Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow
Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow
复制标题
抛物线通道流中布朗刚性杆剪切引起的横向迁移
DOI：
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发表时间：
1997
影响因子：
3.7
通讯作者：
E. Hinch
中科院分区：
文献类型：
--
作者：
L. Nitsche;E. Hinch
本文研究了刚性杆在平板之间的抛物线流动中扩散和平流的横流迁移问题，这是一个具有内部(旋转)自由度的聚合物的简单模型，其概率分布取决于局部剪切速率。在横向位置y和方位角φ的空间中，通过全福克-普朗克方程的有限差分解，得到了通道内可观测的浓度分布的明确结果，为简单起见，极角θ被约束为π/2。忽略了在薄边界层中起作用的空间约束和流体动力壁面效应。这些计算表明，棒应该向墙迁移。对于广泛分离的转动和平移时间标度，渐近分析给出了这种迁移的有效输运系数。基于任意旋转Péclet数的角分布--这里是用三角基函数的最小二乘配置法得到的--壁面上的累积由有效输运系数定量地证实。将结果推广到以球谐函数为基函数的(φ，θ)取向空间中的自由旋转。最后，对聚合物迁移的传统热力学论点进行了批判，因为它们适用于纯旋转内部自由度。
This paper addresses the cross-stream migration of rigid rods undergoing diffusion and advection in parabolic flow between flat plates – a simple model of a polymer that possesses internal (rotational) degrees of freedom for which the probability distribution depends upon the local shear rate. Unequivocal results on the observable concentration profiles across the channel are obtained from a finite–difference solution of the full Fokker–Planck equation in the space of lateral position y and azimuthal angle φ, the polar angle θ being constrained to π/2 for simplicity. Steric confinement and hydrodynamic wall effects, operative within thin boundary layers, are neglected. These calculations indicate that rods should migrate toward the walls. For widely separated rotational and translational timescales asymptotic analysis gives effective transport coefficients for this migration. Based upon angular distributions at arbitrary rotational Péclet number – obtained here by a least–squares collocation method using trigonometric basis functions – accumulation at the walls is confirmed quantitatively by the effective transport coefficients. The results are extended to free rotation using spherical harmonics as the basis functions in the (φ, θ) orientation space. Finally, a critique is given of the traditional thermodynamic arguments for polymer migration as they would apply to purely rotational internal degrees of freedom.