Breakage probability

The kinetic theory equation for bond breakage probability v, namely... 

The conditional breakage probability function used by Luo and Svendsen thus yields ... 

PB di,Xj) breakage probability function, determining the efficiency of the eddy-bubble collisions ( —)... 

Narsimhan, G., Gupta, J. P. Ramkrishna, D. 1979 A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersion. Chemical Engineering Science 34, 257-265. 

If we use the breakage probability (11.146) and substitute it into equation (11.119) disregarding the first two integrals in the right-hand side (this corresponds to drop breakage without coalescence), then, using well-known properties of the delta-function [89], we obtain... 

The collision frequency and the breakage probability are determined by consideration of the interactions between drops in a field of turbulent pulsations. Their definition represents an independent problem. The problem of drop interactions in an emulsion will be considered in detail in Section V. 

Fig. 16a-d. Fit of the model parameters X and R characterizing the Gaussian breakage probability (Eq. (37)) to experimental molecular weight distributions... 

All data have been taken from Ref. Radical scavenger Oj AT is the distance to the demixing temperature (dB/dt),o is the inditial rate of degradation (cf Eq. (42)) is the shear rate and X and R are the parameters characterizing the Gaussian breakage probability (cf Eq. (37))... 

Narsimhan, G., J. P. Gupta and D. Ramkrishna, A Model for Transitional Breakage Probability of Droplets in Agitated Lean Liquid-Liquid Dispersions, Chem. Eng. Sci. 34, 257-265 (1979). 

Besides the breakage probability of the particles, the size distribution determines another important parameter with respect to attrition, namely the volume specific surface area of the bed material. This parameter is particularly relevant with respect to abrasion, where it leads to two contrary effects. 

Fig. 7.12 Breakage probability P of Y-AI2O3 agglomerates = 15 mm, = 15 mm, with different binder content Xb) versus mass related breakage energy during compression.

During the granulation experiments samples were taken at constant time intervals. For each sample the particle size distribution was analyzed by means of a Camsizer (see Section 5.2.2 in Volume 2 of this series). Additionally, the mechanical strength was determined per uniaxial compression (see Chapter 6 in Volume 2 of this series). The results are visualized by plotting the breakage probability versus the breakage energy, similarly to the plot of Fig. 7.12 of Section 7.3.1. 

To analyze the influence of process time on particle strength, tests were performed under dry conditions without liquid injection. In Fig. 7.30 the breakage probability of different samples taken at 5, 10 and 15 min retention time is depicted. 

Fig. 7.28 Influence of binder content on the breakage probability after 3 h of granulation (d32 = 2.9mm, Tbe

Prince and Blanch [102] further postulated that bubble breakage is a result of collisions between particles and turbulent eddies, and that the collision rate can be calculated following arguments from the kinetic theory of gases. A total breakage rate for particles of size di, with units (1/sm ), was thus expressed as a product of an eddy-bubble collision rate o sidi j) and a breakage probability (efficiency) psidi Xj), thus ... 

A severe limitation of the original breakage density closure of Luo and Svendsen [80] is that the model produces too many very small particles whatever numerical size resolution used, the model is thus not well posed. That is, using the surface energy criterion solely a maximum breakage probability is predicted when the breakage fraction approaches zero. This is not in agreement to the real physical situation... 

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