Identification of the Effective Diffusivity Coefficient of Polydisperse Spherical Suspension by using Random Point Approximation

The so-called Random Point Approximation (RPA) is applied to identifying the effective diffusivity of a polydisperse spherical suspension. The RPA is based on truncated Volterra-Wiener Expansion (VWE) with basis function which is a random point function of perfect-disorder type. The VWE is applied consistently to derive the equations for the kernels. The contributions of the different kernels to the overall (effective) modulus are identified. An approximate model based on power-series expansion of the kernels with respect to the volume fraction is developed. It is argued that the contribution of the pure binary interaction (two-sphere solution) is negligible for moderately concentrated suspensions. The quadratures that give the contribution to the effective modulus are derived. The issue connected with the application of the fourth-order (one-sphere solution) are tackled, by evaluating some new kind of integrals.