Growth diffusion layer model

The Chernov bulk diffusion model provides an important link between crystal growth theory and the practical world of industrial crystallization where fluid flow and agitation are important. The effect of hydrodynamics on crystal growth will be discussed in the next section. The Diffusion Layer Model. 

The importance of including soil-based parameters in rhizosphere simulations has been emphasized (56). Scott et al. u.sed a time-dependent exudation boundary condition and a layer model to predict how introduced bacteria would colonize the root environment from a seed-based inoculum. They explicitly included pore size distribution and matric potential as determinants of microbial growth rate and diffusion potential. Their simulations showed that the total number of bacteria in the rhizosphere and their vertical colonization were sensitive to the matric potential of the soil. Soil structure and pore size distribution was also predicted to be a key determinant of the competitive success of a genetically modified microorganism introduced into soil (57). The Scott (56) model also demonstrated that the diffusive movement of root exudates was an important factor in determining microbial abundance. Results from models that ignore the spatial nature of the rhizosphere and treat exudate concentration as a spatially averaged parameter (14) should therefore be treated with some caution. 

Englezos et al. (1987a,b) generated a kinetic model for methane, ethane, and their mixtures to match hydrate growth data at times less than 200 min in a high pressure stirred reactor. Englezos assumed that hydrate formation is composed of three steps (1) transport of gas from the vapor phase to the liquid bulk, (2) diffusion of gas from the liquid bulk through the boundary layer (laminar diffusion layer) around hydrate particles, and (3) an adsorption reaction whereby gas molecules are incorporated into the structured water framework at the hydrate interface. 

The clathrate hydrate growth model presented by Englezos and Bishnoi is based on crystallization and mass transfer theories. It describes the growth of the hydrate as a three step process. The first step is the transport of the gas molecule into the liquid phase. The second step is the diffusion of the gas molecule through a stagnant liquid diffusion layer which surrounds the hydrate particle. The last step is the incorporation of the gas... 

The simplest model of mass transport is the bulk diffusion of growth units through a stagnant diffusion layer adjacent to the crystal surface with complete mixing beyond. For a diffusion layer of thickness 6, the linear growth rate G can be derived by integrating Fick s law as... 

Figure 5.28. The diffusion limited model for growth of a wetting layer, (a) The true situation a wetting layer exists in local equilibrium with the depleted concentration (f>i. Growth of the wetting layer is driven by diffusion of material from the bulk, (b) A schematic box model for the same situation.

Akd] proposed that the value of activity coefficient of A1 in a (Fe, Al, Zn) alloys has a strong influence on the formation and growth kinetics of interfacial diffusion layer. Besides, [2002Bai] compiled the diffusion data in 6, F and F1 phases which were then used to model the mobility of components in these... 

A general treatment of a diffusion-controlled growth of a stoichiometric intermetallic in reaction between two two-phase alloys has been introduced by Paul et al. (2006). A reaction couple in which a layer of Co2Si is formed during inter-diffusion from its adjacent saturated phases was used as a model system. In the discussion it has been emphasized that the diffusion couple is undoubtedly one of the most efficient and versatile techniques in solid-state science it is therefore desirable to have alternative theories that enable us to deduce the highest possible amount of information from the data that are relatively easily attainable in this type of experiments. 

Equation 3.56 indicates that the biofilm essentially behaves like an immobilized water layer, with a resistance that is independent of the biofilm-water partition coefficient. Evidently, when the growth rate of the biofilm and the diffusion rate of the contaminants are of similar magnitude, this highly idealized model breaks down, and it can be expected in those cases that highly hydrophobic compounds will have more difficulty in reaching the membrane than less hydrophobic (more mobile) compounds. Also, Eq. 3.56 will likely fail to predict solute transport in biofilms with sizable populations of invertebrates because of bioturbation. 

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