二分量带电胶体悬浮系统的等效硬球模型

Effective hard sphere model of two-component charged colloidal suspensions

研究由无限稀薄的靶粒子散布于有限浓度 (体积分数为)的主粒子悬浮液中而组成的二分量带电胶体系统 ,计算了靶粒子的短时间平动和转动自扩散系数 .当系统中的粒子浓度和电解质浓度都不太高时 ,只考虑流体力学相互作用对扩散张量的首项两体贡献 .为了计算体系的对分布函数 ,在数值计算的基础上发展了一个等效硬球模型 ,近似地把主粒子和靶粒子看作等效半径为δEHS的相同硬球粒子 .结果表明 。

The charge-stabilized binary colloidal suspensions composed of the host particles (with volume fraction phi and radius a(H)) and tracers (the density of which is very dilute and the radius is a(r)) are studied. We have obtained the numerical results of the short-time translational and rotational tracer-diffusion coefficients, H(s,r)(t) and H(s,r)(r), respectively. In this paper, we would give a plain physical picture of the numerical calculations and therefore use some approximations. Firstly, only the leading two-body hydrodynamic interaction term of the diffusion tensor is taken into account for systems with low particle density and low salinity. Secondly, we develop an effective hard sphere (EHS) model to calculate the pair distribution function of the system in which the particles are strongly charged and the size ratio of the two particles lambda = a(r)/a(H) is not largely different from 1. That is, both the host and tracer particles are regarded as the same hard spheres with the phi-dependent effective diameter delta(EHS). The EHS model indicates the interesting nonlinear scaling relations H(s)(r), (r) approximate to lambda(3)A(r)phi(2) and H(s,r)(t) approximate to 1 - lambdaA(t)phi(4/3). Here A(r) and A(t) are two factors which are independent of the particle densities and charges, and can be determined by approximating the pair distribution function with step function or with Percus-Yevick equation and semi-analytical methods. The calculated results show that these relations fit quite well with the numerical results.