Analytical solutions are derived for both orthokinetic and perikinetic coagulation rate mechanisms by considering bikinetic collisions of the agglomerating particles. The bikinetic behavior assumes that only equal-sized particles collide to form larger aggregates. In addition to the bikinetic assumption used to simplify the rate equations, the coagulating particles are assumed to approach a maximum size class with increasing time. Mechanisms of perikinetic, orthokinetic, differential sedimentation, and flow-induced breakup were examined in the analyses. A solution incorporating flow-induced breakup forced the equilibrium population to a maximum size class that was less than an initially assumed maximum size class, consistent with coagulation modeling. This breakup equation is shown to be beneficial to researchers seeking to develop predictive models for orthokinetic coagulation by establishing estimates for breakup constants. The new solutions are contrasted with the existing simplified models and found to be more characteristic of actual coagulation behavior. The new solutions approach a maximum particle size class and conserve mass at increasing time, rather than an asymptotic approach to zero particles or zero mass as predicted by the existing models. Applications of the new coagulation rate solutions are useful in estimating particle collision efficiency and breakup rate constants and in determining the accuracy of numerical simulations of coagulation processes.