Molecular diffusion, transport

Fig. 7.20 To illustrate the influence of bioturbation (mixing) on the solid phase profile three schematic scenarios are drawn. For all scenarios the same molecular diffusive transport and sedimentation is assumed, yet the particulate...

Molecular Diffusion Transportation of molecular size matter. Molecular diffusion takes place in solids and phases with no motion or in phase boundaries... 

Figure 10.6. Evolution in time of reagent concentrations under the combined effects of molecular diffusion and of an instantaneous chemical reaction. Products A and B are initially contained in streaks of thickness k During the whole process, they are only in contact at the interface between streaks where they react together. Molecular diffusion transport the products along the Ox direction, producing their mixing while concentrations (dark grey for A and light grey for B) decrease in time, while the products are consumed by the reaction...

Although many users of this book are familiar with the subject of chemical molecular diffusion transport, it may be new to others or they may have limited knowledge about the broader subject area of chemical transport and its fundamentals. There are numerous rapid transport mechanisms compared to the slow process of molecular diffusion. These rapid processes efficiently move chemicals within and across the various media compartments of the Earth. We have thus sought to present the subject of chemical mobility in a handbook-type format so as to make the material applied rather than theoretical, while being useful and accessible and relevant to a broad range of users. Our aim is to document and reflect the present state of the science. ... 

Estimating the MTC for the bank water exchange process. Details concerning the theory were presented above in Sections 11.3.2 and 11.3.3. The chemical flux concept in equation form, such as Equation 11.2, requires that advection be connected to other on-going in-bed transport processes such as diffusion. Advection in a chemodynamic context cannot be considered a stand-alone process. The molecular diffusion transport process is used in Equation 11.5 however, it can be generalized to accommodate any diffusive-type process and the appropriate MTC. As such the appropriate sediment-side MTC is... 

The amides are probably molecularly dispersed in the melt but phase separate upon cooling and eventually migrate to free surfaces. The layers are most effective at reducing friction and adhesion other additives may be used to dissipate electrostatic charges. In these systems it seems that stored elastic strains around the precipitajj provide the driving force for molecular diffusive transport. The amide/polythene system also has a... 

Macropore Diffusion. Transport in a macropore can occur by several different mechanisms, the most important of which ate bulk molecular... 

For weU-defined reaction zones and irreversible, first-order reactions, the relative reaction and transport rates are expressed as the Hatta number, Ha (16). Ha equals (k- / l ) where k- = reaction rate constant, = molecular diffusivity of reactant, and k- = mass-transfer coefficient. Reaction... 

The problems that arise when experiments are carried out in a greatly reduced scale can be overcome if the Reynolds number is high and the flow pattern is governed mainly by fully developed turbulence. It is possible to ignore the Reynolds number, the Schmidt number, and the Prandtl number because the structure of the turbulence and the flow pattern at a sufficiently high level of velocity will be similar at different supply velocities and therefore independent of the Reynolds number. The transport of thermal energy and mass by turbulent eddies will likewise dominate the molecular diffusion and will therefore also be independent of the Prandtl number and the Schmidt number. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

Heat is produced by chemical reaction in a reaction zone. The heat is transported, mainly by conduction and molecular diffusion, ahead of the reaction zone into a preheating zone in which the mixture is heated, that is, preconditioned for reaction. Since molecular diffusion is a relatively slow process, laminar flame propagation is slow. Table 3.1 gives an overview of laminar burning velocities of some of the most common hydrocarbons and hydrogen. 

Dead-end Pores Dead-end volumes cause dispersion in unsteady flow (concentration profiles ar> ing) because, as a solute-rich front passes the pore, transport oceurs by molecular diffusion into the pore. After the front has passed, this solute will diffuse back out, thus dispersing. 

The liquid-liquid extraction process is based on the specific distribution of dissolved components between two immiscible fluids, for instance, between aqueous and organic liquids. The process refers to a mass exchange processes in which the mass transport of component (j) from phase (1) to phase (2) by means of convection or molecular diffusion acts to achieve the chemical potential (p) equilibrium (134) ... 

In the film-penetration model (H19), it is assumed that the reactant A penetrates through the surface element by one-dimensional unsteady-state molecular diffusion. Convective transport is assumed to be insignificant. The diffusing stream of the reactant A is depleted along the path of diffusion by its reversible reaction with the reactant B, which is an existing component of the liquid surface element. If such a reaction can be represented as... 

Atmospheric Reaeration. Interfacial properties and phenomena that govern oxygen concentrations in river systems include 1) oxygen solubility (temperature, partial pressure and surface dependency), 2) rate of dissolution of oxygen (saturation level, temperature and surface thin film dependency, i.e., ice, wind), and 3) transport of oxygen via mixing and molecular diffusion. A number of field and empirically derived mathematical relationships have been developed to describe these processes and phenomena, the most common of which is (32) ... 

Under some circumstances transport processes other than fluid motion and molecular diffusion are important. One important example is sedimentation due to gravity acting on particulate matter submerged in a fluid, e.g., removal of dissolved sulfur from the atmosphere by precipitation scavenging, or transport of organic carbon from the surface waters to the deep... 

Diffusion as referred to here is molecular diffusion in interstitial water. During early diagenesis the chemical transformation in a sediment depends on the reactivity and concentration of the components taking part in the reaction. Chemical transformations deplete the original concentration of these compounds, thereby setting up a gradient in the interstitial water. This gradient drives molecular diffusion. Diffusional transport and the kinetics of the transformation reactions determine the net effectiveness of the chemical reaction. 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

---