Fluids diffusion rate

The degree to which inhaled gases, vapors, and particulates are absorbed, and hence their potential to produce systemic toxicity, depends on their solubihty in tissue fluids, any metaboHsm by lung tissue, diffusion rates, and equiUbrium state. 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

The diffusion coefficient in these phases D,j is usually considerably smaller than that in fluid-filled pores however, the adsorbate concentration is often much larger. Thus, the diffusion rate can be smaller or larger than can be expected for pore diffusion, depending on the magnitude of the flmd/solid partition coefficient. 

For amorphous polymers above the T, i.e. in the flexible and rubbery states there is more space available through which diffusing molecules may pass, and so these materials show comparatively high diffusion rates with diffusing fluids. 

At constant conditions, different fluids will diffuse at different rates into a particular elastomer (with their rates raised proportionally by increasing the exposed area), and each will reach the far elastomer-sample surface proportionally more rapidly with decreasing specimen thickness. Small molecules usually diffuse through an elastomer more readily than larger molecules, so that, as viscosity rises, diffusion rate decreases. One fluid is likely to diffuse at different rates through different elastomers. Permeation rates are generally fast for gases and slow for liquids (and fast for elastomers and slow for thermoplastics and thermosets). 

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. 

The reactant solid B is porous and the reaction occurs in a diffuse zone. If the rate of the chemical reaction is much slower compared to the rate of diffusion in the pores, the concentration of the fluid reactant would be uniform throughout the pellet and the reaction would occur at a uniform rate. On the other hand, if the chemical reaction rate is much faster than the pore diffusion rate, the reaction occurs in a thin layer between the unreacted and the completely reacted regions. The thickness of the completely reacted layer would increase with the progress of the reaction and this layer would grow towards the interior of the pellet). 

Alkyl chain heterogeneities cause cell membrane bilayers to remain in the fluid state over a broad temperature range. This permits rapid lateral diffusion of membrane lipids and proteins within the plane of the bilayer. The lateral diffusion rate for an unconstrained phospholipid in a bilayer is of the order of 1 mm2 s 1 an integral membrane protein such as rhodopsin would diffuse 40nm2 s 1. 

External diffusion of reactants. This step depends on the fluid dynamic characteristics of the system. Reactants must first diffuse from the bulk gaseous phase to the outer surface of the carrier through a stagnant thin film of gas. Molecular diffusion rates in the bulk have the activation energy E1 = 2 to 4 kcal/mol and they vary with Tm. 

There is also a diffusion rate factor when polymers are exposed to any gas or liquid. Usually absorption of fluid (swelling) takes place faster than extraction of soluble constituents of the polymer and builds up to an equilibrium condition as shown in Figure 4.2 (curve A). If extraction is also taking place, for example from a plasticised material, a maximum swelling may be reached (curve B). If the absorption of fluid is accompanied by oxidation, the volume may continue to increase (curve C). 

Molecules tend to diffuse randomly, in no particular direction, within any fluid, independently of the flow rate of the mobile phase. Their diffusion rate is determined by the type of molecule, the nature of the mobile phase, and the temperature, and is expressed quantitatively by their diffusion constants. 

As its name suggests, supercritical fluid extraction (SEE) relies on the solubilizing properties of supercritical fluids. The lower viscosities and higher diffusion rates of supercritical fluids, when compared with those of liquids, make them ideal for the extraction of diffusion-controlled matrices, such as plant tissues. Advantages of the method are lower solvent consumption, controllable selectivity, and less thermal or chemical degradation than methods such as Soxhlet extraction. Numerous applications in the extraction of natural products have been reported, with supercritical carbon dioxide being the most widely used extraction solvent. However, to allow for the extraction of polar compounds such as flavonoids, polar solvents (like methanol) have to be added as modifiers. There is consequently a substantial reduction in selectivity. This explains why there are relatively few applications to polyphenols in the literature. Even with pressures of up to 689 bar and 20% modifier (usually methanol) in the extraction fluid, yields of polyphenolic compounds remain low, as shown for marigold Calendula officinalis, Asteraceae) and chamomile Matricaria recutita, Asteraceae). " ... 

Small changes in the temperature or pressure of a supercritical fluid may result in great changes in its viscosity and in the diffusivity and solubility of compounds dissolved within it. In such systems, the bioconversion rate is increased thanks to the high diffusion rates which facilitate transport phenomena. In some cases a high diffusion rate can also facilitate product separation. 

Why adsorption, ion exchange and heterogeneous catalysis in one book The basic similarity between these phenomena is that they all are heterogeneous fluid-solid operations. Second, they are all driven by diffusion in the solid phase. Thus, mass transfer and solid-phase diffusion, rate-limiting steps, and other related phenomena are common. Third, the many aspects of the operations design of some reactors are essentially the same or at least similar, for example, the hydraulic analysis and scale-up. Furthermore, they all have important environmental applications, and more specifically they are all applied in gas and/or water treatment. 

Meade (1966) shows that claystones have a porosity decreasing to 0% at 1 Km depths and sandstones, 20% porosity at the same depth. Manheim (1970) shows that ionic diffusion rates in sediments are 1/2 to 1/20 that of free solutions when the sediments have porosities between 100 - 20%. It is evident that the burial of sediments creates a very different physical environment than that of sedimentation. As a result of reduced ionic mobility in the solutions, a different set of silicate-solution equilibria will most certainly come into effect with the onset of burial. The activity of ions in solution will become more dependent upon the chemistry of the silicates as porosity decreases and the system will change from one of perfectly mobile components in the open sea to one approaching a "closed" type where ionic activity in solution is entirely dictated by the mass of the material present in the sediment-fluid system. Although this description is probably not entirely valid even in rocks with measured zero porosity, for practical purposes, the pelitic or clayey sediments must certainly rapidly approach the situation of a closed system upon burial. 

The amount of adsorption is limited by the available surface and pore volume, and depends also on the chemical natures of the fluid and solid. The rate of adsorption also depends on the amount of exposed surface but, in addition, on the rate of diffusion to the external surface and through the pores of the solid for accessing the internal surface which comprises the bulk of the surface. Diffusion rates depend on temperature and differences in concentration or partial pressures. The smaller the particle size, the greater is the utilization of the internal surface, but also the greater the pressure drop for flow of bulk fluid through a mass of the particles. 

The last term in Equation 1 represents the global kinetics, expressed as the rate of adsorption per unit volume of bed. It cannot be written in terms of concentrations in the fluid phase—the equations must be solved to do this—but it may be expressed quantitatively in terms of Ci by writing an expression for the diffusion rate ... 

There have been few studies reported in the literature in the area of multi-component adsorption and desorption rate modeling (1, 2,3., 4,5. These have generally employed simplified modeling approaches, and the model predictions have provided qualitative comparisons to the experimental data. The purpose of this study is to develop a comprehensive model for multi-component adsorption kinetics based on the following mechanistic process (1) film diffusion of each species from the fluid phase to the solid surface (2) adsorption on the surface from the solute mixture and (3) diffusion of the individual solute species into the interior of the particle. The model is general in that diffusion rates in both fluid and solid phases are considered, and no restrictions are made regarding adsorption equilibrium relationships. However, diffusional flows due to solute-solute interactions are assumed to be zero in both fluid and solid phases. 

Phenol and dodecyl benzene sulfonate are two solutes that have markedly different adsorption characteristics. The surface diffusion coefficient of phenol is about fourteen times greater than that for dodecyl benzene sulfonate. The equilibrium adsorption constants indicate that dodecyl benzene sulfonate has a much higher energy of adsorption than phenol (20,22). The adsorption rates from a mixture of these solutes can be predicted accurately, if (1) an adequate representation is obtained for the mixture equilibria, and (2) the diffusion rates in the solid and fluid phases are not affected by solute-solute interactions. 

Solute-solute Interactions may affect the diffusion rates In the fluid phase, the solid phase, or both. Toor (26) has used the Stefan-Maxwell equations for steady state mass transfer In multicomponent systems to show that, in the extreme, four different types of diffusion may occur (1) diffusion barrier, where the rate of diffusion of a component Is zero even though Its gradient Is not zero (2) osmotic diffusion, where the diffusion rate of a component Is not zero even though the gradient Is zero (3) reverse diffusion, where diffusion occurs against the concentration gradient and, (4) normal diffusion, where diffusion occurs In the direction of the gradient. While such extreme effects are not apparent in this system, it is evident that the adsorption rate of phenol is decreased by dodecyl benzene sulfonate, and that of dodecyl benzene sulfonate increased by phenol. 

A mathematical model has been developed to describe the kinetics of multicomponent adsorption. The model takes into account diffusional processes in both the solid and fluid phases, and nonlinear adsorption equilibrium. Comparison of model predictions with binary rate data indicates that the model predictions are in excellent for solutes with comparable diffusion rate characteristics. For solutes with markedly different diffusion rate constants, solute-solute interactions appear to affect the diffusional flows. In all cases, the total mixture concentration profiles predicted compares well with experimental data. 

Enhanced Mass Transfer, Diffusivity Supercritical fluids share many of the advantages of gases, including lower viscosities and higher diffusivities relative to liquid solvents, thereby potentially providing the opportunity for faster rates, particularly for diffusion-limited reactions. 

The change in the two-state distribution is easily monitored by a convenient one-wavelength measurement of the neutral form fluorescence, and this can be used for probing the membrane. The fairly large differences in wavelengths of excitation (300 nm), fluorescence of the neutral form (360 nm), and fluorescence of the anion form (480 nm) makes the fluorescence free from spectral interference. The variation of the P form fluorescence intensity with temperature showed a maximum at phase-transition temperatures (Tc) for both DMPC (23°C) (Fig. 2) and DPPC (42°C) membranes (Fig. 3). Figures 2 and 3 show a very nice correspondence of this variation with DPH fluorescence polarization and self-diffusion rate [93] of 22Na+. The coexistence of solid gel and fluid liquid-crystalline phases at Tc and the consequent imperfection of the membrane [93] result in a redistribution of... 

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