Convection mixing

In what follows, both macromixing and micromixing models will be introduced and a compartmental mixing model, the segregated feed model (SFM), will be discussed in detail. It will be used in Chapter 8 to model the influence of the hydrodynamics on a meso- and microscale on continuous and semibatch precipitation where using CFD, diffusive and convective mixing parameters in the reactor are determined. 

It follows from (1) that the more negative metal, at a bimetallic junction, can be subject to more aggravated attack because of this lowered cathodic polarisation. In part, this may result from the greater ease of replenishment of dissolved oxygen under conditions where the ratio of surface area to electrolyte volume is very high. Rosenfel d has also produced evidence to show that rapid convective mixing in the condensed layer, under conditions of lowered relative humidity which permit rapid evaporation, further hastens the arrival of dissolved oxygen at the cathode and results in an additional... 

An infrequently used method (in pharmaceutical research) for determining the UWL permeability involves measuring transport of molecules across a high-porosity microfilter that is not coated by a lipid. The molecules are able to diffuse freely in the water channels of the microfilter. The filter barrier prevents convective mixing between the donor and acceptor sides, and an UWL forms on each sides of the microfilter. Camenisch et al. [546] measured the effective permeabilities of a series of drug molecules in 96-well microtiter plate-filterplate (Millipore GVHP mixed cellulose ester, 0.22 pm pore) sandwich where the filters were not coated by a lipid. The permeabilities were nearly the same for all the molecules, as shown in Fig. 7.8a. Our analysis of their data, Fig. 7.8b, indicates / aq = 460 pm (sandwich stirred at 150 rpm). We have been able to confirm similar results in our laboratory with different microfilters, using the lipid-free method. 

Ennis-King J.P. and Paterson L. Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations. 2003 SPE 10 349-356. 

PMS stars with M < 0.35 M0 have a simple structure - they are fully convective balls of gas all the way to the ZAMS. As the star contracts along its Hayashi track the core heats up, but the temperature gradient stays very close to adiabatic except in the surface layers. Li begins to burn in p, a reactions when the core temperature, Tc reaches c 3x 106 K and, because the reaction is so temperature sensitive (oc Tc16-19 at typical PMS densities) and convective mixing so very rapid, all the Li is burned in a small fraction of the Kelvin-Helmholtz timescale (see Fig. 1). 

The difference in the Li abundances in the G-stars of the Pleiades and the Sun, combined with the probable similarities in their overall chemical composition tell us that PMS Li depletion cannot be the whole story. Another mechanism, additional to convective mixing, must be responsible for Li depletion whilst solar-type stars are on the main-sequence. Recent PMS models that have their convective treatments tuned to match the structure of the Sun reproduce the mass dependence of Li depletion, but deplete too much Li compared with the Pleiades, and can even explain the solar A (Li) in the case of full spectrum turbulence models [9]. The over-depletion with respect to the Pleiades gets worse at lower masses. Better fits to the Pleiades data are achieved with PMS models that feature relatively inefficient convection with smaller mixing lengths. 

The axial dispersion coefficient [cf. Eq. (16-51)] lumps together all mechanisms leading to axial mixing in packed beds. Thus, the axial dispersion coefficient must account not only for molecular diffusion and convective mixing but also for nonuniformities in the fluid velocity across the packed bed. As such, the axial dispersion coefficient is best determined experimentally for each specific contactor. 

In principle these should be predictable from theory, but in practice there are many grey areas such as the effects of rotation, convective mixing, mass loss, the mechanism of stellar explosions, nuclear reaction rates such as 12C(a, y)160, the evolution of close binaries and the corresponding mass limits between which various things happen for differing initial chemical compositions. Figure 5.14 shows a version of what may happen in single stars with different initial masses and two metallicities, Z Z and Z Z /20. 

These mechanisms operate to varying extents in different kinds of mixers and with different kinds of particles. A trough mixer with a ribbon spiral involves almost pure convective mixing, and a simple barrel-mixer involves mainly a form of diffusion mixing. 

Thus, with convective mixing, 1 — b depends on the size of the sample. 

Willis, G. E., and Deardorff, J. W. (1980). A laboratory study of dispersion from a source in the middle of the convectively mixed layer. Atmos. Environ. 15, 109-117. 

Bakd et al. theoretically analyzed simultaneous gas flow and diffusion in Weibel s symmetric model. Th applied a time-varying flow with simultaneous longitudinal diffusion and concluded that convective mixing is much less important than mixing induced by molecular diffusion. 

This sol-gel procedure is an elaboration on well established entrapment methods [29], but with the added advantage of stability and better flow properties. Interestingly, none of the examples presented thus far demonstrate competitive behavior between multiple ligands (i.e. displacement) in the FAC analysis of trimethoprim and pyrimethamine a reversed order of elution based on is described, but this could simply be due to the shift towards an on-rate limited situation for higher affinity compounds, as described earlier. Erosion of dynamic competition between ligands could occur if the sol-gel allows convective mixing of the entrapped protein however the bimodal pore structure of these materials would... 

This study has been conducted with the objectives 1) to analyze and determine the effect of the free convective mixing in the melted zone upon the over-all solute transfer process in zone refining under various conditions and 2) to take into account the solute transfer both in the melted zone and in the adjacent P.S.Z. (mushy region) in predicting the rate of over-all solute transfer. The temperature distribution, composition, zone travel speed, zone dimension and other important parameters are considered in this study. 

Though free convective mixing in the melted zone increases the separation rate, its effect is far less important than the opposed effect of the Frame ter, D/ud. The theoretical maximum separation rate from a single zone pass may be expected if the D/ud value is less than 10 and no separation may result if the experimental value of D/ud is greater than about 10. ... 

Experimental data (57) show that the efficiency is not markedly decreased if the sample is injected faster provided that the volume at the top of the column into which the sample is injected is filled with some kind of porous material to prevent convective mixing. This permits the injection of large sample volumes. In actual practice the injection time seems to be the critical parameter (57). 

In what follows, the preceding evaluation procedure is employed in a somewhat different mode, the main objective now being to obtain expressions for the heat or mass transfer coefficient in complex situations on the basis of information available for some simpler asymptotic cases. The order-of-magnitude procedure replaces the convective diffusion equation by an algebraic equation whose coefficients are determined from exact solutions available in simpler limiting cases [13,14]. Various cases involving free convection, forced convection, mixed convection, diffusion with reaction, convective diffusion with reaction, turbulent mass transfer with chemical reaction, and unsteady heat transfer are examined to demonstrate the usefulness of this simple approach. There are, of course, cases, such as the one treated earlier, in which the constants cannot be obtained because exact solutions are not available even for simpler limiting cases. In such cases, the procedure is still useful to correlate experimental data if the constants are determined on the basis of those data. 

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