Transfers by molecular

It was again Natta who discovered transfers to hydrogen in coordination polymerizations [71]. He assumed breakage of the metal-polymer bond in the active centre 

Vandenberg has shown that H2 is an efficient transfer agent in polymerizations of ethylene, propene and styrene with TiCl4 + iso-Bu3Al (Et,AlCl, Et,Al) [76], 

Most catalytic systems used in industrial production yield polyalkenes with very long chains which are unsuitable for current processing procedures and applications. For regulating molecular mass, H2 is preferred to organometal-lics. Hydrogen is not a suitable transfer agent in diene polymerizations on cobalt complexes [67] because it reduces the Co (II) zr-allylic centre to inactive Co (I) particles. 

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For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

If the motion of the fluid is turbulent, the transfer of fluid by eddy motion is superimposed on the molecular transfer process. In this case, the rate of transfer to the surface will be a function of the degree of turbulence. When the fluid is highly turbulent, the rate of transfer by molecular motion will be negligible compared with that by eddy motion. For small degrees of turbulence the two may be of the same order. 

For mass transfer by molecular diffusion from a single sphere of diameter d to an infinite stationary medium, it can be shown that... 

We considered above the limit of propagation which depends on the heat transfer by molecular heat conduction to the walls of the tube in which the combustion is being studied, and so depends on the diameter of the tube. 

Laminar sub-layer. 0 < y+ < 5, Newton s Law of Viscosity (4), describes the flow and gives u+ = y+ here laminar flow and transfer by molecular diffusion dominate. 

Transfer by molecular diffusion is discussed in Section 12.2 and the concept of the mixing length in Section 12.3.2. By analogy with kinetic theory, the eddy kinematic viscosity, E, is given by ... 

In the absence of momentum transfer by molecular movement, the shear stress is given by ... 

The data available on the molecular diffusion coefficient of organic vapors in air are meager, but they indicate (in accordance with approximate theory) an inverse proportionality to the square root of molecular weight. The rate of mass transfer by molecular diffusion will be proportional to the diffusion coefficient and to the SVC, itself proportional to vapor pressure times molecular weight (M). We should expect, therefore, under standard conditions of ventilation, that the rate of loss will be proportional to vapor pressure X The ratio of observed rate to... 

Momentum quantity transferred by turbulent mechanism Momentum quantity transferred by molecular mechanism... 

Prandtl CpTl momentum quantity transfered by molecular mechanism all heat transfer prob-... 

Several possibilities are summarized in Figure 14—30. In the trivial case (case homogeneous mixture, there will be no mass transfer by molecular diffusion or convection since there is no concentration gradient or bulk motion. The next case (case b) corresponds to the flow of a well-mixed fluid mixture tlvrough a pipe. Note that there is no concentration gradients and thas molecular diffusion in this case, and all species move at the bulk flow velocity of Vt The mixture in the thud case (case c) is stationary (17= 0) and thus it corresponds to ordinary molecular diffusion in sfationary mediums, which we discussed before. Note that the velocity of a species at a location in this... 

As explained in Section II,A, when a soluble gas is mixed with an insoluble gas, it must diffuse through the latter to reach the interface. It is usual to refer to a gas film resistance. This implies a stagnant film of gas across which the soluble gas is transferred by molecular diffusion from the bulk gas with partial pressure p to the interface where the partial pressure is p,. If the component B has negligible vapor pressure, the reaction will proceed only in the liquid phase. 

Mass transfer by molecular diffusion is a result of molecular collisions on the microscopic scale. Fick s law states that mass flux due to molecular diffusion is proportional to the gradient of concentration ... 

Fourier s law of heat conduction states that heat transfer by molecular interactions at any point in a solid or fluid is proportional in magnitude and coincident with the direction of the negative gradient of the temperature field [48] ... 

Schliinder was originally derived to describe the effective radial conductivity in fixed beds. By using a cell concept the heat is assumed to be transferred by molecular conduction both in a pure gas phase with surface fraction 1 —. 77, and through a gas-solid bulk phase with the complimenting portion of the surface fraction, Deviations from sphericity and inter-particle point-... 

INTERPRETATION OF DIFFUSION EQUATIONS. Equation (21.16) is the basic equation for mass transfer in a nonturbulent fluid phase. It accounts for the amount of component A carried by the convective bulk flow of the fluid and the amount of A being transferred by molecular diffusion. The vector nature of the fluxes and concentration gradients must be understood, since these quantities are characterized by directions and magnitudes. As derived, the positive sense of the vectors is in the direction of increasing b, which may be either toward or away from the interface. As shown in Eq. (21.6), the sign of the gradient is opposite to the direction of the diffusion flux, since diffusion is in the direction of lower concentrations, or downhill, like the flow of heat down a temperature gradient. 

Ammonia, NH3, is being selectively removed from an air-NH3 mixture by absorption into water. In this steady-state process, ammonia is transferred by molecular diffusion through a stagnant gas layer 5 mm thick and then through a stagnant water layer 0.1 mm thick. The concentration of ammonia at the outer boundary of the gas layer is 3.42 mol% and the concentration at the lower boundary of the water layer is essentially zero. 

Pictures of bubbles and clouds have inspired some workers to develop reactor models based on the predicted behavior of individual bubbles [3,10]. In these models, the equations for gas interchange include a term for flow out of the bubble and a second term for mass transfer by molecular diffusion to the dense phase. In some models, the cloud is included as part of the bubble in others, diffusion from bubble to cloud and cloud to dense phase are treated as mass transfer steps in series. In these models, the mass transfer coefficient is assumed to vary with following the penetration theory, and the diffusion contribution is the major part of the predicted gas interchange rate. 

Monte Carlo simulation was carried out by Blauch and Saveant based on a percolation process, and Z>app was obtained as shown in Eq. (14-4) considering charge hopping and bounded motion of the redox center [14]. Bounded motion is a kind of local oscillation of redox molecules. In this model, charge transfer by molecular diffusion is not taken into account. 

The basic equation for mass transfer by molecular diffusion is Pick s law... 

The Higbie penetration model for mass transfer compensates for transient behavior. It assumes that mass transfer occurs during brief phase contacts that do not allow enough time for steady-state conditions. In other words, the phases collide but do not have a definitive and continuous interface with respect to time. The mass transfer is prompted by turbulence that refreshes the interface, and the refresh rate is the limiting step in mass transfer. Eddies approach the surface at which point mass transfer by molecular diffiision is initiated and is described by Azbel (1981) ... 

Introduction. When a fluid is flowing in laminar flow and mass transfer by molecular diffusion is occurring, the equations are very similar to those for heat transfer by conduction in laminar flow. The phenomena of heat and mass transfer are not always completely analogous since in mass transfer several components may be diffusing. Also, the flux of mass perpendicular to the direction of the flow must be small so as not to distort the laminar velocity profile. 

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