Aggregation breakup

Kramer, T. A. Clark, M. M. 1999 Incorporation of aggregate breakup in the simulation of orthokinetic coagulation. Journal of Colloid and Interface Science 216, 116-126. 

Note on notation Relations from breakup, coalescence, fragmentation, and aggregation are based on either actual experiments or numerical simulations, the latter commonly referred to as computer experiments. Computer experiments are often based on crude simplifying assumptions and actual experiments are always subject to errors the strict use of the equality sign in many of the final results may therefore be misleading. In order to accurately represent the uncertainty associated with the results, the following notation is adopted ... 

This paper is divided into two main, interconnected parts—breakup and coalescence of immiscible fluids, and aggregation and fragmentation of solids in viscous liquids—preceded by a brief introduction to mixing, this being focused primarily on stretching and self-similarity. 

Fluid advection—be it regular or chaotic—forms a template for the evolution of breakup, coalescence, fragmentation, and aggregation processes. Let v(x, t) represent the Eulerian velocity field (typically we assume that V v = 0). The solution of... 

The current level of understanding of how aggregates form and break is not up to par with droplet breakup and coalescence. The reasons for this discrepancy are many Aggregates involve multibody interactions shapes may be irregular, potential forces that are imperfectly understood and quite susceptible to contamination effects. 

The interaction between the dispersed-phase elements at high volume fractions has an impact on breakup and aggregation, which is not well understood. For example, Elemans et al. (1997) found that when closely spaced stationary threads break by the growth of capillary instabilities, the disturbances on adjacent threads are half a wavelength out of phase (Fig. 43), and the rate of growth of the instability is smaller. Such interaction effects may have practical applications, for example, in the formation of monodisperse emulsions (Mason and Bibette, 1996). 

In cases where static LALLS results were obtained for the DVB-linked samples, poor agreement was found with SEC/LALLS. In both cases sh n in Table I ((Sl-4) DVB) and ((SB-1) E B), the SEC/LALLS Mw is considerably less than the off-line Mw The concentration detector (DRl) response showed no significant sample loss ("Experimental") following injection, and this discrepancy possibly results from breakup of sample aggregates during chromatography ("Discussion", below). 

The situation is similar qualitatively but differs quantitatively for isoprene and 1,3-buta-diene. The dependence of Rp on initiator varies from g- to -order depending on the specific reaction system. The reaction orders for all monomers are affected hy the relative as well as absolute concentrations of initiator and monomer. Thus the dependence of Rp on initiator for the n-butyllithium polymerization of isoprene in benzene at 30°C is -order at initiator concentrations above 10-4 M but -order at initiator concentrations below 10 4 M [Van Beylen et al., 1988]. Higher initiator concentrations yield higher degrees of aggregation and lower kinetic orders. The excess of monomer over initiator is also important. Higher kinetic orders are often observed as the monomer initiator ratio increases, apparently as a result of breakup of initiator and propagating ion-pair associations by monomer. 

As Tatterson [55] notes, There is much more volume on scale-up than is typically recognized. This is one feature of scale-up that causes more difficulty than anything else. For disperse systems, a further mechanistic impUcation of the changing volume and surface-area ratios is that particle size reduction (or droplet breakup) is more likely to be the dominant process on a small scale while aggregation (or coalescence) is more likely to be the dominant process on a large scale [55]. 

Experimental methods presented in the literature may prove of value in combustion studies of both solid and liquid suspensions. Such suspensions include the common liquid spray. Uniform droplets can be produced by aerosol generators, spinning disks, vibrating capillary tubes, and other techniques. Mechanical, physicochemical, optical, and electrical means are available for determination of droplet size and distribution. The size distribution, aggregation, and electrical properties of suspended particles are discussed as well as their flow and metering characteristics. The study of continuous fuel sprays includes both analytical and experimental procedures. Rayleigh s work on liquid jet breakup is reviewed and its subsequent verification and limitations are shown. 

FIGURE 6.35 Schematic of the experimental protocol for streptavidin affinity chromatography. (1) The channel is initially filled at room temperature with a suspension of biotinylated, PNIPAAm-coated beads (100 nm). (2) The temperature in the channel is then raised to 37°C, and the beads aggregate and adhere to the channel walls. (3) Buffer is then pumped through the channel (the presence of flow is indicated in this schematic by an arrow), washing out any unbound beads. (4) A fluorescently labeled streptavidin sample (2.5 pM) is then introduced into the flow stream. (5) Streptavidin binds to the beads, and any unbound streptavidin is washed out of the channel. (6) Finally, the temperature is reduced to room temperature, leading to the breakup of the bead aggregates. Beads, bound to labeled streptavidin, elute from the channel [203], Reprinted with permission from the American Chemical Society. 

Shamlou, P. A., and Titchener-Hooker, N., Turbulent aggregation and breakup of particles in liquids in liquids in stirred vessels, in "Processing of Solid-Liquid Suspensions" (P. A. Shamlou Ed.), pp. 1-25. Butterworth-Heinemann Ltd, Oxford (1993). 

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