Suspensions are ubiquitous in nature (e.g., milk, blood, crude oil) and in different industries (e.g., food or pharmaceutical). Understanding how the suspended particles affect the macroscopic flow and properties of the suspension is the prerequisite to design and optimize the flow and processes which involve suspensions. The shape of the particles can be irregular, e.g., asphaltene aggregates in heavy crude oil, sedimentation and dispersion of particles in oceans/atmosphere, shape-anisotropic particles in colloidal crystals to produce robust photonic band-gap materials, colloidal lithography for nanopatterns, or hierarchically structured porous materials with high surface-to-volume ratios for catalyst supports. We are extending our current numerical tools to simulate the flow of many particles with arbitrary shapes and sizes. The main challenge that we are tackling in simulating many particles with irregular shapes is identifying and modeling their collisions. In contrast to spherical particles, the collision of irregularly shaped particles cannot be determined just by the distance between their centroids.