Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland.
J Chem Phys. 2010 Aug 28;133(8):084906. doi: 10.1063/1.3474804.
We determine the high-frequency limiting shear viscosity, eta(infinity), in colloidal suspensions of rigid, uniformly porous spheres of radius a as a function of volume fraction phi and (inverse) porosity parameter x. Our study covers the complete fluid-state regime. The flow inside the spheres is modeled by the Debye-Bueche-Brinkman equation using the boundary condition that fluid velocity and stress change continuously across the sphere surfaces. The many-sphere hydrodynamic interactions in concentrated systems are fully accounted for by a precise hydrodynamic multipole method encoded in our HYDROMULTIPOLE program extended to porous particles. A truncated virial expansion is used to derive an accurate and easy-to-use generalized Saito; formula for eta(infinity). The simulation data are used to test the performance of two simplifying effective particle models. The first model describes the effective particle as a nonporous sphere characterized by a single effective radius a(eff)(x)<a. In the more refined second model, the porous spheres are modeled as spherical annulus particles with an inner hydrodynamic radius a(eff)(x) defining the nonporous dry core and characterizing hydrodynamic interactions, and an outer excluded volume radius a characterizing the unchanged direct interactions. Only the second model is in a satisfactory agreement with the simulation data.
我们确定了刚性、均匀多孔球胶体悬浮液的高频剪切黏度 η(infinity)，作为半径 a、体积分数 φ 和（倒数）孔隙率参数 x 的函数。我们的研究涵盖了完整的流体状态范围。使用边界条件，即流体速度和应力在球表面连续变化，通过 Debye-Bueche-Brinkman 方程来模拟球内的流动。在浓度较高的系统中，通过我们的 HYDROMULTIPOLE 程序中编码的精确的多球流体动力学方法来充分考虑多球流体动力学相互作用，该程序扩展到多孔粒子。采用截断的 Virial 展开式推导出了一个准确且易于使用的广义 Saito 公式，用于计算 η(infinity)。模拟数据用于测试两种简化的有效粒子模型的性能。第一种模型将有效粒子描述为具有单个有效半径 a(eff)(x)<a 的非多孔球体。在更精细的第二种模型中，多孔球体被建模为具有内流体力半径 a(eff)(x)的球形环粒子，该半径定义了无孔干核并描述了流体动力学相互作用，以及外排除体积半径 a 描述了不变的直接相互作用。只有第二种模型与模拟数据吻合良好。
