Breakage frequency

Ratcliffe, D.A. (1970). Changes attributable to pesticides in egg breakage frequency and eggshell thickness in British Birds. Journal of Applied Ecology 7, 67-107. 

Werfel U, Langen V, Eickhoff I, et al. 1998. Elevated DNA single-strand breakage frequencies in lymphocytes of welders exposed to chromium and nickel. Carcinogenesis 19(3) 413-418. 

Combining these equations, the following expressions for the breakage frequencies of drops of size a are obtained ... 

The drops behave as segregated entities between flow and coalescence-redispersion simulation. The coalescence and breakage frequencies can be varied with vessel position. The computational time was related to coalescence frequency data available in the literature. Figure 15 shows the steady-state dimensionless droplet number size distribution as a function of rotational speed for continuous-flow operation. As expected the model predicts smaller droplet sizes and less variation of the size distribution with increase in rotational speed. Figure 16 is a comparison of the droplet number size distribution with drop size data of Schindler and Treybal (Sll). 

During the last decades a few models have been developed for the bubble breakage frequency, s(d), under turbulent conditions ([58, 119]). Several different categories of breakage frequency models are distinguished in the literature models based on reaction kinetic concepts (e.g., [101]), phenomenological models based on the turbulent nature of the system (e.g., [114]), and models based based on purely kinematic ideas (e.g., [78, 79]). 

To illustrate this problem a pure breakage process is considered, i.e., Dq = Be = 0, while Db 7 0 and Bb 7 0. In addition, as an example only, a generalized formulation of the breakage death term Db) is analyzed in the following. Assuming that the breakage frequency, 6b(d), can be represented... 

Ayazi Shamlou, P, Stravrinides, S., Titchener-Hooker, N. Hoare, M. 1994 Growth-independent breakage frequency of protein precipitates in turbulently agitated bioreactors. Chemical Engineering Science 49, 2647-2656. 

Figure 9. Relation between foam breakage frequencies in a microvisual cell and the lamella number for four different oils. (Reproduced with permission from reference 47. Copyright 1992 Elsevier Science Publishers.)...

Figure 10. Mobility reduction factors for foams flowing in Berea sandstone at residual oil saturation versus the breakage frequencies of foam lamellae flowing in a microvisual cell when in contact with the same oil (Reproduced with permission from reference 40. Copyright 1990 Society of Petroleum Engineers.)...

Plotting the same foam stability data versus lamella number (39) shows that for these four oils, the same variation of foam breakage frequency with lamella number is observed. Thus, even though for a given foaming surfactant solution the foam does not have the same stability in the presence of each oil, the stability is still well predicted by the surface properties, as reflected in the lamella number (equations 4 and 5). Also, using the surface properties allows the effects of the dodecane to be... 

These data can be used to statistically infer the position of chromosomal breaks, and, from that point on, the procedures for map construction are similar to those used in linkage mapping. A map function is used to convert estimates of breakage frequency to additive units of distance measured in centirays (cR), with 1 cR representing a 1% probability that a chromosomal break has occmred between two markers in a single hybrid. The resolution of a radiation hybrid map depends on the size of the chromosomal fragments contained in the hybrids, which in turn is proportional to the amount of irradiation to which the human cell line was exposed. 

Assume that energy dissipation in the vicinity of the drop has a uniform distribution, with the average value e(t). Then breakage frequency, that is, the number... 

Paper [84] discusses the solution of this equation in the form of the sum of independent solutions with discrete spectra. Special cases of monodisperse and uniform over some interval of initial distributions are examined. On the basis of the obtained solutions, the first four moments of the volume distribution of drops are found, and a Pearson diagram (see Fig. 11.1) is used to show that the solution converges to a lognormal distribution. It is consistent with the result of [86], where it was supposed that breakage frequency /(V) is constant and does not depend on the size of drops. 

To calculate the drop breakage rate in liquid-liquid dispersions, several models have been proposed [33, 38, 42, 49-52]. Some of these models have been applied to the suspension polymerization process with great success [ 8,36,49,53 ]. In these models, the drop breakage rate is expressed in terms of a breakage frequency, c% v), and a respective Maxwellian efficiency term ... 

The function fc(x, r, Y, t) has the dimensions of reciprocal time and is often called the breakage frequency. It is also sometimes referred to as the... 

---