Large deformations of a cylindrical liquid-filled membrane by a viscous shear flow
Large deformations of a cylindrical liquid-filled membrane by a viscous shear flow
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粘性剪切流导致圆柱形液体填充膜发生大变形
DOI：
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发表时间：
1987
影响因子：
3.7
通讯作者：
S. Sutera
中科院分区：
文献类型：
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作者：
G. Zahalak;P. Rao;S. Sutera
本文研究了当膜被置于另一种粘性流体的二维剪切流中时，充满不可压缩粘性流体的初始圆形、不可扩展的圆柱形膜内外产生的定常流场。内部和外部流动的雷诺数都假定为零（“爬行流动”），但在公式中没有进一步的近似。通过五阶构造了无量纲剪切速率参数的幂次自由边值问题的级数解。当与保形坐标变换相结合时，该系列给出了膜的大变形（高达2.5的纵横比）的准确结果。获得级数解所需的相当繁琐的代数运算是由计算机用符号处理程序（reduce）完成的，该程序既表述了每个连续阶的边值问题，又求解了它们。结果表明，剪切速率和流体粘度对内外速度场和压力场、膜变形及其“踏槽”频率以及膜张力的影响。这项工作表明，经典的微扰技术与计算机代数相结合，为这类问题提供了一种有用的替代纯数值方法。
This paper treats the steady flow fields generated inside and outside an initially circular, inextensible, cylindrical membrane filled with an incompressible viscous fluid when the membrane is placed in a two-dimensional shear flow of another viscous fluid. The Reynolds numbers of both the interior and exterior flows were assumed to be zero (‘creeping flow’), but no further approximations were made in the formulation. A series solution of the resulting free boundary-value problem in powers of a dimensionless shear rate parameter was constructed through fifth order. When combined with a conformal coordinate transformation this series gave accurate results for large deformations of the membrane (up to an aspect ratio of 2.5). The rather tedious algebraic manipulations required to obtain the series solution were done by computer with a symbol-manipulation program (reduce), which both formulated the boundary-value problems for each successive order and solved them. Results are presented which show how the shear rate and fluid viscosities influence the internal and external velocity and pressure fields, the membrane deformation and its ‘tank-treading’ frequency, and the membrane tension. This work demonstrates that classical perturbation techniques combined with computer algebra offer a useful alternative to purely numerical methods for problems of this type.