This paper presents a new generation coalescence kernel that is capable of modeling various seemingly contradictory experimental observations. The proposed kernel is size-independent with the added feature that only collisions with an effective size less than a critical value is successful. Simulation studies based on this approach show that a variety of seemingly contradictory experimental observations can be modeled by this kernel. If the critical size is high enough, this kernel becomes size-independent possessing the characteristics of the so called 'constant' kernel. In addition, the kernel clearly demonstrates the three regimes of granulation as proposed by Kapur and Fuerstenau [P.C. Kapur, D.W. Fuerstenau, Trans. AIME 229 (1964) 348-355.] and compares favorably well with the performance of the two stage sequential model developed by Adetayo et al. [A.A. Adetayo, J.D. Litster, S.E. Pratsinis, B.J. Ennis, Powder Tech. (1995).] for the drum granulation of fertilizer salts. This approach could be used to develop models for simulation, control and start-up studies.