A method for the calculation of the effective transport properties of suspensions of interacting particles

摘要: The early attempts at calculating effective transport properties of suspensions interacting spherical particles resulted in non-absolutely convergent expressions. In this paper we provide a physical interpretation for these convergence difficulties and present new method determining the which clarifies existing methods. This method, is described simplicity context thermal conduction problem, based on an expression that gives temperature gradient ∇ T point x matrix terms integrals over surrounding integral large surface Γ encloses term ‘macroscopic boundary’. Without Γ, would be convergent, contribution to ( ) from distant particle proportional 1/ r 3 , where distance . On comparing with formula used by Rayleigh (1892) his investigation conductivity cubic array spheres, find Rayleigh's arose simply incorrect assessment macroscopic boundary integral. By combining dipole strength sphere placed ambient field, obtain relating particles. An random suspension spheres correct O (ϕ 2 obtained averaging strength. similar procedure expressions viscosity elastic moduli ). Most results have been earlier workers using ‘renormalization’ due Batchelor; presented here has advantage renormalization quantity arises naturally referred earlier, so there no uncertainty about its choice.