THE BREAKUP OF SMALL DROPS AND BUBBLES IN SHEAR FLOWS
THE BREAKUP OF SMALL DROPS AND BUBBLES IN SHEAR FLOWS
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DOI：
10.1111/j.1749-6632.1983.tb19410.x
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发表时间：
1983-01-01
影响因子：
5.2
通讯作者：
ACRIVOS, A
中科院分区：
文献类型：
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作者：
ACRIVOS, A
在许多具有实际意义的物理过程中，确定自由悬浮在另一种流体中受剪切作用的单个液滴的变形和破裂问题具有根本的重要性；例如，乳剂的流变性和一种流体相向另一种流体相的分散。GI Taylor从理论上和实验上对其进行了研究。正如他在流体力学的许多其他课题上所做的那样，他获得的定量结果不仅是该学科的第一个，而且仍然是该领域最重要和最基本的结果之一。泰勒在实验中考虑的系统如图a和b所示。将半径为a、粘度为Ap的初始球形液滴放入密度相等、粘度为p的不混相流体中。然后施加强度为G的稳定剪切，发现如果G保持在临界值G以下，液滴就会变形为稳定形状，但当G超过G时，液滴就会破裂。泰勒设立的两个剪切流”:(I)“双曲线”流,u = Gx ug与u = -Gy3,和u,被相应的速度组件沿着x和y方向,分别是一个纯粹的紧张动作没有涡度,和(2)简单的剪切流,u = Gy3 ug = 0,,众所周知,由一个纯粹的紧张动作,主轴的扩展在xy平面上沿对角线,加上一个坚实的身体绕原点旋转。在没有惯性竖架的情况下（这在泰勒的实验中确实是可以忽略不计的），除了被施加的剪切类型之外，独立参数是：C，剪切流的强度；A，初始球滴的半径，p，周围流体的粘度；A，粘度比；y，界面张力。因此，变形D=(LB)/(L+ B)，其中L和B分别为液滴的半长和半宽，成为两个无量纲群的函数，即毛细数（k- ‘ = Gwa/y）和粘度比a . Taylor ’发现，对于固定a，当毛细数k- '较小时，D与Gpa/y呈线性关系，但在一定范围内，在许多情况下，D对k曲线的斜率迅速增加，直到达到一个点，在这个点上，水滴的形状不再能保持稳定，水滴破裂。然而，在某些条件下——最明显的是在简单剪切流中出现高粘度滴（A b> > 1）——可以达到极限变形，并且不会发生滴破碎。这两种变形曲线的示例如图2所示。从实用的角度来看，最重要的量是临界剪切量
The problem of determining the deformation and burst of a single drop freely suspended in another fluid undergoing shear is of fundamental importance in a variety of physical processes of practical significance; for example, the rheology of emulsions and the dispersion of one fluid phase into another. It was studied both theoretically and experimentally by GI Taylor,’.’who, as he has with many of the other topics in fluid mechanics, obtained quantitative results that were not only the first on the subject but which remain among the most important and fundamental in this field. The systems considered experimentally by Taylor’are depicted in FIGURES la and I b. An initially spherical liquid drop of radius a and viscosity Ap was placed in a fluid, with which it was immiscible, of equal density and of viscosity p. A steady shear of strength G was then applied and the drop was found to deform into a steady shape if G was maintained below a critical value G,, but the drop broke when G exceeded G,. The two shear flows set up by Taylor’were:(I) the “hyperbolic” flow, u,= Gx, ug=-Gy3 with u, and u, being the corresponding velocity components along the x and y directions, respectively, which is a pure straining motion without vorticity, and (2) the simple shear flow, u,= Gy3 ug= 0, which, as is well known, consists of a pure straining motion, with its principal axis of extension along the diagonal in the xy plane, plus a solid body rotation about the origin.In the absence of inertial erects, which were indeed negligible in Taylor’s experiments,’the independent parameters, in addition to the type of shear being impressed, are: C, the strength of the shear flow; a, the radius of the initially spherical drop, p, the viscosity of the ambient fluid; A, the viscosity ratio; and y. the interfacial tension. Hence, the deformation, D=(LB)/(L+ B), where L and B are the half-length and the half-breadth of the drop, respectively, becomes a function of only two dimensionless groups, ie, the capillary number (k-’= Gwa/y) and the viscosity ratio, A. Taylor’found that, for fixed A, D was linear in Gpa/y for small values of the capillary number k-’, but that, beyond a certain range, the slope of the D versus k-’curve increased rapidly in many cases until a point was reached where a steady drop shape could no longer be maintained and the drop burst. There were conditions, however-most notably with high viscosity drops (A>> 1) in a simple shear flow-for which a limiting deformation was attained and drop breakup did not occur. Examples of these two types of deformation curves are sketched in FIGURE 2. From a practical point of view, the quantity of primary interest is the critical shear