The interaction of particles, drops, and bubbles with a fluid (gas or liquid) is important in a number of engineering problems. The present works seeks to extend the understanding of these interactions through numerical simulation. To model many of these relevant flows, it is often important to consider finite Reynolds number effects on drag, lift, torque and history force. Thus, the present work develops an equation of motion for spherical particles with a no-slip surface based on theoretical analysis, experimental data and surface-resolved simulations which is appropriate for dispersed multiphase flows. The equation of motion is then extended to account for finite particle size. This extension is critical for particles which will have a size significantly larger than the grid cell size, particularly important for bubbles and low-density particles. The extension to finite particle size is accomplished through spatial-averaging (both volume-based and surface-based) of the continuous flow properties. This averaging is consistent with the Faxen limit for solid spheres at small Reynolds numbers and added mass and fluid stress forces at inviscid limits. Further work is needed for more quantitative assessment of the truncation terms in complex flows.;The new equation of motion is then used to assess the relative importance of each force in the context of two low-density particles (an air bubble and a sand particle) in a boundary layer of water. This relative importance is measured by considering effects on particle concentration, visualization of particle-fluid interactions, diffusion rates, and Lagrangian statistics collected along the particle trajectory. Strong added mass and stress gradient effects are observed for the bubble but these were found to have little effect on a sand particle of equal diameter. Lift was shown to be important for both conditions provided the terminal velocity was aligned with the flow direction. The influence of lift was found to be negligible (in terms of particle concentration predictions) when terminal velocity was oriented in the wall-normal direction. The history force was shown to damp particle diffusion and have some minor impacts on particle concentration. This effect was augmented by using the creeping flow Basset expression and shows that the creeping flow expression should not be used in finite-Reynolds number conditions. The effects due to the finite-size extensions are also considered as are effects due to spatial reconstruction of the fluid properties. In general, little effect of the finite-size model or choice of spatial interpolation was observed in terms of particle concentration. However, Lagrangian statistics show some interesting sensitivities.;Finally, the new equation of motion was applied to air bubbles and sand particles of several different diameters. Particle-fluid interactions observed through flow-visualization, particle concentration, particle-wall interactions, and Lagrangian statistics were all considered. These results were interpreted and compared to heavy-particle results where appropriate. Particle deposition was found to be well-described by the heavy-particle model of Young & Leeming and root-mean-square relative velocities were found to also agree with previous heavy-particle work. A model for the latter is suggested for heavy-particles and found to work similarly well for low-density particles. Non-tracer behavior was observed for bubbles with small Stokes numbers, a result not expected based on heavy-particle expectations. Local clustering of particles was observed in certain fluid structures which may indicate the importance of modeling particle collisions in future studies.