Interception of two spheres with slip surfaces in linear Stokes flow
Interception of two spheres with slip surfaces in linear Stokes flow
复制标题
线性斯托克斯流中两个具有滑移面的球体的截取
DOI：
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发表时间：
2007
影响因子：
3.7
通讯作者：
C. Pozrikidis
中科院分区：
文献类型：
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作者：
Haoxiang Luo;C. Pozrikidis
研究了两个任意大小的球形粒子在无限大线性环境Stokes流中的拦截问题。颗粒表面允许根据Navier-Maxwell-Basset定律将剪切应力与切向速度相关联的滑移。在任何时刻，在原点位于一个粒子中心的参考系中，使用其旋转轴穿过第二个粒子中心的圆柱极坐标系来计算流动。利用在粒子坐标系中的流动的边界的轴对称性，问题被制定为一个系统的积分方程的第零，第一，和第二傅立叶系数的边界牵引相对于夹角。施加在每个颗粒上的力和扭矩由第零和第一傅立叶系数确定，而应力波由第零、第一和第二傅立叶系数确定。导出的积分方程求解高精度使用边界元法具有自适应单元分布和自动调整时间步长根据颗粒间的间隙。结果强烈建议存在一个临界值的滑移系数低于两个粒子的表面碰撞后，有限的拦截时间。临界值取决于相对初始粒子位置。本文讨论了简单剪切流中稀悬浮液有效粘度按浓度展开时的颗粒应力张量和线性项及二次项系数。表面滑移显著降低了两个系数和纵向颗粒自扩散系数的值。
The interception of two spherical particles with arbitrary size in an infinite linear ambient Stokes flow is considered. The particle surfaces allow for slip according to the Navier–Maxwell–Basset law relating the shear stress to the tangential velocity. At any instant, the flow is computed in a frame of reference with origin at the centre of one particle using a cylindrical polar coordinate system whose axis of revolution passes through the centre of the second particle. Taking advantage of the axial symmetry of the boundaries of the flow in the particle coordinates, the problem is formulated as a system of integral equations for the zeroth, first, and second Fourier coefficients of the boundary traction with respect to the meridional angle. The force and torque exerted on each particle are determined by the zeroth and first Fourier coefficients, while the stresslet is determined by the zeroth, first, and second Fourier coefficients. The derived integral equations are solved with high accuracy using a boundary element method featuring adaptive element distribution and automatic time step adjustment according to the inter-particle gap. The results strongly suggest the existence of a critical value for the slip coefficient below which the surfaces of two particle collide after a finite interception time. The critical value depends on the relative initial particle positions. The particle stress tensor and coefficients of the linear and quadratic terms in the expansion of the effective viscosity of a dilute suspension in terms of the concentration in simple shear flow are discussed and evaluated. Surface slip significantly reduces the values of both coefficients and the longitudinal particle self-diffusivity.