Spherical particle in Poiseuille flow between planar walls.
Spherical particle in Poiseuille flow between planar walls.
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平面壁之间的泊肃叶流中的球形粒子。
DOI：
10.1063/1.1738637
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
R. Jones
中科院分区：
文献类型：
--
作者：
R. Jones
我们研究了悬浮在牛顿流体中的具有入射泊肃叶流的平面平行壁之间的球形介粒子。使用二维傅里叶变换技术，我们获得了描述该几何中蠕动流的斯托克斯方程的格林张量的对称解析表达式。根据完全矢量调和基的格林张量的矩阵元素，我们获得了球体的摩擦矩阵。格林张量的矩阵元素的计算大部分是通过分析完成的，将这些元素的评估简化为一维数值积分。笛卡尔形式的大阻力和迁移率矩阵以 13 个标量摩擦和迁移率函数给出，这些函数以球基计算的某些矩阵元素表示。这些函数的数值计算显示出良好的收敛性，并且与早期基于边界配置的数值计算一致。对于相对于粒子半径而言宽的通道宽度，我们表明由单壁函数的叠加定义的近似是相当准确的，但对于窄通道来说它具有很大的误差。在双壁几何结构中，描述平移-旋转耦合的摩擦和移动函数随着两壁之间的位置而改变符号。通过对受到外部场产生的扭矩作用的极性粒子进行斯托克斯动力学计算，我们发现平移-旋转耦合会引起与流体流动方向成直角的侧向迁移。
We study a spherical mesoparticle suspended in Newtonian fluid between plane-parallel walls with incident Poiseuille flow. Using a two-dimensional Fourier transform technique we obtain a symmetric analytic expression for the Green tensor for the Stokes equations describing the creeping flow in this geometry. From the matrix elements of the Green tensor with respect to a complete vector harmonic basis, we obtain the friction matrix for the sphere. The calculation of matrix elements of the Green tensor is done in large part analytically, reducing the evaluation of these elements to a one-dimensional numerical integration. The grand resistance and mobility matrices in Cartesian form are given in terms of 13 scalar friction and mobility functions which are expressed in terms of certain matrix elements calculated in the spherical basis. Numerical calculation of these functions is shown to converge well and to agree with earlier numerical calculations based on boundary collocation. For a channel width broad with respect to the particle radius, we show that an approximation defined by a superposition of single-wall functions is reasonably accurate, but that it has large errors for a narrow channel. In the two-wall geometry the friction and mobility functions describing translation-rotation coupling change sign as a function of position between the two walls. By Stokesian dynamics calculations for a polar particle subject to a torque arising from an external field, we show that the translation-rotation coupling induces sideways migration at right angles to the direction of fluid flow.