Particle formation, rate

The ambient concentration of small atmospheric ions (positive + negative) is -1000-10,000/cm3, increasing with height in the troposphere [94]. In situations where slow nucleation (with average particle formation rates <0.1-0.01/sec) is observed,... 

It is quite interesting to see (figure 8) that in one of these series (varying emulsifier) a linear relationship is obeyed between the polymerization rate and the particle formation rate. 

The flocculation process is more clearly observed in experiments with high monomer contents (2.7 moles) and rather moderate SDS concentration (4 g). As shown in figure 10, most of the emulsifier is used to stabilize the particles, when droplets are still present, and at the same time particle average size tends to decrease, while their number rapidly increases. At a point where prac tically all the emulsifier has been used, which possibly incidental ly corresponds to disappearance of droplets, particle formation rate decreases to a lower value, particle size tends to increase, while a part of the emulsifier is desorbed. 

Table III - Polymerization rate and particle formation rate...

Usually particle formation by initiation in the monomer droplets droplet nucleation) is not considered important in conventional emulsion polymerization. This is because of the low absorption rate of radicals into the monomer droplets, relative to the other particle formation rates. However, when the monomer... 

Estimates of fuel sooting tendency have been made using various types of flames and chemical systems. In the context to be used here, the term sooting tendency generally refers to a qualitative or quantitative measure of the incipient soot particle formation rate. In many cases, this tendency varies strongly with the type of flame or combustion process under investigation. This variation is important because the incipient soot particle formation rate determines the soot volume fraction formed in a combustion system. 

The particle formation rate depends on the rale of production of free radicals and on the relative rates of the various mechanisms in which these free radicals participate. A high rate of particle formation in the presence of small amounts of free emulsifier will contribute to unstable cyclic behavior. 

Typical droplet lifetimes and hence particle formation rates can occur over a range of time.scales from milliseconds to minutes. Particle formation time is controlled by both the initial liquid droplet size and evaporation rate. The latter is dictated by the heat transfer to the droplet, mass transfer of the vapor away from the droplet into the process gas stream and the specific formulation components. The rate of particle formation is a key parameter which dictates the size of the drying chamber, and hence the scale of equipment required to produce a desired particle size at the target production rate. 

FIGURE 15 Computer simulation indicates multiple particle formation paths exist in bench scale spray dryer particle formation rate and residence time dependent upon flow streamline. 

In a free turbulent jet, the length of the shear layer is 5 to 10 times the nozzle diameter, d. If nucleation is confined to the shear layer, according to (10.61) the particle formation rate is proportional to d and is independent of the initial jet velocity kq. Because the volumetric flowrate of a turbulent Jet ( 2> is proportional to u d and Y to N Q, the panicle concentration in the gas exiting the initial region (/Vj) is proportional to rf/wo- Moreover, because the particle concentration downstream of the shear layer changes only by dilution, N N,d/z, and the group Nu z/d should be constant at any point on the Jet axis fora given initial temperature and vapor concentration conditions. 

Tlie scaling relationships can be exploited to decrease the overall particle formation rate by splitting a large nozzle flow into multiple smaller streams. Consider a Utrge stream ( T ) split into n smaller, noninteracting jets with equal diameters. The temperatures and vapor concentrations are the same in both sy.stems. Two additional relations are needed to compare their piuticle formation rates. The first is that the total ma. s flow for the multiple jets is equal to the single jet flow m = n m . The ratio of total particle formation rates in the two. systems, Fn, , = n Y and Ki. is then... 

If the. system is operated such that the main flow and the individual small jet flows have the same Reynolds numbers, Rej = Re , then d /di = Un/d = 1 /n and f nim/f i = 1 / -The ratio of particle number concentrations in the two systems is also equal to I / . By splitting a large jet flow into 10 smaller jets, in the case of constant Reynolds number and total mass flow, the overall particle formation rate should be decreased by a factor of 100. Stream. splitting leads to a decrease in particle formation because the condensable vapor has a shorter residence time in the shear layer, or nucleation zone of the smaller jets, and the residence time in the shear layer is proportional to d/tta, which is smaller in the split streams. For the analysis to hold, both the large and small jets must be turbulent. The scaling relationships hold in jets with low nucleation rates, in the region downstream of the shear layer, where no new particles form. 

Asgrowth continues, the aerosol surface area becomes sufficiently large to accommodate the products of gas-to-particle conversion. The saturation ratio decreases, leading to a reduction in the particle formation rate. The decay in the number concentration for r > 80 min in Fig. 11.4 is probably due to coagulation calculations for free molecule aerosols support this hypothesis. 

The influence of the emulsifier (SHS) concentration on Np is more pronounced in the conventional emulsion polymerization system (Rp°c[SHS]y, y= 0.68) than in mini-emulsion polymerization (y=0.25). This result is caused by the different particle formation mechanism. While homogeneous nucleation is predominant in the conventional emulsion polymerization, monomer droplets become the main locus of particle nucleation in mini-emulsion polymerization. In the latter polymerization system, most of the emulsifier molecules are adsorbed on the monomer droplet surface and, consequently, a dense droplet surface structure forms. The probability of absorption of oligomeric radicals generated in the continuous phase by the emulsifier-saturated surface of minidroplets is low as is also the particle formation rate. 

Figure 9.19 Use of Damkholer number (Da, ratio of mixing and process characteristic time) for correlation of data. As the pseudo-first order constant used to model the particle formation rate, is not always known, but is obviously the same for each polymer, (Da/ly) is used to correlate the different sets of data (referring to particles produced using different mixing intensity and different initial polymer concentration in the same mixer) quench volumetric ratio = 0.2. Upper graph PEGylated copolymer in acetone at different inlet concentrations and mixing intensities in Tee mixer (d. = 1 mm). Lower graph comparison of different polymers and solvents (fiUed symbols, acetone open symbols, THF) in CIJ mixer (dj = 1 mm) > PCL = 80,000 , PCL = 14,000 A, PEGylated copolymer O, PHDCA (symbols as in Figure 9.6).

The maximum degree of polymerization of a growing MMA chain radical with a sulfate or sulfonate end-group in aqueous solution is on the order of 65 to 75 units, according to the APO data in Table I. From the time required to polymerize to this chain length and from the Fickian diffusion coefficient, it is possible to calculate the distance, L, a growing radical will diffuse before it precipitates out to form a primary particle. This is required in order to calculate the particle formation rate and final number of particles as described in the preceding paper. 

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