Material characteristics diffusion rate

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. 

We have established that the volume change kinetics of responsive gels are usually diffusion-controlled processes. Even when the diffusion analysis failed, the rates were comparable to or slower than a classical diffusive process. The implications of this for practical applications are quite negative, since diffusive processes are quite slow. A gel slab 1 mm thick with a diffusion coefficient of 10-7 cm2/s will take over an hour to reach 50% of equilibrium and more than six hours to reach 90% of equilibrium in response to a stimulus. This is far too slow for almost all potential applications of these materials. Since diffusion times scale with the square of dimension, decreasing the characteristic dimension of a sample will increase the rates dramatically. Thus if an application can make use of submillimeter size gels, millisecond response times become possible. Unfortunately, it may not always practical to use gels of such small dimension. 

Thermal desorption is a dynamic (non-equilibrium) technique in which a sample of hydrated corneum is heated at a constant rate in a dry atmosphere. The water desorption rate is plotted as a function of temperature. The general shape and temperature maxima of the desorption rate vs. temperature curves (Figure 12) are characteristic of the material s diffusion and equilibrium sorption behavior as well as experimental conditions such as heating rate. In a simple desorption process where... 

Intra-particle pores can form during weathering, upon solid formation, or may be partially collapsed interlayer space between mineral sheets, i.e., vermiculite and montmorillonite. The rate of diffusion through a pore is dependent on pore size, particle size, tortuosity, chemical interactions, chemical flux, and whether the pore is continuous or discontinuous. Besides pore diffusion, solid-phase diffusion is also a transport-limited process. Solid phase diffusion is dependent on the characteristics and interactions of the diffusant and the solid (53). Since there exists a range of diffusion rates in the soil, it follows that with increasing residence time the fraction of contaminants in the more remote areas of particles (accessible via slow diffusion) will increase. This slow sorption phenomenon is often the explanation researchers use to account for the slow continuous sorption and desorption observed between metals and natural materials (42,50,54). 

Substances with lower or no solubility in the membrane material cannot be dissolved or reach only low concentrations and thus low transport rates. As the diffusion coefficients of small molecules in a polymeric matrix do not differ too much, the separation characteristics of the membrane are primarily governed by the different solubifities of the components in the membrane material and to a lesser extent by their diffusion rates. When a smaller molecule is better dissolved in the membrane substance solubility and diffusion enhance each other. This is at least the case in dehydration processes where water is both the better soluble and faster diffusing component. In the removal of VOCs from gases where large molecules are removed and the larger molecule is the better soluble one, the diffusion step may counteract solubihty and reduce the overall selectivity towards smaller molecules. 

This mechanism means that diffusion of °Co from the water phase into the oxide film may be the first obstacle for °Co species to be overcome. Larger crystals with higher porosity in the film may facilitate the diffusion process, and vice versa. Thus, the characteristics of the oxide film can be expected to play an important role in °Co deposition and incorporation on stainless steel surfaces. A thick oxide film with a high density, as is obtained by pretreatment of the surfaces with oxygen-containing water, is therefore assumed to be effective in reducing °Co deposition since it lowers the diffusion rates of cobalt into the oxide layer and reduces the corrosion rates of the underlying base materials. 

Mass transport is the diffusion of compounds into, out of, or within the hydrogel network, and their diffusion rate depends on both the material and compound characteristics and interactions. 

Structure and water sorption characteristics of fuel cell media determine their transport properties. The dynamic properties of water determine microscopic transport mechanisms and diffusion rates of protons in PEM and CLs. Protons must be transported at sufficiently high rates, away from or toward the active Pt catalyst in anode and cathode catalyst layers, respectively. Effective rates of proton transport in nanoporous PEM and CLs result from a convolution of microscopic transport rates of protons with random network properties of aqueous pathways. Accounting for the geometry of these materials, namely, their external surface area and thickness, gives their resistances. 

In non-porous materials, gas permeation is described by a solution diffusion mechanism. Each gaseous conponent being transported through a non-porous material has a characteristic permeation rate that is a function ofits ability to dissolve and diffuse through the membrane material. The two relationships are expressed by Pick s law (diffusion) and Henry s law (solubility). Thus, permeation (P) through the membrane is a function of... 

The ultimate design, consequently, requires us to deal with the equilibrium characteristics of the system, material balances, diffusional rates, fluid dynamics, and ener requirements. In what follows, basic considerations of diffusion rates are discussed first (Part One) and these are later applied to specific operations. The principal operations, in turn, are subdivided into three categories, depending upon the nature of the insoluble phases contacted, gas-liquid (Part Two), liquid-liquid (Part Three), and solid-fluid (Part Four), since the equilibrium and fluid dynamics of the systems are most readily studied in such a grouping. 

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