Semi-analytical solutions for two-dimensional elastic capsules in Stokes flow
Semi-analytical solutions for two-dimensional elastic capsules in Stokes flow
复制标题
斯托克斯流中二维弹性胶囊的半解析解
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Booty
中科院分区：
文献类型：
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作者：
M. Higley;M. Siegel;M. Booty
弹性胶囊在自然界中以细胞和囊泡的形式出现，并被制造用于生物医学应用。它们被广泛地建模，但很少有分析结果。本文利用复变技术，导出了Stokes流中内部无粘的二维弹性胶囊的稳态响应和随时间演化的半解析解。这提供了初始圆形胶囊在线性应变和剪切流动中作为毛细管数Ca的函数的稳定响应的完整图像。这一分析还得到了时间相关演化的光谱精确数值计算的补充。用来模拟泰勒四辊磨机远场速度的外加非线性应变被发现在Hookean胶囊的临界毛细管数CAC处导致了尖峰稳定的形状。对Ca>；CAC随时间演化的数值模拟显示了有限时间尖点奇点的发展。尖点形成前的动力学是渐近自相似的，相似指数被解析地预测并被数值证实。这是具有弹性界面的流体流动中有限时间奇异性形成的有力证据。
Elastic capsules occur in nature in the form of cells and vesicles and are manufactured for biomedical applications. They are widely modelled, but there are few analytical results. In this paper, complex variable techniques are used to derive semi-analytical solutions for the steady-state response and time-dependent evolution of two-dimensional elastic capsules with an inviscid interior in Stokes flow. This provides a complete picture of the steady response of initially circular capsules in linear strain and shear flows as a function of the capillary number Ca. The analysis is complemented by spectrally accurate numerical computations of the time-dependent evolution. An imposed nonlinear strain that models the far-field velocity in Taylor's four-roller mill is found to lead to cusped steady shapes at a critical capillary number Cac for Hookean capsules. Numerical simulation of the time-dependent evolution for Ca>Cac shows the development of finite-time cusp singularities. The dynamics immediately prior to cusp formation are asymptotically self-similar, and the similarity exponents are predicted analytically and confirmed numerically. This is compelling evidence of finite-time singularity formation in fluid flow with elastic interfaces.