolated droplet in shear flow can be governed by the ratio of shear and interfacial stresses (Ca), the viscosity ratio of droplet and surrounding fluid, and the ratio of inertia force and viscous force (i.e., Reynolds number Re). In practice, such as in a microfluidic chip, the flow and droplet deformation in the tube are affected by the wall confinement, thus the wall confinement effect must be considered. In this study, the deformation behavior of an initially circular droplet in 2D moving wall driven shear flow is studied by using the discrete uniform gas kinetic scheme (DUGKS) combined with the phase field model. Besides the above physical parameters, two numerical parameters affecting the droplet deformation are also considered. They are the Peclet number (the ratio of advective transport to the phase-field inherent diffusive transport) and the Cahn number ( , the ratio of the numerical interfacial thickness, W，and initial radius of droplet, R) which can affect the numerical accuracy and numerical stability. The main part of the research is to analyze the effects of capillary number, viscosity ratio, wall confinement and Reynolds number on droplet deformation. By conducting a series of numerical experiments, it is found that for low shear rate cases the numerical dissipation becomes too large to simulate correctly the deformation when the Peclet number is smaller than one and the initial droplet radius is fixed at 10W. For a given W, the numerical dissipation increases with increasing Ch. Numerical results show that, if R is less than 10W or Ch is larger than 0.1, the deformation parameter cannot be accurately simulated. An initially circular droplet deforms to an approximate ellipse when the capillary number is sufficiently small. The larger the capillary number, the larger the deformation parameter is and the smaller the inclination angle is. Considering the wall effect, the deformation parameters of to-dimensional droplets in shear flow under different viscosity ratios depend roughly linearly on the capillary number. The scaling factor is related to the wall constraint and the viscosity ratio. When the wall confinement parameter is larger than 0.4, the Taylor model is no longer applicable even if the droplet deforms into an ellipse, indicating that the wall effect cannot be neglected. The DUGKS results at large capillary number and viscosity ratio deviate from 3D numerical results in the literature. But our 2D DUGKS results are in good agreement with the prediction for 2D droplet deformation in the existing literature, meaning that the 2D droplet deformation problem is quantitatively different from the 3D problem and our phase-field DUGKS simulations provide additional data for this difference. We also find that, when the fluid inertia is considered as reflected by a finite Re and a finite Ca, the steady-state droplet shape deviates from ellipse, and this deviation is further enhanced by wall confinement. This study proves that the two-phase DUGKS model combined with the phase field can be successfully applied to liquid-liquid two-phase flow research.

剪切流 液滴变形 相场模型 DUGKS

shear flow droplet deformation phase field DUGKS

中文

联合培养

南方科技大学

苏明宇. 基于DUGKS 方法的液滴在剪切流中变形过程的数值研究[D]. 深圳. 哈尔滨工业大学,2020.