On the effective thermal conductivity of a random suspension of spheres

We consider the effective thermal conductivity, λ¹, of a random suspension of spheres in the limit of small concentrations. The results are also directly applicable to a variety of other transport properties, e.g. electrical or magnetic. We study the problem using an iterative procedure and introduce nearest neighbor probability density functions. To lowest order we find the expression for a well separated geometric arrangement. To next order we obtain the effects of sphere interaction. We treat a number of probability density functions and consider the effect of clustering. The results are then studied in relation to the bounds for λ¹ which have been found previously.