Cluster breakup

Al-Roub et all421 identified three basic modes of liquid breakup during droplet impingement onto a liquid film (1) rim breakup, (2) cluster breakup, and (3) column breakup. The rim breakup mode involves the breakup and ejection of one or a few small droplets at the outer edge of the film, while the cluster breakup mode involves the breakup of liquid into clusters of many small droplets at the outer edge of the film. In the column breakup mode, liquid breaks up into one or a few droplets from a column of liquid at the center of the spreading droplet as a result of the surface waves reflecting back to their source. The diameter and number of the... 

The second cluster analysis involved attaching twice as much importance to the interaction term than to any of the other 12 attributes. We obtained basically the same cluster tree as with the first method, with only a few modifications some cluster breakups were more severe than before, indicating more cluster-to-cluster distinctiveness, and some were less severe. Inspection of the tree indicated that there were either two clusters, in which case one cluster was approximately twice as big as the other cluster, or there were three clusters, with the larger cluster subdivided into two clusters. (See Figure 4.) Further examination of spatial plots revealed no clear separation of cluster, whether the number of clusters was designated two or three (Figures 5a and b),... 

X is the crossover time when the balance between the aggregation processes is established. The validity of this approach was confirmed by Montecarlo simulations of the full equation using a constant coagulation kernel and a breakup probability equal to k(i+j) where a and k were adjustable parameters [15]. Spatial fluctuations were compensated by cluster breakup and the generalized Smoluchowski equation had a critical dimension dc < 1. 

Several works over the past decade or so (Ziff, 1991 Ziff and McGrady, 1986 McGrady and Ziff, 1987,1988 and Williams, 1990) have addressed the behavior of systems with specified breakup kernels. Certain specific forms for the breakup kernels lead to analytical solutions for the cluster size distribution. For example, Ziff (1991) obtained explicit forms of the size distribution for homogeneous breakup kernels of the form... 

A solution to this problem (Hansen and Ottino, 1996a) reveals that the cluster size distribution is bimodal, as expected, with c(x,t) for large x dependent upon the initial conditions (Fig. 35a). The distribution thus does not approach a self-similar form and the scaling results just given are not valid for this problem. This is a result of the non-homogeneous relative rate of breakup. 

To determine the existence of stable steady state, a model [109] was studied of the destmction of clusters in the case vp = 700. At the initial instant of time 10 uniformly distributed clusters of 300 vacancies each, were put into the crystal , and interstitial atoms in the intervals between them (Uq 10). Then pairs of randomly distributed defects of different types were created in the crystal . The newly generated defects break up the orginally existing clusters and the concentration of defects declines to a steady-state value. The values of Uo were obtained by averaging a region of the curve of length 2.5 x 104 events of defect creation. The result unambiguously implies the existence of stable steady state in the problem of accumulation of point defects and in the problem of breakup of clusters. 

A competing reaction is trimerization to Fc3(CO)i2. This process can be reversible and the dimers or clusters are suitable staging grounds for breakup of the clusters. These often lead to complex equilibria, which have been investigated by Bor and coworkers for a number of systems. ... 

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