Many-body microhydrodynamics of colloidal particles with active boundary layers
Many-body microhydrodynamics of colloidal particles with active boundary layers
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DOI：
10.1088/1742-5468/2015/06/p06017
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发表时间：
2014-11
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影响因子：
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通讯作者：
Rajesh K. Singh;Somdeb Ghose;R. Adhikari
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文献类型：
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作者：
Rajesh K. Singh;Somdeb Ghose;R. Adhikari
具有活跃边界层的胶体颗粒（非平衡过程产生大速度梯度的颗粒周围区域）在许多物理、化学和生物环境中很常见。边界层边缘的速度或应力决定了外部流体流动，从而决定了多体颗粒间流体动力相互作用。在这里，我们提出了一种计算由外部微流体动力流引起的 N 个球形活性粒子之间的多体流体动力相互作用的方法。首先，我们使用斯托克斯方程的边界积分表示来消除体流体自由度。然后，我们在张量球谐函数的无限维基础上展开积分表示的边界速度和牵引力，并在每个粒子表面上施加弱意义上的边界条件，获得未知展开系数的线性代数方程组。无限级数的截断（由所需的精度确定）产生可以通过迭代方法准确有效地求解的有限线性系统。该解决方案将未知的刚体运动与已知的膨胀系数值线性相关，从而促进了推进矩阵的引入。这些矩阵完全表征了主动悬架中的流体动力相互作用，就像迁移率矩阵完全表征了被动悬架中的流体动力相互作用一样。问题维数的降低，从三维偏微分方程到二维积分方程，允许在多核计算架构上动态模拟数十万个活动粒子。在对谐波陷阱中 104 个活性胶体粒子的模拟中，我们发现获得稳态对流（即所谓的“自组装泵”）的必要且充分的成分是（a）单体自推进和（b）来自陷阱中引起的斯托克斯勒涡量的两体旋转。
Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.