Coalescence time

The charge on a droplet surface produces a repulsive barrier to coalescence into the London-van der Waals primary attractive minimum (see Section VI-4). If the droplet size is appropriate, a secondary minimum exists outside the repulsive barrier as illustrated by DLVO calculations shown in Fig. XIV-6 (see also Refs. 36-38). Here the influence of pH on the repulsive barrier between n-hexadecane drops is shown in Fig. XIV-6a, while the secondary minimum is enlarged in Fig. XIV-6b [39]. The inset to the figures contains t,. the coalescence time. Emulsion particles may flocculate into the secondary minimum without further coalescence. 

The inset in Figure XIV-6 shows the coalescence time tc for the droplets for the pH corresponding to each DLVO curve. Does DLVO theory adequately explain the variation of tc with pH What additional factors may play a role ... 

If the average lifetime in one state (rex) is longer than the shutter speed, we will see two distinct peaks in the spectrum. If the average lifetime is shorter than the shutter time we will only see one averaged peak. This shutter time is formally called the coalescence time, rc, for the exchange process, or simply the NMR timescale . 

The ratio recommended by Barton [20] is five for settlers without considering the coalescence time for the droplets. 

The quasi-equilibrium film thickness was attained, before the van der Waals forces became effective. It amounted to several 100 A to 1 pm. The time to achieve this thickness was 10 to 10 s, which was negligibly small compared with the measurable coalescence time in foams, which as a rule was of the order of magnitude of 0.1 to 1 s or more. There must therefore be another slower process in which the lamella is thinned until it bursts. 

In general it can be said that droplets with full surface mobility possess a much higher coalescence probability than those with rigid surfaces. This also confirms Aderangis study [2], which was concerned with the effect of surface active substances on coalescence and came to the conclusion that the coalescence times do not correlate with the surface tension, but with the surface viscosity. 

The duration of the actual particle-particle interactions taking place in real flow situations in process vessels is however limited and may vary considerably in time and space. The net force which compresses the fluid particle must thus act for a sufficient time to ensure that the intervening film drains to the critical thickness so that film rupture and coalescence take place. In an early view it was postulated that for these processes to occur, the actual particle-particle collision (contact) time interval Atcoi must exceed the coalescence time interval Zitcoai of the coalescence processes, Z fcoi > fcoai- The probability of coalescence was thus generally defined as a function of the ratio... 

The probability of oscillatory fluid particle coalescence which is induced by turbulent fluctuations, is generally expected to be determined by physical mechanisms on various scales. Coulaloglou and Tavlarides [16], Luo [73], Luo and Svendsen [74], Hagesaether et al [28, 29, 30[, among others, adopted the same functional relationship as presented above describing these processes, basically because no extended models were available. However, modified relations for estimating the collision and coalescence time intervals were derived for these problems. 

Prince and Blanch [92] thus obtained an estimate of the coalescence time for binary bubble collisions in bubble columns solving a simplified form of... 

Figure 12.7 Compiiier. sinnilaiions of coalescence times for particles composed of varying numbers of silicon atoms. The dotted lines connecuhe molecular dynamic compulations based on the approach of the moment of inertia of two coalescing particles in contact to the value for the sphere of (he same volume. The solid lines show calculations ba.scd on the phenomenological theories, (12.3) and (12.6). Values calculated from (12.6) (for the liquid) were multiplied by a factor of 10 on the grounds that viscosity values fur bull silicon are (oo smalt for nanoparticles. (After Zachariah and Carrier. 1099.)...

According to the analysis in the previous sections, the primary particle size in flame reactors is determined by the relative rates of particle collision and coalescence. For highly refractory materials, the characterislic coalescence time (12.6) depends on the solid-state diffusion coefficient, which is a very sensitive function of the temperature. The mechanisms of solid-.staie diffusion depend in a complex way on the structure of the solid. For example, a perfect cubic crystal of the substance AB consists of alternating ions A and B. Normally there are many defects in the lattice structure even in a chemically pure single crystal defect types are shown schematically in Fig. 12.8. The mechanism of diffusion in cry.stalline solids depends on the nature of the lattice defects. Three mechanisms predominate in ionic... 

As shown by (12.19) the behavior of the system depends on the relative values of the collision and coalescence times which are determined by the process conditions and material properties. If the size distribution remains nearly self-preserving throughout the time of interest, the fractional change in average particle volume with time in the free molecule regime (Chapter 7), i.s... 

Figure 12.12 Effect of variation of collision and coalescence ruic.s on the formation of necks between primary panicle.s. (a) The coalescence time increa.ses sharply while the time between collisions changes little. This results in agglomerates composed of weakly bonded primary panicles, (b) The coalescence and collision processes proceed ai similar rales producing suong necks between the primary paniclc.s.

FIGURE 13.16 Coalescence of protein stabilized emulsion drops, (a) Experimental setup. The coalescence time at the planar oil-water interface is observed, (b) Average coalescence time as a function of droplet size for three proteins. Protein concentration lg per m3 aging time of the interface 20 min. (From results by E. Dickinson et al. J. Chem. Soc. Faraday Trans. 1, 84 (1988) 871.)... 

Assuming that coalescence time is equal to drop-formation time, and that the drop spreads at the interface of the two phases, exposing a fresh film of area A, it can be shown (S8) that the ratio of transfer efficiencies in the drop-formation and coalescence regions can be approximated by... 

The problems related to an influence of size effects on formation of nanoscale aerosol particles are studied theoretically. Dependence of the trapping coefficient of vapor molecules and the characteristic coalescence time on the particle size is considered. 

Let us consider an influence of size effects on coalescence of small aerosol particles. The characteristic coalescence time in a solid-state diffusion model is given by [1]... 

---