Interphase gradient

In order to identify the interphase gradients, two diagnostic tests have been applied ... 

In our kinetic study, working conditions in absence of interphase gradients were investigated. The stirring speed was varied from 2000 to 3500 r.p.m. and the gas flow rate from 6000 to 10000 std.cu.ft./bbl. The increase of gas/liquid ratio above 6000 std.cu.ft bbl and the stirring speed above 2500 r.p.m. did not influence the S, Ni and V conversion. Nevertheless in order to assure the absence of interphase gradients, the kinetic study was carried out at 10000 std.cu.ft bl gas/liquid ratio and 3500 r.p.m. stirring speed. 

To this point we have dealt only with transport effects within the porous catalyst matrix (intraphase), and the mathematics have been worked out for boundary conditions that specify concentration and temperature at the catalyst surface. In actual fact, external boundaries often exist that offer resistance to heat and mass transport, as shown in Figure 7.1, and the surface conditions of temperature and concentration may differ substantially from those measured in the bulk fluid. Indeed, if internal gradients of temperature exist, interphase gradients in the boundary layer must also exist because of the relative values of the pertinent thermal conductivities [J.J. Carberry, Ind. Eng. Chem., 55(10), 40 (1966)]. 

Reformulation of the problems previously explained to account for interphase gradients essentially requires only the change of the surface boundary conditions. Assuming that we may see traditional mass- and heat-transfer coefficients as the rate constants characteristic of interphase transport, the boundary conditions for mass and energy conservation equations become... 

Now we may substitute from (ix) the expressions for the interphase gradients into equations (iii) and (iv). These substitutions end up more or less as might be expected. 

External diffusional effects were examined by varying the amoimt of the catalyst loa d in the reactor and the space-velocity. It was found that the best system to minimize interphase gradients is upflow since very similar sulfur removals were obtained when the amount of catalyst in the reactor was changed. 

The relevance of interphase gradients distinguishes between two different classes of problems, and this is reflected on the type of boundary condition at the pellet s surface. It is known that specifying the value of the concentration (or temperature) at the surfece (Dirichlet boundary condition) may not be realistic, and thus finite external transfer effects have to be considered (in a Robin-type boundary condition) [72]. Apart from these, a large number of additional effects have also been considered. Some examples include the nonuniformity of the porous pellet structure (distribution of pore sizes [102], bidisperse particles [103], etc.), nonuniformity of catalytic activity [104], deactivation by poisoning [105], presence of multiple reactions [106], and incorporation of additional transport mechanisms such as Soret diffusion [107] or intraparticular convection [108]. 

Diffusion theory involves the interdiffusion of macromolecules between the adhesive and the substrate across the interface. The original interface becomes an interphase composed of mixtures of the two polymer materials. The chemical composition of the interphase becomes complex due to the development of concentration gradients. Such a macromolecular interdiffusion process is only... 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Evidently, the critical pressure to cause failure decreases with a stiffer interphase modulus, E, or a reduced interlayer thickness, h, or both. This hypothesis has been tested on several simulation systems, which confirm that increased adhesion is possible with a negative transversal modulus gradient at the material interface. 

Under certain conditions, it will be impossible for the metal and the melt to come to equilibrium and continuous corrosion will occur (case 2) this is often the case when metals are in contact with molten salts in practice. There are two main possibilities first, the redox potential of the melt may be prevented from falling, either because it is in contact with an external oxidising environment (such as an air atmosphere) or because the conditions cause the products of its reduction to be continually removed (e.g. distillation of metallic sodium and condensation on to a colder part of the system) second, the electrode potential of the metal may be prevented from rising (for instance, if the corrosion product of the metal is volatile). In addition, equilibrium may not be possible when there is a temperature gradient in the system or when alloys are involved, but these cases will be considered in detail later. Rates of corrosion under conditions where equilibrium cannot be reached are controlled by diffusion and interphase mass transfer of oxidising species and/or corrosion products geometry of the system will be a determining factor. 

First, we must consider a gas-liquid system separated by an interface. When the thermodynamic equilibrium concentration is not reached for a transferable solute A in the gas phase, a concentration gradient is established between the two phases, and this will create a mass transfer flow of A from the gas phase to the liquid phase. This is described by the two-film model proposed by W. G. Whitman, where interphase mass transfer is ensured by diffusion of the solute through two stagnant layers of thickness <5G and <5L on both sides of the interface (Fig. 45.1) [1—4]. 

When discontinuous sucrose gradient centrifugation is used, two different density sucrose solutions should be piled up into the tube. If 20% (w/w) and 30% (w/w) density solutions are piled up, the ER-enriched fraction should be layered on the interphase between 20% (w/w) and 30% (w/w) sucrose solutions. 

Against simplistic views of the FIAM, it is necessary to stress that the model does not imply that the free metal ion is the only species available to the microorganism [2,14], Indeed, the internalisation flux (i.e. the rate of acquisition) depends on the free metal ion concentration at the biological interphase (which in the FIAM is practically cj ), but metal bound to a ligand in the solution can dissociate, can diffuse (under a negligible gradient according to the FIAM), and can eventually be taken up. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

When charges are separated, a potential difference develops across the interface. The electrical forces that operate between the metal and the solution constitute the electrical field across the electrode/electrolyte phase boundary. It will be seen that although the potential differences across the interface are not large ( 1 V), the dimensions of the interphase region are very small (—0.1) and thus the field strength (gradient of potential) is enormous—it is on the order of 10 V cm. The effect of this enormous field at the electrode/electrolyte interface is, in a sense, the essence of electrochemistry. 

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