Coagulation rate coefficient

A dynamic ordinary differential equation was written for the number concentration of particles in the reactor. In the development of EPM, we have assumed that the size dependence of the coagulation rate coefficients can be ignored above a certain maximum size, which should be chosen sufficiently large so as not to affect the final result. If the particle size distribution is desired, the particle number balance would have to be a partial differential equation in volume and time as shown by other investigators ( ). 

In addition to the various parameters needed for entry and exit, the additional parameters required to model nucleation using Equations (5.25)-(5.39), are the values of agg> Oj, rmiceiie. j> Whatever quantities are needed to specify the coagulation rate coefficient B(V, V ), and the size dependence of Cp. Evidence has been presented [76] for the acceptability of the expression suggested by Maxwell et al. [21] for j ... 

Although the coalescence influence on the Brownian coagulation rate coefficient can be neglected, its influence on the final equations of the Smoluchowski theory remains. It can be shown that Smoluchowski s equation for the total number of particles ... 

What is meant by rapid coagulation What is the basic principle behind the Smoluchowski theory of rapid coagulation What is the rate coefficient for rapid 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 ... 

Thus far, we have calculated the coagulation rate J for a pair of particles separated by an initial distance r0. However, the coagulation coefficient 0 is given by... 

The terms oc(i,j)s and A(i,/)s collectively describe a kinetic coefficient for the coagulation or aggregation of suspended particles of sizes i and j. They have analogies with but are not identical to the terms a(p, c) and tj(p, c) used previously in describing the kinetics of particle deposition processes in porous media. Like q p, c), the term l i,j)s incorporates information about various processes of particle transport, although as used here hydrodynamic retardation is not considered. Unlike t/(p, c), X(iJ)s is not a ratio of fluxes. It is a rate coefficient that includes most physical aspects the second-order coagulation reaction. Like a(p, c), the term a(i, j)s incorporates chemical aspects of the interactions between two colliding solids however, as used here, the effects of hydrodynamic retardation are subsumed in ot(iJ)s. The term a(i,j)s is a ratio defined here as follows ... 

Simple diffusion equations of this type have also been applied to much wider classes of reaction, for example, to cases of sinks and particles being absorbed that are both moving and similar in size (e.g., colloid coagulation and small molecule reactions). The physical background for such applications is widely discussed in the literature." When the sink density is not small, competition effects come into play and it is no longer sufficient to consider reaction at a single sink." " These competition effects lead to a nonanalytic dependence of the rate coefficient on the sink density. Such effects are not discussed here. 

Coagulation Rates Table 12.3 indicates that the smallest value of the coagulation coefficient occurs when both particles are of the same size. The coagulation coefficient rises... 

It has been described elsewhere [12] that the flow pattern in the tanks investigated and described by the dimensionless dispersion number (DN = D/[u.L], where D is the turbulent dispersion coefficient, u the convective transport, and L a characteristic length) has, in conjunction with the floe properties, a more pronounced effect upon the separation effectivity than can be concluded from the coagulation rate alone. 

Chemical Family a group of elements that share similar chemical properties and share the same column in the periodic table, for example, halogens, alkali earth Chirality condition that describes the handedness of a molecule or whether a molecule exists in forms that can be superimposed on each other Chlorofluorocarbons also called CFCs, compounds consisting of chorine, fluorine, and carbon that are responsible for stratospheric ozone destruction Coagulation precipitation or separation from a dispersed state Coefficient of Thermal Expansion measure of the rate at which a substance will expand when heated... 

The first group, consisting of Sections 2.2-2.4, covers sedimentation. After some preliminaries, we discuss Stokes s law, a hydrodynamic equation that will appear again when we discuss electrokinetic phenomena in Chapter 12 and the kinetics of coagulation in Chapter 13. Stokes s law is a key relationship in understanding the rate of sedimentation and is used in the derivation of the sedimentation equation for spherical particles. Following this, the equation for the sedimentation coefficient, a... 

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