Population balance equation, dispersive growth

The fundamental derivation of the population balance equation is considered general and not limited to describe gas-liquid dispersions. However, to employ the general population balance framework to model other particulate systems like solid particles and droplets appropriate kernels are required for the particle growth, agglomeration/aggregation/coalescence and breakage processes. Many droplet and solid particle closures are presented elsewhere (e.g., [96, 122, 25, 117, 75, 76, 46]). 

The state (py, pg, pj) = (p, 0,0) is the final state, is stable, and represents a completely invaded state where all the host cells were killed producing new viruses. We are interested in studying a front of invasion connecting both states. Since lysis of bacteria results in a precipitous dechne in the culture turbidity, virus population growth produces circular clearings called plaques. The growth of these plaques in size is not only a result of the kinetics but also due to the dispersal movement of the viruses within the bacterial culture. To derive an equation for vims dispersal in agar, we start with the mesoscopic balance equation for the vims density at point x at time t obtained from Model C (see Sect. 3.4.3) [121] ... 

---