Capture radius

Illustration Aggregation in chaotic flows with constant capture radius. 

Here we consider aggregation in a physically realizable chaotic flow, the journal bearing flow or the vortex mixing flow described earlier. The computations mimic fast coagulation particles seeded in the flow are convected passively and aggregate upon contact. In this example the clusters retain a spherical structure and the capture radius is independent of the cluster size. 

Fig. 39. (a) The growth of average cluster size for clusters with a constant capture radius in various 2D flows, (b) Variation of polydispersity with average cluster size, (c) Scaled distribution of the cluster sizes at different times. The regular flow is the journal bearing flow with only the inner cylinder rotating. One time unit is equivalent to the total displacement of the boundaries equal to the circumference of the outer cylinder (Hansen and Ottino, 1996b). 

Illustration Aggregation of area-conserving clusters in two dimensional chaotic flows. Particles, converted passively in a two-dimensional chaotic flow, aggregate on contact to form clusters. The capture radius of the clusters increases with the size of the cluster. Since these simulations are in two dimensions, the area of the aggregating clusters is conserved. 

Note that only one system, the one corresponding to constant capture radius clusters in chaotic flows, behaves as expected via mean field predictions. In general, the average cluster size grows fastest in the well-mixed system. However, in some cases the average cluster size in the regular flow grows faster than in the poorly mixed system. 

Grows algebraically for compact structures linearly for constant capture radius clusters in a well-mixed system. 

An equation of the type (16) makes most physical sense when there exists a large capture radius Rc however, it can be applied to any diatomic capture case if regarded simply as a definition of Rc. Its utility is twofold. For one thing, physical common sense can sometimes give a value, or a bound, for Rc. When there is a Coulomb attraction between the reacting species, as for our case of H+ and A-, Rc can be plausibly estimated from... 

Consider first the fate of an H+. In a region with an average density nB of B- ions, each with a Coulomb capture radius of the order of 50A [from (17)], the mean lifetime rc of an H+ with respect to capture into BH will... 

A simple but risky assumption would be that r2 1 is given by an equation analogous to (20) with a capture radius Rc of the order of atomic dimensions. Then, t2 > 2hr at 250°C would imply a binding energy AE2 for the reaction (132)... 

The effective neutron capture radius of a nucleus having a cross section by 1.0 barn, calculated ... 

---