Turbulent Coagulation

Brunk, B. K., Koch, D. L., and Lion, L. W., Hydrodynamic pair diffusion in isotropic random velocity fields with application to turbulent coagulation. Phys. Fluids 9,2670-2691 (1997). 

A history of various studies and theories of aerosol coagulation is given by Gucker 41). Kivnick and Johnstone 71) treat the subject of coalescence of droplets in a turbulent jet. Aerosol build-up techniques are presented by Fahnoe, Lindroos, and Abelson 31). 

Frazil crystal are ice crystals that form in supercooled water too turbulent to permit coagulation into smooth sheet ice. This is most common in swiftly fluwing streams, but is also found in a turbulent sea (cf. lolly ice. defined below). It may accumulate as anchor ice on submerged objects obstructing the water flow. ... 

Among the numerous approaches studied so far to minimize such phenomena in ED, it is worth citing pretreatment of the feed solution by coagulation (De Korosy et al., 1970) or microfiltration (MF) or ultrafiltration membrane processing (Ferrarini, 2001 Lewandowski et al., 1999 Pinacci et al., 2004), turbulence in the compartments, optimization of the process conditions, as well as modification of the membrane properties (Grebenyuk et al., 1998). However, all these methods are partially effective and hydraulic or chemical cleaning-in-place (CIP) is still needed today, thus... 

A condition of flow in which all elements of a fluid passing a certain point follow the same path, or streamline there is no turbulence. Also referred to as streamline flow . A dispersion (suspension or emulsion) of polymer in water. Latex rubber, a heavily cross-linked polymer solid, is produced either by coagulating natural latex or by synthetic means through emulsion polymerization. Example Latex paint is a latex containing pigments and filling additives. 

Once particles are present in a volume of gas, they collide and agglomerate by different processes. The coagulation process leads to substantial changes in particle size distribution with time. Coagulation may be induced by any mechanism that involves a relative velocity between particles. Such processes include Brownian motion, shearing flow of fluid, turbulent motion, and differential particle motion associated with external force fields. The theory of particle collisions is quite complicated even if each of these mechanisms is isolated and treated separately. 

Three main processes appear to control the modification and loss (or transport) of analyte aerosol in the spray chamber droplet-droplet collisions resulting in coagulation, evaporation, and impact of larger droplets into the walls of the spray chamber. Aerosol droplets can be lost (impact the walls and flow down the drain) as a result of several processes in the spray chamber [11,20]. Because turbulent gas flows are key to generating aerosols with pneumatic nebulizers, the gas in the spray chamber is also turbulent. Droplets with a variety of diameters... 

Conceptually similar results were demonstrated by Krutzer et al. [14], who measured the orthokinetic coagulation rate under laminar Couette flow and isotropic turbulent flow (as well as other flow conditions). Despite equal particle collision rates, significance differences were observed in the overall rates indicating different collision efficiencies (higher collision efficiencies were found under a turbulent flow regime). Thus, identical chemical properties of a dispersion do not determine a single collision efficiency the collision efficiency is indeed dependent upon the physical transport occurring in the system. 

Turbulent agglomeration. Far turbulent agglomeration two cases should be considered. First, if the inertia of the aerosol particles is approximately the same as that of the medium, the particles will move about with the same velocities as associated air parcels and can be characterized by a turbulence or eddy diffusion coefficient DT. This coefficient can have a value 104 to 106 times greater than aerosol diffusion coefficients. Turbulent agglomeration processes can be treated in a manner similar to conventional coagulation except that the larger diffusion coefficients are used. 

The second method for aerosol coagulation in turbulent flows arises because of inertial differences between particles of different sizes. The particles accelerate to different velocities by the turbulence depending on their size, and they may then collide with each other. This mechanism is unimportant for a monodisperse aerosol. For a polydisperse aerosol of unspecified size distribution, Levich (1962) has shown that the agglomeration rate is proportional to the basic velocity of the turbulent flow raised to the 9/4 power, indicating that the agglomeration rate increases very rapidly with the turbulent velocity. Since very small particles are rapidly accelerated, this mechanism also decreases in importance as the particle size becomes very small, being most important for particles whose sizes exceed 10-6 to 10"4 cm in diameter. In all cases brownian diffusion predominates when particles are less than 10-6 cm in diameter. 

It is easily observed that at high aerosol concentrations, individual particles coalesce to form larger chains or floes made up of many par-tides. The process of coagulation may be brought about solely by the random motion and subsequent collision of partides (often called thermal coagulation) or the collisions could be caused by such external forces as turbulence or electricity. In general, these external forces will act to increase the rate of coagulation. 

On a more local scale, the effects of turbulence are to impart random motions to particles that are then added to the motions that those particles experience owing to other effects. The details of the resulting motions are beyond the scope of this chapter (comprehensive discussion and equations are provided in Cuzzi Weidenschilling 2006 Ormel Cuzzi 2007). A characteristic velocity that describes these motions is the root-mean-square turbulent velocity, /acs which is the overturn velocity of the largest eddies, and an estimate of the maximum velocity two particles (both of St = 1) would develop with respect to one another (Cuzzi Hogan 2003). Under nominal conditions, such velocities can exceed 100 m s-1 (for a = 0.01). These velocities are important to consider when developing models for dust coagulation and planetesimal formation (see Section 3.4.1 and Chapters 7 and 10). 

Delichatsios and Probstein (D4-7) have analyzed the processes of drop breakup and coagulation/coalescence in isotropic turbulent dispersions. Models were developed for breakup and coalescence rates based on turbulence theory as discussed in Section III and were formulated in terms of Eq. (107). They applied these results in an attempt to show that the increase of drop sizes with holdup fraction in agitated dispersions cannot be attributed entirely to turbulence dampening caused by the dispersed phase. These conclusions are determined after an approximate analysis of the population balance equation, assuming the size distribution is approximately Gaussian. 

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