剪切流中液滴变形破碎机理的分析研究

G. Ivanitsky, B. Tselen, N. Radchenko, L. P. Gozhenko
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摘要

剪切流中液滴的变形和破碎问题在学术界和实践中都引起了广泛的关注。液滴分解在工程和生物医学领域有着广泛的应用,包括乳剂、气雾剂等的生产和加工。尽管液滴破碎操作广泛应用于各个行业,然而,迄今为止,对导致剪切流中分散体破碎的物理机制还没有明确的处理。本文考虑了建立一个数学模型的原理,该模型可以预测黏性液体剪切流动中初始球形液滴在大范围流型上的演变以及两种液相的物理参数。建立了一个数学模型,描述了悬浮在另一种非混相液体中的单个液滴在流体动力、毛细力和耗散粘性力三种力共同作用下的变形。本文讨论了这些作用力对液滴变形过程的影响。研究的重点是更深入地分析剪切流中液滴变形的动力学以及与当前液滴形状相关的过渡效应。特别注意的是分析了导致液滴破坏的不可逆变形发生的临界条件。假设变形液滴为长椭球体形式。液滴变形被认为是半液滴质心的运动,相对于液滴中心是对称的。给出了剪切流中液滴变形的数值计算结果,并与其他作者的实验数据进行了比较。得到了剪切流中液滴破坏的一个简单判据。分析结果证实了模型的可靠性和假设的胜任性。与现有的经验关系相比,该模型能够以更高的精度预测已知操作参数的剪切流中液滴变形的性质及其破坏条件。
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ANALYTICAL STUDY OF THE MECHANISM OF DROPLET DEFORMATION AND BREAKUP IN SHEAR FLOWS
The problem of drop deformation and breakup in shear flow represents academic and practical interest and has attracted close attention over the intervening decades. Drop breakup is important for a wide range of engineering and biomedical applications including production and processing of emulsions, aerosols, etc. Although drop breakup operations are widely used in various industries, however, till quite presently there is no unequivocal treatment of the physical mechanism, which causes the fragmentation of dispersions in shear flows. In this paper the principles of constructing a mathematical model, which predicts the evolution of initially spherical droplet in shear flows of viscous liquid over a wide range of flow regimes as well physical parameters of both liquid phases, are considered. A mathematical model is presented that describes the deformation of a single drop suspended in another immiscible liquid under the combined action of three forces, namely, hydrodynamic force, capillary force and dissipative viscous force. The influence of each of these forces on the process of droplet deformation is discussed in the paper. The focus of the study is to more deeply analyze the dynamics of droplet deformation in shear flows and the transitional effects associated with current droplet shapes. Particular attention is paid to the analysis of critical conditions for the onset of irreversible deformation of droplets, which leads to their destruction. The deformed droplet is assumed to be in the form of prolate ellipsoid of revolution. The drop deformation is regarded as motion of the centers mass of the half-drops, symmetrical with respect to the drop center. The results of numerical calculations for droplet deformation in shear flows in comparison with experimental data of other authors are presented. A simple criterion for destruction of droplets in shear flows has been obtained. The results of the analysis confirm the reliability of the model and the competency of the assumption made. The model is able to predict the nature of droplet deformation and the conditions for their destruction in shear flows with known operating parameters with a greater degree of accuracy than the existing empirical relationships.
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