AGGREGATION AND GELATION .2. MIXING EFFECTS IN CONTINUOUS-FLOW VESSELS

The state of mixing in a continuous flow vessel is shown to affect the extent of aggregation and the extent of aggregation at which mathemat ical gelation occurs. Three aspects of the state of mixing in vessels where aggregation alone occurs are considered: the degree of segregati on, the residence-time distribution (RTD) and the earliness or latenes s of mixing. The effect of the stare of mixing is different for each k ernel and depends primarily on the order of the moment rate law for th e zeroth and sixth moments. For example, the sum kernel has a first-or der decay moment rate law for its zeroth moment and is not affected ei ther by the degree of segregation or the earliness or lateness of mixi ng. On the other hand, the product kernel (omega = 1) has a second-ord er growth moment rate law for its sixth moment and its gelling behavio ur is strongly affected by the degree of segregation and the earliness or lateness of mixing. Our results follow directly from an analogy wi th reaction engineering based on the formal equivalence of our moment rate law for aggregating systems and a well-known reaction rate law. W e show the following striking progression of the dependence of the gel ling behaviour of the sum kernel on the RTD: it is a non-gelling kerne l in a plug flow vessel, a gelling kernel in a well-mixed vessel and a n instantaneously gelling kernel when a vessel contains a partially st agnant zone. We propose that these observations be used for predicting the effects of scale-up and also of departures from ideal mixing. For gelling kernels, any deviation from the ideal case of plug flow alway s leads to a reduction in the extent of aggregation at which mathemati cal gelation occurs. Finally, we recommend that batch experiments be u sed to obtain aggregation rate data because of the difficulty of inter preting unambiguously the data from continuous flow vessels where the state of mixing is not well defined.