This research thesis considers non-linear and transient interactions between particles flowing through viscous fluid. These interactions may arise due to different transport mechanisms. In the present work we focus on two major mechanisms: (i) convective heat transport due to interfacial flow and (ii) momentum advection due to fluid inertia.

   First we consider the influence of the weak convective transport on the spontaneous thermocapillary interaction of spherical fluid particles caused by the local variations in their surface properties as a result of interphase mass transfer. It is found that the spontaneous attraction of droplets is retarded as a result of the weak convective mass transport, while their repulsion is enhanced. It means that the convective transport acts to smoothen the inhomogeneities of the concentration of the transferring substance in the continuous phase and to oppose coalescence. Next, we examine the effect of the weak convective heat transport arising due to interfacial flow on the thermocapillary interaction of spherical gas bubbles moving under the externally imposed temperature gradient. Our theory suggests that the convective heat transport results in a relative motion of equal-sized bubbles, that otherwise migrate with the same velocities when the conduction is the only transport mechanism. The tendency of the bubbles of the same size to cluster in plane normal to the direction of the applied temperature gradient, which was previously predicted in direct numerical simulations, is shown analytically. The tendency of unequal bubbles to segregate by size in the course of their migration that was also observed in the numerical simulations, is also predicted by our theory.

     Finally we consider the influence of the fluid inertia on the motion of rigid particles in a viscous fluid. It is found that the leading effect of the fluid inertia on particles' velocity in the long-time limit scales as given that the Stokeslet strength associated with disturbance flow field changes with time. We revisit the classical problem of particles settling in a constant gravity field and show that the leading effect of fluid inertia in this case scales as Re. As illustration the Oseen velocity of the two spherical particles falling along the line of their centers is calculated and it is shown that the particles would approach each other as a result of their inertial interaction.