Bulk flow chemical composition

For automotive applications, there is a need to develop specific membranes with custom surface/bulk properties in order to meet kinetics requirements (in particular cold start and acceleration). As discussed in Section 18.3, the permeation mechanism consists of two main steps (i) a surface step characterized by a surface resistance Rg and (ii) a bulk (diffusion-controlled) resistance Rj). For permeation in transient conditions of flow, the ratio Rg/Ro (Rs is the surface resistance and R the bulk diffusion resistance) is critical because the two steps are connected in series. Schematically, Rg is rate-controlling in transient conditions and R is rate-controlling in stationary conditions of flow. The value of the surface resistance Rg is a function of surface state (chemical composition of surface and roughness factor defined as the dimensionless ratio of the surface of the true to the geometrical solid-gas interface). The value of the bulk resistance R is a function of bulk state (chemical composition and microstructure) and membrane thickness (5).Therefore, the development of metallic membranes with custom properties requires the adjustment of all these physical parameters. 

The self-diffusion coefficient is determined by measuring the diffusion rate of the labeled molecules in systems of uniform chemical composition. This is a true measure of the diffusional mobility of the subject species and is not complicated by bulk flow. It should be pointed out that this quantity differs from the intrinsic diffusion coefficient in that a chemical potential gradient exists in systems where diffusion takes place. It can be shown that the self-diffusion coefficient, Di, is related to the intrinsic diffusion coefficient, Df, by... 

Once an appropriate frame of reference is chosen, a two components (A, B) system may be described in terms of the mutual diffusion coefficient (diffusivity of A in B and vice versa). Unfortunately, however, unless A and B molecules are identical in mass and size, mobility of A molecules is different with respect to that of B molecules. Accordingly, the hydrostatic pressure generated by this fact will be compensated by a bulk flow (convective contribution to species transport) of A and B together, i.e., of the whole solution. Consequently, the mutual diffusion coefficient is the combined result of the bulk flow and the molecules random motion. For this reason, an intrinsic diffusion coefficient (Da and Db), accounting only for molecules random motion has been defined. Finally, by using radioactively labeled molecules it is possible to observe the rate of diffusion of one component (let s say A) in a two component system, of uniform chemical composition, comprised of labeled and not labeled A molecules. In this manner, the self-diffusion coefficient (Da) can be defined [54]. Interestingly, it can be demonstrated that both Da and Da are concentration dependent. Indeed, the force/acting on A molecule at point X is [1]... 

There are instances where a qualitative test for comparative or quality control (QC) purposes may be desired and the quantitative test methods used for equipment design or analysis purposes described in the preceding sections are not essential for the flow concerns being assessed. These non-scalable, qualitative tests may be used to measure cenain attributes/characteristics of the bulk solid within a pre-defined range. These attributes may include chemical composition, particle size, color, moisture, and often, flow properties. 

SEM microphotogaphs and EDAX scans of the cross section and outer surface of the slag deposit, illustrated in Figure 10, indicate the chemistry of the deposit is not uniform. The bulk of the fused material is rich in silica, low in iron, and virtually depleted of potassium. The outermost layers, no more than 2 to 3p thick, are very rich in iron and frequently also rich in calcium. On occasion, the outer surface is covered with small particulate, several microns in diameter, or undissolved cubic or octahedral crystals whose origin is pyrites. Similar formations have been observed in full-scale operation. The evidence indicates deposits form under axial symmetric flow conditions in the furnace by the fluxing action at the heat transfer surface of small particles, <8p in diameter, of decidedly different chemical composition and mineral source. Migration of the fly ash to the surface is by means of eddy diffusion, thermophoresis, or Brownian motion. 

The laser irradiation induced the formation of polymer cylinders in the bulk of the film. Acrylic monomers underwent a volume decrease of 10 to 15% when polymerized. The underlying reason was that the gradient of chemical composition resulting from the spatially controlled conversion of monomer into polymer immediately induced the flowing of monomer and photoinitiator molecules to the illuminated areas. Hollows created by volume shrinkage were almost immediately filled by reactive species. 

The equilibrium distribution of a mixture of volatile liquids between a vapor phase and a liquid phase in a closed vessel was introduced in Sections 3.3.7.1 and 4.1.2 as the basis for tbe separation process of distillation. The preferential enrichment of the vapor phase with the more volatile species and the liquid phase with the less volatile species was illustrated in Section 4.1.2 for a variety of systems, along with the procedures for calculating the composition of each phase in a closed system. How chemical reactions in the liquid phase affect such vapor-liquid equilibrium was demonstrated in Section 5.2.I.2. In Section 6.3.2.1, open systems of flash vaporization and batch distillation in the context of bulk flow of the vapor and liquid phases parallel to the direction of the force were studied, and the separation achieved was quantified. The most common configuration of separation based on vapor-liquid equilibrium employs, however, a vertical column in which the vapor stream flows up and the liquid stream flows down. How the vapor and the liquid phases may contact each other was illustrated, for example, in Figure 2.1.2(b) for a... 

Chemical interdiffusion on a substitutional lattice can therefore be considered from two viewpoints. In the V-frame, it is described by a single diffusivity (i.e., the interdiffusivity). In a local C-frame fixed with respect to the local bulk material, the material flows locally with the velocity v% relative to the V-frame and the description of the fluxes of the two components requires two diffusivities (i.e., the intrinsic diffusivities). These three diffusivities are related by Eq. 3.25, and each is generally a function of the local composition. 

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