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The ·dissertation is divided into six chapters. The first chapter contains introductory remarks and sets the scene for the work that is to follow. Chapter 2 is devoted to the conduction of heat or electricity through granular materials, the conductivity of the grains greatly exceeds that of the matrix and the grains are closely-packed. Frornan analysis of the temperature distribution near the point of contact between a pair of particles we derive an expression for the effective conductivity of this type of material. In chapter 3 we study the conduction of heat across a bundle of fibres. It is shown that small deviations in fibre straightness or in fibre alignment have a marked effect on the conductivity of these types of materials, and expressions are obtained for the effective conductivity of two classes of fibre bundles. The work in chapter 4 is concerned with general aspects of the determination of effective transport properties. A new method is described for obtaining the effective transport properties of suspensions of interacting spherical particles in both regular and random arrays. This new method does not encounter divergence difficulties, and provides a rigorous basis for the rather ad hoc procedures devised earlier to deal with divergence difficulties. Some old results are rederived by these new techniques and expressions are obtained for the effective modulus of compr ession of r igid spheres in random and regular arrays in an elastic matrix. Chapter 5 is devoted to a study of the coagulation of particles in shear flow. We are mainly concerned with the coagulation of particles at "high" shear_ rates, in which case the Brew nian motion of the particles is negligible and the Van der Waals forces between the particles only affect the motion of nearly touching particles. Expressions are obtained for the rate at which single spherical particles coagulate for form doublets, per unit volume of suspension. Finally, in chapter 6 we present the results of a numerical study on the effect of Van der Waals attraction and electrical repulsion on the motion of a pair of spherical particles in shear flow. It is shown that at very low shear rates, pairs execute closed orbits about each other. As the shear rate increases the pairs are pulled apart, and finally, at very high shear rates pairs are pushed together with such force by the flow that some are able to overcome the electrical repulsive forces and coagulation occurs.