Aerosol coagulation, theory

The most complete theory for aerosol coagulation is that of Fuchs (1964). Since the attachment of radon progeny to aerosols can be considered as the coagulation of radon progeny (small diameter particle) to aerosols (large diameter particle), it is reasonable to use Fuchs theory to describe this process. The hybrid theory is an approximation to Fuchs theory and thus can be used to describe the attachment of radon progeny to aerosols over the entire aerosol size spectrum. 

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). 

Otto, E., et al. (1999). Log-normal size distribution theory of Brownian aerosol coagulation for the entire particle size range Part 11—Analytical solution using Dahneke s coagulation kernel. J. Aerosol Science. 30, 1, 17-34. 

Early advances in aerosol science were closely lied to the development of certain fundamental physical concepts. For example, aerosol transport theory is based on Stokes law including semiempirical corrections made by Millikan in his measurements of the electronic charge. Einstein s theory of the Brownian motion plays a central role in aerosol diffu.sion which i.s discussed in the next chapter. The Brownian motion results in coagulation first... 

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. 

In the second edition, I have sharpened the focus on aerosol dynamics. The field has grown rapidly since its original applications to the atmospheric aerosol for which the assumption of panicle sphericity is u.sually adequate, especially for the accumulation mode. Major advances in the eighties and nineties came about when we learned how to deal with (I) the formation of solid primary panicles, the smallest individual panicles that compose agglomerates and (ii) the formation of agglomerate structures by collisions. These phenomena, which have important industrial applications, are covered in two new chapters. One chapter describes the extension of classical coagulation theory for coalescing... 

Interstitial aerosol particles collide with cloud droplets and are removed from cloud interstitial air. The coagulation theory of Chapter 13 can be used to quantify the rate and effects of such removal. If n(Dp,t) is the aerosol number distribution and nd(Dp,t) the droplet number distribution at time r, the loss rate of aerosol particles per unit volume of air due to scavenging by cloud drops is governed by... 

The original theory of diffusional coagulation of spherical aerosol particles was developed by von Smoluchowski (1916,1917). The underlying hypothesis in this theory is that every aerosol particle acts as a sink for the diffusing species. The concentration of the diffusing species at the surface of the aerosol particle is assumed to be zero. At some distance away, the concentration is the bulk concentration. 

Zl. Zebel, G., On the theory of coagulation of electrically uncharged aerosols, KolloidZ. 

To follow the coagulation process, samples of the smoke were taken from the flask at intervals over a period of 4 min and were passed into a centrifugal aerosol collector and classifier. Size distribution curves were measured, together with values for the total number of panicles per unit volume, obtained by the graphical integration of the size distribution curves. The volume fraction of aerosol material was 0 = 1.11 x 10. Theory and experiment are compared in Figs. 7,9 and 7.10, In Fig. 7.9, the experimental points for... 

The first edition of this book, published in 1977, included an extended discussion of aerosol dynamics, the study of the factors that determine the distribution of aerosol properties with respect to particle size. The distributions change with position and time in both natural and industrial processes. The ability to predict and measure changes in the distribution function are of central importance in many appl ications from air pollution to the commercial synthesis of powdered materials. The aerosol dynamics approach makes it possible to integrate abroad set of topics in aerosol science usually treated in an unconnected manner. These include stochastic processes, aerosol transport, coagulation, formation of agglomerates, classical nucleaiion theory, and the synthesis of ulirafine solid particles,... 

There exists an extensive literature on the theory of coagulation (Fuchs, 1964 Zebel, 1966 Hidy and Brock, 1970 Twomey, 1977), and we can treat here only the most salient features. In the absence of external forces, the aerosol particles undergo collisions with each other due to their thermal (Brownian) motion. The mathematical description of thermal coagulation goes back to the classical work of Smoluchowski (1918) on hydrosols. Application to aerosols seems to have been made first by Whitlaw-Gray and Patterson (1932). Let dN, = f(r,) dr, and dN2=f(r2) dr2 describe the number densities of particles in the size intervals r, + dr, and r2+dr2,... 

The theory of coagulation will be presented in two steps. At first, we will develop an expression describing the rate of collisions between two monodisperse particle populations consisting of N particles with diameter Dpl and N2 with diameter Dp2. In the next step a differential equation describing the rate of change of a full coagulating aerosol size distribution will be derived. 

Brock, J.R. and Hidy, G.M. (1965). Collision-rate theory and the coagulation of free-molecule aerosols. J. Appl. Phys., 36, 1857-1862. 

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