Diffusion single-phase

At room temperature, diffusion is so slow that the alloy just stays like this, frozen as a single phase. But if you heat it up just a little - to 160°C, for example - and hold it there ("ageing"), the copper starts to diffuse together to form an enormous number of very tiny (nm) plate-like particles, of composition roughly CuAlj. On recooling to room temperature, this new structure is again frozen in. 

It seems probable that a fruitful approach to a simplified, general description of gas-liquid-particle operation can be based upon the film (or boundary-resistance) theory of transport processes in combination with theories of backmixing or axial diffusion. Most previously described models of gas-liquid-particle operation are of this type, and practically all experimental data reported in the literature are correlated in terms of such conventional chemical engineering concepts. In view of the so far rather limited success of more advanced concepts (such as those based on turbulence theory) for even the description of single-phase and two-phase chemical engineering systems, it appears unlikely that they should, in the near future, become of great practical importance in the description of the considerably more complex three-phase systems that are the subject of the present review. 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

The theoretical treatment which has been developed in Sections 10.2-10.4 relates to mass transfer within a single phase in which no discontinuities exist. In many important applications of mass transfer, however, material is transferred across a phase boundary. Thus, in distillation a vapour and liquid are brought into contact in the fractionating column and the more volatile material is transferred from the liquid to the vapour while the less volatile constituent is transferred in the opposite direction this is an example of equimolecular counterdiffusion. In gas absorption, the soluble gas diffuses to the surface, dissolves in the liquid, and then passes into the bulk of the liquid, and the carrier gas is not transferred. In both of these examples, one phase is a liquid and the other a gas. In liquid -liquid extraction however, a solute is transferred from one liquid solvent to another across a phase boundary, and in the dissolution of a crystal the solute is transferred from a solid to a liquid. 

A. Comments on Diffusion Coefficients in Single-Phase Media... 

FIG. 5 Order parameter for disperse pseudophase water (percolating clusters versus isolated swollen micelles and nonpercolating clusters) derived from self-diffusion data for brine, decane, and AOT microemulsion system of single-phase region illustrated in Fig. 1. The a and arrow denote the onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The other arrow (b) indicates where AOT self-diffusion begins to increase. 

As for a single phase system, the rate of the reaction is still dependent on the probability of reactants meeting and therefore on the concentration of the reagents. However, in the biphasic system, the critical concentration of these components is no longer their total concentration in the whole system but the concentration where the reaction takes place. This concentration will be dependent on a number of factors, and the most influential are the rate of diffusion of the reactants to the catalyst and the relative solubility of the reagents in each phase. These two factors are interdependent, and will be considered in turn. 

Piret, E. L., Ebel, R. A., Kiang, C. T. and Armstrong, W. P. Chem. Eng. Prog. 47 (1951) 405 and 628. Diffusion rates in extraction of porous solids-1. Single phase extractions 2. Two-phase extractions. 

Relative permeability is defined as the ratio between the permeability for a phase at a given saturation level to the total (or single-phase) permeability of the studied material. This parameter is important when the two-phase flow inside a diffusion layer is investigated. Darcy s law (Equation 4.4) can be extended to two-phase flow in porous media [213] ... 

The diffusive models treat the membrane system as a single phase. They correspond more-or-less to the vapor-equilibrated membrane (panel c of Figure 6). Because the collapsed channels fluctuate and there are no true pores, it is easiest to treat the system as a single, homogeneous phase in which water and protons dissolve and move by diffusion. Many membrane models, including some of the earliest ones, treat the system in such a manner. 

Diffusion is that irreversible process by which matter spontaneously moves from a region of higher concentration to one of lower concentration, leading to equalization of concentrations within a single phase. 

Basically, whenever isotopic exchanges occur between different phases (i.e., heterogeneous equilibria), isotopic fractionations are more appropriately described in terms of differential reaction rates. Simple diffusion laws are nevertheless appropriate in discussions of compositional gradients within a single phase— induced, for instance, by vacancy migration mechanisms, such as those treated in section 4.10—or whenever the isotopic exchange process does not affect the extrinsic stability of the phase. 

Figure 6.1 shows the apparatus diagram. The diffusion flame burner consisted of an air plenum with an exit diameter of 22 mm, forced at a Strouhal number of 0.73 (100 Hz) by a single acoustic driver, and a coaxial fuel injection ring of diameter 24 mm, fed by a plenum forced by two acoustic drivers at either 100 Hz (single-phase injection) or 200 Hz (dual-phase injection). The fuel was injected circumferentially directly into the shear layer and roll-up region for the air vortices. In addition, this fuel injection was sandwiched between the central air flow and the external air entrainment. Thus the fuel injection was a thin cylindrical flow acted upon from both sides by air flow. 

Chemical reactions may be classified by the number of phases involved in the reaction. If the reaction takes place inside one single phase, it is said to be a homogeneous reaction. Otherwise, it is a heterogeneous reaction. For homogeneous reactions, there are no surface effects and mass transfer usually does not play a role. Heterogeneous reactions, on the other hand, often involve surface effects, formation of new phases (nucleation), and mass transfer diffusion and convection). Hence, the theories for the kinetics of homogeneous and heterogeneous reactions are different and are treated in different sections. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

The diffusivity of a species in a phase depends on both the species and the phase (in addition to temperature and pressure). In this section, we examine relations on the diffusivity of a species in different phases, and the diffusivity of different species in a single phase. 

Geospeedometry based on diffusion and zonatlon In a single phase... 

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