General dynamic equation growth

In the approach adopted in my first edition, the derivation and use of the general dynamic equation for the particle size distribution played a central role. This special form of a population balance equation incorporated the Smoluchowski theory of coagulation and gas-to-panicle conversion through a Liouville term with a set of special growth laws coagulation and gas-to-particle conversion are processes that take place within an elemental gas volume. Brownian diffusion and external force fields transport particles across the boundaries of the elemental volume. A major limitation on the formulation was the assumption that the panicles were liquid droplets that coalesced instantaneously after collision. 

In the absence of nucleation (Jq(v) = 0), sources (S(v) = 0), sinks (R(v) = 0), and growth [/( ) = 0], we have the continuous coagulation equation (13.61). If particle concentrations are sufficiently small, coagulation can be neglected. If there are no sources or sinks of particles then the general dynamic equation is simplified to the condensation equation (13.7). 

Gelbard, F., and Seinfeld J. H. (1979) The General Dynamic Equation for aerosols—theory and application to aerosol formation and growth, J. Colloid Interface Sci. 68, 363-382. 

Such an equation has been identified as a general dynamic equation (Friedlander, 1977)) for n r, which, to be exact, should be represented as n rp, v, tl , f) namely, it depends on particle size, fluid velocity, internal particle velocity and time. This equation does not include one term, namely a diffusion term on the right-hand side, D V n rp), which arises from random fluctuations in crystal growth rate for which the diffusion coefficient is D and the coordinate dimensions are x, y and z . 

The relatively mild growth and the violent collapse processes predicted by the asymptotic forms (4-210) and (4-211) are characteristic of the dynamics obtained by more general numerical studies of the Rayleigh-Plesset equation, but additional results for cases of large volume change are not possible by analytic solution. In the remainder of this section, we consider additional results that can be obtained by asymptotic methods. 

To deseribe the dynamie interaction of bubble with polymeric solution it is necessary to invoke equations of liquid motion, heat transfer and gas dynamics. General approach to description of bubble growth or collapse in a non-Newtonian liquid was formulated and de-veloped. The radial flow of incompressible liquid around growing or collapsing bubble is described by equations, following from [7.2.21], [7.2.22] ... 

The overall crystallization rate is used to follow the course of solidification of iPP. Differential scanning calorimetry (DSC), dilatometry, dynamic X-ray diffraction and light depolarization microscopy are then the most useful methods. The overall crystallization rate depends on the nucleation rate, 1(0 and the growth rate of spherulites, G(0. The probabilistic approach to the description of spherulite patterns provides a convenient tool for the description of the conversion of melt to spherulites. The conversion of melt to spherulites in the most general case of nonisothermal crystallization is described by the Avrami equation ... 

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