Mixing bulk convective

For mass transfer in a simple ternary system without chemical reaction, the solute concentration profiles near the interface are as shown in Fig. 3. The concentration in the bulk of each phase is uniform because of convective mixing effects, but very near the interface the rate of mass transfer depends increasingly on molecular diffusion. 

The output of the mass spectrometer, P u is proportional to the rate of entry of a specific gas species into the vacuum system (Equation 5). At membrane steady-state conditions, the output of the mass spectrometer is also proportional to partial pressures at the membrane-fluid interface, Pji A relationship between Pr. and the partial pressure in the bulk fluid, Pf. is needed. For P7i = Pf. a negligible rate of gas transport out of the fluid or a high degree of concentration uniformity within the fluid is required. The latter can be approached through vigorous convective mixing or by rapid fluid diffusing properties. Because of the sensitivity limitations of the mass spectrometer, the necessary membrane transport, is relatively fixed. 

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-... 

In shear mixing, shear stresses give rise to slip zones and mixing takes place by interchange of particles between layers within the zone. Diffusive mixing occurs when particles roll down a sloping surface. Convective mixing is by deliberate bulk movement of packets of powder around the powder mass. 

Distributive or simple mixing is induced by plug or bulk convection. Bulk convection can be random or ordered. Ordered bulk convection rearranges constant volumina in a well defined way, and the progress of mixing action can be predicted mathematically. In random bulk convection, chunks of material are randomly redistributed, and modeling the mixing action is for most cases not possible. 

Chung and Lange [26] studied convective diffusion and dispersion in steel melts and the relative contributions of bulk convection and eddy diffusion to the Peclet number. It was found that for Peclet numbers less than five the mixing time was determined by turbulent diffusion, while for increasing Peclet number, the contribution of the bulk convection to mixing increased due to the decrease in the effective diffusion distance. 

All of these might occur under natural convection, mixed convection, or natural-circulation conditions and each of these as laminar or turbulent flow. At the same time, detailed descriptions of the wall-to-fluid friction must also consider the states of the fluid near the wall and in the bulk. The number of empirical correlations needed to cover all possibilities for heat transfer and wall friction is large. 

The difficulties of bulk polymerization are compounded by the inherent nature of the reaction mass. Vinyl monomers have rather large exothermic heats of polymerization, typically between -10 and -21 kcal/mol. Organic systems also have low heat capacities and thermal conductivities, about half those of aqueous solutions. Thus, the temperature can rise very quickly. To top it all off, the tremendous viscosities prevent effective convective (mixing) heat transfer. As a result, the overall heat-transfer coefficients are very low, making it difficult to remove the heat generated by the reaction. This raises the temperature, further increasing the rate of reaction (see Example 9.2) which in turn increases the rate of heat evolution, and can ultimately lead to disaster To quote Schildknecht [2] on laboratory bulk polymerizations, If a complete rapid polymerization of a reactive monomer in large bulk is attempted, it may lead to loss of the apparatus, the polymer or even the experimenter. ... 

Although molecular diffusion itself is very slow, its effect is nearly always enhanced by turbulent eddies and convection currents. These provide almost perfect mixing in the bulk of each Hquid phase, but the effect is damped out in the vicinity of the interface. Thus the concentration profiles at each... 

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. 

In conduction, heat is conducted by the transfer of energy of motion between adjacent molecules in a liquid, gas, or solid. In a gas, atoms transfer energy to one another through molecular collisions. In metallic solids, the process of energy transfer via free electrons is also important. In convection, heat is transferred by bulk transport and mixing of macroscopic fluid elements. Recall that there can be forced convection, where the fluid is forced to flow via mechanical means, or natural (free) convection, where density differences cause fluid elements to flow. Since convection is found only in fluids, we will deal with it on only a limited basis. Radiation differs from conduction and convection in that no medium is needed for its propagation. As a result, the form of Eq. (4.1) is inappropriate for describing radiative heat transfer. Radiation is... 

Convection involves the transfer of heat by means of a fluid, including gases and liquids. Typically, convection describes heat transfer from a solid surface to an adjacent fluid, but it can also describe the bulk movement of fluid and the associate transport of heat energy, as in the case of a hot, rising gas. Recall that there are two general types of convection forced convection and natural (free) convection. In the former, fluid is forced past an object by mechanical means, such as a pump or a fan, whereas the latter describes the free motion of fluid elements due primarily to density differences. It is common for both types of convection to occur simultaneously in what is termed mixed convection. In such instance, a modified form of Fourier s Law is applied, called Newton s Law of Cooling, where the thermal conductivity is replaced with what is called the heat transfer coefficient, h ... 

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