Coalescing efficiency

The effectiveness of a coalescing agent is based upon the MFFT test. 

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An attempt has been made by Tsouris and Tavlarides[5611 to improve previous models for breakup and coalescence of droplets in turbulent dispersions based on existing frameworks and recent advances. In both the breakup and coalescence models, two-step mecha-nisms were considered. A droplet breakup function was introduced as a product of droplet-eddy collision frequency and breakup efficiency that reflect the energetics of turbulent liquid-liquid dispersions. Similarly, a coalescencefunction was defined as a product of droplet-droplet collision frequency and coalescence efficiency. The existing coalescence efficiency model was modified to account for the effects of film drainage on droplets with partially mobile interfaces. A probability density function for secondary droplets was also proposed on the basis of the energy requirements for the formation of secondary droplets. These models eliminated several inconsistencies in previous studies, and are applicable to dense dispersions. 

Feng et al. [138] found that coalescence efficiency could be improved with increasing frequency. Draxler et al. [103] demonstrated that for a given degree of demulsification the voltage could be reduced if the frequency was enhanced. It has... 

There are many factors that determine whether a collision results in a coalescence. The processes by which two drops coalesce are those of film thinning and final rupture of the intervening film. These processes are determined by factors such as surfactants, mass transfer, surface tension gradients, physical properties, Van der Waals forces, and double-layer forces. In a turbulent flow field the situation is more involved.The droplets must first collide and remain in contact for a sufficient time for the coalescence to take place. A realistic coalescence efficiency will account for these factors. 

The coalescence efficiency (a, a ) is defined as the fraction of collisions between drops of diameter a and a that result in coalescences. 

Howarth (H15) developed an expression for collision efficiencies by assuming an analogy to bimolecular gas reactions. He assumed that a critical relative velocity IV exists along the lines of centers of two colliding drops which must be exceeded for a collision to result in a coalescence. By assuming that the three-dimensional Maxwell s equation describes the drop turbulent velocity fluctuations, he obtained the coalescence efficiency as the fraction of drops which have kinetic energy exceeding IV. Thus,... 

Combining Eqs. (67)-(69) and (71), Ross and Curl obtained the coalescence efficiency for two deformable drops... 

At this point, it is instructive to note that Eqs. (72), (75), and (76) predict that the small drops will continuously coalesce up to a minimum size flniin. Where the coalescence rate approaches some arbitrary value close to zero. In this case, the exponential term dominates the behavior of the coalescence efficiency function. Thus,... 

Valentas et al. (VI) also used a coalescence efficiency of exponential form, but gave no rigorous arguments to support their model. 

The coalescence efficiency in a turbulent pipe flow was correlated by Kuboi et al. (K17) with the modifled kinetic energy of collision = a Vc as... 

Here t is given by Eq. (48) and G is given by either Eq. (50) or (51), depending on whether the range of flow is laminar or transitional. Thus, he obtained the following expression for the coalescence efficiency between rigid drops in dispersions under laminar and transition range flows... 

The coalescence efficiency thus represents the fraction of particles that coalesce out of the total number of particles that have been colliding. 

Population-balance analysis has been adapted to both coalescence and dispersion of drops in numerous papers by Calabrese, Ramkrishna, and Tavlarides. The analyses with these tools have led to a considerably better understanding of breakage kernels, breakage rates, coalescence efficiency, and collision rates. However, the description and use of these tools goes beyond the scope of this chapter. For a detailed understanding, see Ramkrishna [66]. 

Calculations for larger drops are complicated by phenomena such as shape deformation, wake oscillations, and eddy shedding, making theoretical estimates of E difficult. The overall process of rain formation is further complicated by the fact that drops on collision trajectories may not coalesce but bounce off each other. The principal barrier to coalescence is the cushion of air between the two drops that must be drained before they can come into contact. An empirical coalescence efficiency Ec suggested by Whelpdale and List (1971) to address droplet bounce-off is... 

Williams plotted the film-thinning time for deformable and nondeformable droplets against droplet radius. While an increase in droplet size increases the time required for thinning of a deformable droplet, nondeformable droplets experience a reduction in film thinning time as their size increases. It is interesting also to note the square relationship on thinning rate wifii nondeformable droplets and an inverse square relationship for deformable droplets. Clearly, increasing the apphed field across a system with deformable droplets could result in a reduction in coalescence efficiency. 

The task of modeling binary droplet collisions in Euler-Lagrangian simulations of spray flows was first taken up by O Rourke and coworkers. Their model in [83] first estimates the coalescence efficiency, which is the probability that coalescence occurs after the collision, once it has taken place ... 

T. B. Low, R. List Collision, coalescence and breakup of raindrops. Part I Experimentally established coalescence efficiencies and fragment size distributions in breakup, J. Atmos. Sci. 39, 1591-1606 (1982). 

N. Ashgriz, P. Givi Coalescence efficiencies of fuel droplets in binary collisions, Int. Commun. Heat Mass Transfer 16, 11-20 (1989). 

Minimum Rim Formation Temperature (MFFT)- Coalescent Efficiency... 

Superficial gas velocity has an influence over the collision frequency. If more gas is present, there is a higher probability of colhsion (Martin et al., 2008b). Coalescence efficiency and drainage rate depend on the film properties which are a function of the liquid properties. The collision force, however, is the controlhng factor because the bubble diameter is a function of the power input (Bouaifi et al., 2001 Nocentini et al., 1993). 

Coalescing efficiency Excellent for most polymer systems ... 

In general, the increase of holdup fraction of the dispersed phase, cp, decreases the turbulent intensity (i.e., the average energy dissipation rate per unit mass) and, thus, the drop breakage rate. On the other hand, the coalescence frequency increases due to the higher number of droplets, while the coalescence efficiency decreases due to the lower average energy dissipation rate. However, the effect of tp on the coalescence frequency is more important, and, thus, for a constant input power, as the holdup fraction increases the droplet size increases [43]. 

It is assumed in (2.38,40) that the sticking (and coalescence) efficiency is unity. Deviations from unity are sometimes represented by introducing a coefficient a for this efficiency— that is, bl. = a b-.. However, there is no viable theory... 

For practical application of macroscopic theory where Brownian motion is the only factor causing collision, the semi-empirical theory of FUCHS [2.7] is most widely used because it gives correctly the values of b in the limits, (2.38,40). The careful experimental results of WAGNER and KERKER [2.52] for b. j at large Kn. agree with the theory of FUCHS to within 8 to 10 percent upon the assumption of a coalescence efficiency of unity. 

Since coalescence occurs only after a collision, we define the coalescence efficiency, h, , as the probability that a collision will result in a coalescence. Then the overall probability of a bubble coalescing with another while rising one equivalent diameter is the product of the collision probability and coalescence efficiency, The coalescence efficiency determined from the data is... 

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