Particle size correlations and the effects of limited mixing on agglomerating particulate systems
Abstract Population balance equations for particulate systems are derived based on two basic but tacit assumptions. The first is that a local volume of thorough particle mixing exists over which a more detailed balance equation may be averaged to obtain the population balance equation. The second is that there is a large enough population in the mixing volume that particle correlation effects do not become important. Both the foregoing assumptions are investigated for Brownian agglomeration. The volume of mixing is estimated by scaling arguments. Monte Carlo simulation techniques have been used to show that particle populations in the local mixing volume may be sufficiently small to cause correlation effects implying that the population balance predictions can be in error.
The Statistical Foundation of Population Balances
This chapter deals with the statistical foundation of the population balance equation. As a smooth function capable of differentiation with respect to time as well as particle state coordinates, the number density in the population balance equation is clearly an averaged quantity. Thus the population balance equation is to be considered as an “averaged” equation designed to predict average information. When dealing with stochastic problems, it is clear that one is frequently faced with lack of closure, especially in situations where interaction occurs between particles or between particles and their environment. Such lack of closure arises because of the development of correlations between particle states promoted by preferential behavior between particle pairs of specific states or between the particle and its environment. The population balance equation, which generally comes about by making the crudest closure approximation, does not make accurate predictions in such cases of the average behavior of the system.
Proliferative kidney disease: first reported outbreak in North America
Abstract. Proliferative kidney disease (PKD) was diagnosed in rainbow trout, Salmo gairdneri Richardson, at the Hagerman, Idaho, State Fish Hatchery. Wild fish from Riley Creek, one of the hatchery water supplies, were infected with PKD organisms. Clinical signs, gross pathology and histopathology of affected fish were typical of those reported for PKD in salmonids from European hatcheries. In addition to lesions normally seen, we observed a severe vasculitis and occlusion of renal and hepatic vessels. Ultrastructure of the PKD organism and possible inclusion body production sites are described. The disease outbreak was complicated by the presence of other infectious diseases. This is the first recorded outbreak of PKD in North America.