Convective mixing, solids

In general, mass transfer is not limited by diffusion rates in the supercritical phase. In fact, significant buoyancy effects in supercritical fluids enhance mass transfer rates with convective mixing (58). Usually, mass transfer limitations will occur in either a liquid or solid phase. 

The parameter 8 which we can see in Eq. (5.2) can be interpreted as one-half of the effective thickness of the sample if the sample is solid and if the stationary distribution of the charge carriers has already been established. In case of a melt where convective mixing in the bulk occurs, the value 5 should correspond to the thickness of the diffusive layer where mixing is absent. The exact value of 5 in sulphide melts at free convection conditions was not a subject of experimental investigatirms the order of value about 10 cm can be estimated from hydrodynamic considerations. That is why we are not able to extract the precise value of xj from the data on limiting electron currents ioo-... 

A slab of porous solid 1/2-in. thick is soaked in pure ethanol [1]. The void space in the solid occupies 50% of its volume. The pores are fine, so that molecular diffusion can take place through the liquid in the passages there is no convective mixing. The effective diffusivity of the system ethanol-water in the pores is one-tenth that in the free liquid. 

Typical phase diagram of a binary system with complete liquid and solid solubility. The first-to-freeze component will have composition Cl. The rejected B component will be pushed ahead of the solidification front and, if convectively mixed with the remaining melt, the solid will become richer in 6 as the process continues. 

If convective mixing can be avoided, after the first-to-freeze composition solidifies the rejected component will build up as a diffusion layer ahead of the moving solidification front, increasing the amount of the rejected component incorporated into the solid. Eventually, the composition in the melt will build up to C2 at the solidification interface and the solid will have composition Co and a steady-state situation is reached in which solute is being incorporated into the solid at the same rate as it is entering the advancing diffusion layer. 

Final composition profile of a directionally solidified ingot with complete convective mixing. The composition of the solid varies continually with distance and the solute that was rejected initially is later incorporated into the solid so that the overall average composition is the starting composition Co-... 

Composition along a directionally solidified sample in which a fraction /has been solidified with no convective mixing. The first to freeze has composition is Ci =kCa- The rejected B-rich component builds up a diffusion layer ahead of the advancing solidification front. When the composition in the melt C2 = kCo, the solid will have the composition Co. 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

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