Coagulation, theories Fuchs

From the theoretical point of view a similarity exists between electrostatic retardation of ion transport and coagulation retardation, known as slow coagulation (Fuchs, 1934). Both phenomena arise from electrostatic repulsion caused by the existence of the diffuse part of the DL. In the slow coagulation theory, the electric field if the DL is derived from the Gouy-Chapman model (cf. Chapter 2). This model does not consider a deviation of the diffuse layer from equilibrium. Initially, the same simplification was used by Dukhin et al. (1973) in describing the DL effect on the electrostatic retardation of adsorption. 

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. 

What is meant by slow coagulation What is the basic principle behind the Fuchs theory of slow coagulation What is the rate coefficient for slow coagulation How is it defined, and what properties of the dispersion determine its magnitude What are the limitations of this theory as presented in the text ... 

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,... 

Large differences between slow coagulation and ion adsorption consist in the chosen geometry and in the boundary conditions of ion (particle) distribution. Slow coagulation is assumed to be an irreversible process and particles which overcame the electrostatic barrier and occupy places in the potential well, are not considered any longer in the particle distribution. The particle distribution only contains mobile particles which can move in any direction, while particles in the potential well are considered as bounded. Thus, Fuchs theory does not describe particles in the coagulated state and the boundary condition chosen sets the particle concentration in the well equal to zero. Consequently, the Eq. (7.4) contains only the bulk concentration c. For the process of ion adsorption a completely different situation exists. The concentration of ion is not assumed to be zero in the subsurface and the ions can move in any direction. The state of ions... 

The kinetics of coagulation were first analyzed by Smoluchowski [32], who assumed that no repulsive barrier was present, and that aggregation occurred by the attachment of single particles to clusters (ignoring cluster-cluster aggregation). The theory was further developed by Fuchs [33], who showed that a repulsive potential F(r) would reduce the coagulation rate by the faetor JV, called the stability ratio ... 

Here, the theory of Fuchs, originally developed for coagulations of smokes or mists, gives a new starting point. 

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