Coalescence, process collision frequency

Aerosols are unstable with respect to coagulation. The reduction in surface area that accompanie.s coalescence corresponds to a reduction in the Gibbs free energy under conditions of constant temperature and pressure. The prediction of aerosol coagulation rates is a two-step process. The first is the derivation of a mathematical expression that keeps count of particle collisions as a function of particle size it incorporates a general expression for tlie collision frequency function. An expression for the collision frequency based on a physical model is then introduced into the equation Chat keep.s count of collisions. The collision mechanisms include Brownian motion, laminar shear, and turbulence. There may be interacting force fields between the particles. The processes are basically nonlinear, and this lead.s to formidable difficulties in the mathematical theory. 

Processes of breakage and coalescence can be controlled. If we add demulsifier to the emulsion, it will be adsorbed at the drop surface, reducing the surface tension S and thus increasing Weber s number. At a certain demulsifier concentration, Weber s number exceeds the critical value and the drop splits. On the other hand, we can increase the collision frequency and coalescence rate of drops by... 

The process of drop coalescence consists of two stages. The first one - the transport stage - involves the mutual approach of drops until their surfaces come into contact. The second - kinetic stage - involves coalescence itself, that is, merging of drops into a single drop. The transport stage is assumed to take a predominant share of the total duration of the process. We also assume that each collision of drops results in their coalescence. Then the primary goal is to determine the collision frequency for drops of various sizes. 

The ELALR can be used for these processes because gas disengagement is very efficient. The bnbbles have a relatively fast rise velocity and slow radial velocity. Hence, bubble-bnbble interactions are diminished in the external-loop variant relative to the bnbble colnmn or stirred-tank bioreactor, which, in turn, leads to higher gas holdnp sensitivity to liquid property variations in bubble columns than in ELALRs (Chisti, 1989 Joshi et al., 1990 Shariati et al., 2007). In other words, the bnbble-bnbble collision frequency is lower in ELALRs, which makes coalescence-adjnsting liqnid properties, such as viscosity, surface tension, or ionic strength, less important. So, while bubble column and internal-loop airlift bioreactor gas holdnp are nsnally similar, the downcomer gas holdup in an external-loop airlift bioreactor is only 0-50% of the riser gas holdup (Bello et al., 1984), which leads to much lower global gas holdup in ELALRs. 

Coalescence depends on the collision rate, which increases with dispersed phase concentration. To quantify this process, it is convenient to define a collision frequency (d, d ), between drops of diameter d and d, which is independent of concentration. The collision frequency depends on agitation rate and drop size. As shown in Figures 12-14 and 12-17, the collision of two drops does not ensure coalescence. As the drops approach each other, a film of continuous phase fluid keeps them apart. Coalescence depends on the rupture of this film. It must drain to a critical thickness before coalescence can occur. The critical drainage time is the time it takes for the film to thin sufficiently that rupture occurs or in other words, coalescence occurs only if the collision interval, referred to as the contact time, exceeds Ihe critical film drainage time. The probability that this will occur is called the coalescence efficiency, k(d,d0. It depends on a different set of hydro-dynamic factors as well as drop size and physicochemical variables. Because collision frequency and coalescence efficiency depend on different factors, then-contributions to coalescence are treated separately. As a result, the coalescence frequency F(d, d ) between two drops of diameter d and d is defined as... 

Thus, to determine the frequency of collision of particles or drops, it is necessary to determine the forces of particle interaction first, and then to find the trajectories of their motion and the collision cross-section or the diffusion flux. In the latter case, it is necessary to And the turbulent diffusion factor. As a result, the kernel of the kinetic equation is determined. If the kernel thus derived appears to be asymmetric, it should be symmetrized. After that, one can proceed to study the kinetics of coalescence for the considered process, including the time rate of change of size distribution of particles and the parameters of this distribution. 

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