高浓度悬浮液中可渗透颗粒的短时间动力学。

Institute of Theoretical Physics, University of Warsaw, Hoza 69, Warsaw 00-681, Poland.

J Chem Phys. 2010 Jan 7;132(1):014503. doi: 10.1063/1.3274663.

We study short-time diffusion properties of colloidal suspensions of neutral permeable particles. An individual particle is modeled as a solvent-permeable sphere of interaction radius a and uniform permeability k, with the fluid flow inside the particle described by the Debye-Bueche-Brinkman equation, and outside by the Stokes equation. Using a precise multipole method and the corresponding numerical code HYDROMULTIPOLE that account for higher-order hydrodynamic multipole moments, numerical results are presented for the hydrodynamic function, H(q), the short-time self-diffusion coefficient, D(s), the sedimentation coefficient K, the collective diffusion coefficient, D(c), and the principal peak value H(q(m)), associated with the short-time cage diffusion coefficient, as functions of porosity and volume fraction. Our results cover the full fluid phase regime. Generic features of the permeable sphere model are discussed. An approximate method by Pusey to determine D(s) is shown to agree well with our accurate results. It is found that for a given volume fraction, the wavenumber dependence of a reduced hydrodynamic function can be estimated by a single master curve, independent of the particle permeability, given by the hard-sphere model. The reduced form is obtained by an appropriate shift and rescaling of H(q), parametrized by the self-diffusion and sedimentation coefficients. To improve precision, another reduced hydrodynamic function, h(m)(q), is also constructed, now with the self-diffusion coefficient and the peak value, H(q(m)), of the hydrodynamic function as the parameters. For wavenumbers qa>2, this function is permeability independent to an excellent accuracy. The hydrodynamic function of permeable particles is thus well represented in its q-dependence by a permeability-independent master curve, and three coefficients, D(s), K, and H(q(m)), that do depend on the permeability. The master curve and its coefficients are evaluated as functions of concentration and permeability.

我们研究了中性可渗透粒子胶体悬浮液的短时间扩散性质。单个粒子被建模为相互作用半径为 a 和均匀渗透性 k 的溶剂可渗透球体，粒子内部的流体流动由 Debye-Bueche-Brinkman 方程描述，而外部由 Stokes 方程描述。使用精确的多极方法和相应的数值代码 HYDROMULTIPOLE，考虑了更高阶的流体动力多极矩，给出了流体动力函数 H(q)、短时间自扩散系数 D(s)、沉降系数 K、集体扩散系数 D(c)和与短时间笼扩散系数相关的主峰值 H(q(m))的数值结果，这些都是作为孔隙率和体积分数的函数。我们的结果涵盖了整个流体相状态。讨论了可渗透球体模型的一般特征。Pusey 确定 D(s)的近似方法被证明与我们的精确结果非常吻合。结果表明，对于给定的体积分数，在给定的体积分数下，单个主曲线可以估计减少的流体动力函数的波数依赖性，而与粒子渗透性无关，该主曲线由硬球模型给出。通过适当的平移和缩放 H(q)来获得简化形式，其参数由自扩散和沉降系数表示。为了提高精度，还构建了另一个简化的流体动力函数 h(m)(q)，现在将自扩散系数和流体动力函数的峰值 H(q(m))作为参数。对于波数 qa>2，该函数的渗透性独立精度非常高。因此，可渗透粒子的流体动力函数在其 q 依赖性方面由一个与渗透性无关的主曲线和三个依赖于渗透性的系数 D(s)、K 和 H(q(m))很好地表示。主曲线及其系数被评估为浓度和渗透性的函数。