Diffusional flow

These authors classified solids on the basis of capiUaiy and diffusional flow ... 

Diffusional flow is important when grains are small (as they often are in ceramics) and when the component is subject to high temperatures at low loads. To select a material which resists it, you should... 

Metallic alloys are usually designed to resist power-law creep diffusional flow is only rarely considered. One major exception is the range of directionally solidified ( DS ) alloys described in the Case Study of Chapter 20 here special techniques are used to obtain very large grains. 

Ceramics, on the other hand, often deform predominantly by diffusional flow (because their grains are small, and the high lattice resistance already suppresses power-law creep). Special heat treatments to increase the grain size can make them more creep-resistant. 

As shown in Fig. 1.12, diffusional flow contributions in engineering situations are usually expressed by Fick s Law for molecular diffusion... 

Although the foregoing example in Sec. 4.2.1 is based on a linear coordinate system, the methods apply equally to other systems, represented by cylindrical and spherical coordinates. An example of diffusion in a spherical coordinate system is provided by simulation example BEAD. Here the only additional complication in the basic modelling approach is the need to describe the geometry of the system, in terms of the changing area for diffusional flow through the bead. 

The total diffusional flow into a pellet must allow for the fraction of pellet which is pore, and the tortuous path through the pore system. 

Several modifications of Poiseuille s equation have been attempted by various authors to describe permeability in the transitional region between viscous and diffusional flow. The assumptions underlying these modifications are often questionable and the results obtained offer little or no theoretical or experimental advantage over the BET theory for surface area measurements. Allen" " discusses these modifications as well as diffusional flow at low pressures. 

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. 

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. 

The contents of the parenthesis show velocity of the salt relative to water and is called the diffusional flow JD. The dissipation function provides a natural basis for the analysis of systems in which mechanical energy derived from the volume flow and the hydrostatic pressure gradient are utilized to produce a separation of salt from water in the face of an adverse concentration gradient. 

LP is the hydraulic conductivity coefficient and can have units of m s-1 Pa-1. It describes the mechanical filtration capacity of a membrane or other barrier namely, when An is zero, LP relates the total volume flux density, Jv, to the hydrostatic pressure difference, AP. When AP is zero, Equation 3.37 indicates that a difference in osmotic pressure leads to a diffusional flow characterized by the coefficient Lo Membranes also generally exhibit a property called ultrafiltration, whereby they offer different resistances to the passage of the solute and water.14 For instance, in the absence of an osmotic pressure difference (An = 0), Equation 3.37 indicates a diffusional flux density equal to LopkP. Based on Equation 3.35, vs is then... 

Hougen, McCauley, and Marshall [Tram. Am. Imt. Chem. Eng., 36, 183 (1940)] discussed the conditions under which capillary and diffusional flow may be expected in a drying solid and analyzed the published experimental moisture-gradient data for the two cases. Their curves indicate that capillary flow is typified by a moisture gradient involving a double curvature and point of inflection (Fig. 12-40a) while diffusional flow is a smooth curve, concave downward (Fig. 12-40b), as would be predicted from the diffusion equations. They also showed that the liquid-diffusion coefficient is usually a function... 

S. L. Marchiano and A. J. Arvia, "Diffusional Flow under Non-Isothermal Laminar Free Convection at a Thermal Convective Electrode," Electrochimica Acta, 13 (1968) 1657-1669. 

A computer program has been developed which simulates the diffusional flow through geological environments. The model is based on the following simplifications ... 

For a binary mixture, with the introduction of the diffusional flow j Ai according to (1.161) with DAB = DBA = D, this is transformed into... 

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