Exact tensor closures for the three-dimensional Jeffery's equation
Exact tensor closures for the three-dimensional Jeffery's equation
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三维 Jeffery 方程的精确张量闭包
DOI：
10.1017/jfm.2011.165
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发表时间：
2011
影响因子：
3.7
通讯作者：
Douglas E. Smith
中科院分区：
文献类型：
--
作者：
S. Montgomery;Wei He;D. Jack;Douglas E. Smith
本文给出了由三维Jeffery方程的二阶矩张量计算四阶矩张量的精确公式。虽然这种方法属于福尔斯一类的矩张量封闭，它不依赖于近似，无论是分析或曲线拟合，四阶矩张量做以前的封闭。这种闭合在辛特拉和塔克（J. Rheol.，vol.39，1995，p.1095），或等价地，Verleye & Dupret（Developments in Non-Newtonian Flow，1993，p.139）意义上的自然闭合。这些明确的公式的存在已断言以前，但据作者所知，明确的形式尚未公布。该公式涉及椭圆积分，并有效时，纤维取向是各向同性在某个时间点。最后，本文给出了求解Jeffery方程的快速精确闭包法，它不需要近似闭包，也不需要椭圆积分计算。
This paper presents an exact formula for calculating the fourth-moment tensor from the second-moment tensor for the three-dimensional Jeffery's equation. Although this approach falls within the category of a moment tensor closure, it does not rely upon an approximation, either analytic or curve fit, of the fourth-moment tensor as do previous closures. This closure is orthotropic in the sense of Cintra & Tucker (J. Rheol., vol. 39, 1995, p. 1095), or equivalently, a natural closure in the sense of Verleye & Dupret (Developments in Non-Newtonian Flow, 1993, p. 139). The existence of these explicit formulae has been asserted previously, but as far as the authors know, the explicit forms have yet to be published. The formulae involve elliptic integrals, and are valid whenever fibre orientation was isotropic at some point in time. Finally, this paper presents the fast exact closure, a fast and in principle exact method for solving Jeffery's equation, which does not require approximate closures nor the elliptic integral computation.