Convection multicomponent

The simple picture of diffusion given above ignores several issues that can be important. These include diffusion-engendered convection, multicomponent diffusion, and the limits of Fick s law. Each of these merits discussion. 

This chapter complements Refs. 21 and 22 in reviewing the progresses made on the transient, convective, multicomponent droplet vaporization, with particular emphasis on the internal transport processes and their influences on the bulk vaporization characteristics. The interest and importance in stressing these particular features of droplet vaporization arise from the fact that most of the practical fuels used are blends of many chemical compounds with widely different chemical and physical properties. The approximation of such a complex mixture by a single compound, as is frequently assumed, not only may result in grossly inaccurate estimates of the quantitative vaporization characteristics but also may not account for such potentially important phenomena as soot formation when the droplet becomes more concentrated with high-boiling point compounds towards the end of its lifetime. Furthermore, multi-... 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

It is known that, in a water phase, immiscible liquids such as gasoline or other petroleum products may form multicomponent droplets of various forms and sizes, under dispersive conditions. These droplets are transported by convection and diffusion, which contributes to the contamination of fresh water systems. However, during droplet transport, more volatile substances partition to the gas phase at the droplet surface, leaving less volatile material that volatilizes more slowly. More volatile material still exists in the droplet interiors, and it tends to diffuse toward the surface because of concentration gradients created by prior volatilization. Different components in a droplet have different volatilization rates, which may vary significantly during droplet transport, and as a result, the contamination of fresh water is affected accordingly. 

For the calculation of convective dissolution rate of a falling crystal in a silicate melt, the diffusion is multicomponent but is treated as effective binary diffusion of the major component. The diffusivity of the major component obtained from diffusive dissolution experiments of the same mineral in the same silicate melt is preferred. Diffusivities obtained from diffusion-couple experiments or other types of experiments may not be applicable because of both compositional effect... 

Richter F., Liang Y., and Minarik W.G. (1998) Multicomponent diffusion and convection in molten Mg0-Al203-Si02. Geochim. Cosmochim. Acta 62, 1985-1991. 

First a derivative is given of the equations of change for a pure fluid. Then the equations of change for a multicomponent fluid mixture are given (without proof), and a discussion is given of the range of applicability of these equations. Next the basic equations for a multicomponent mixture are specialized for binary mixtures, which are then discussed in considerably more detail. Finally diffusion processes in multicomponent systems, turbulent systems, multiphase systems, and systems with convection are discussed briefly. 

For a system with no kinetic or adsorption complications, the forward transition time x decreases while xr increases until finally x = xr in the limit, at steady state. (Because the convergence rate is slow, equality of x and xr is not commonly achieved experimentally before the onset of natural convection and nonplanar diffusion effects.) Quantitative treatments for single component systems, multicomponent systems, stepwise reactions, and systems involving chemical kinetics have been derived. The technique has not been used extensively. 

The balance over the ith species (equation IV. 5) consists of contributions from diffusion, convection, and loss or production of the species in ng gas-phase reactions. The diffusion flux combines ordinary (concentration) and thermal diffusions according to the multicomponent diffusion equation (IV. 6) for an isobaric, ideal gas. Variations in the pressure induced by fluid mechanical forces are negligible in most CVD reactors therefore, pressure diffusion effects need not be considered. Forced diffusion of ions in an electrical field is important in plasma-enhanced CVD, as discussed by Hess and Graves (Chapter 8). 

In Equation (9.6), x is the direction of flux, nt [mol m-3 s 1 ] is the total molar density, X [1] is the mole fraction, Nd [mol m-2 s 1] is the mole flux due to molecular diffusion, D k [m2 s 1] is the effective Knudsen diffusion coefficient, D [m2 s 1] is the effective bimolecular diffusion coefficient (D = Aye/r), e is the porosity of the electrode, r is the tortuosity of the electrode, and J is the total number of gas species. Here, a subscript denotes the index value to a specific specie. The first term on the right of Equation (9.6) accounts for Knudsen diffusion, and the following term accounts for multicomponent bulk molecular diffusion. Further, to account for the porous media, along with induced convection, the Dusty Gas Model is required (Mason and Malinauskas, 1983 Warren, 1969). This model modifies Equation (9.6) as ... 

Thermal diffusion, also known as the Ludwig-Soret effect [1, 2], is the occurrence of mass transport driven by a temperature gradient in a multicomponent system. While the effect has been known since the last century, the investigation of the Ludwig-Soret effect in polymeric systems dates back to only the middle of this century, where Debye and Bueche employed a Clusius-Dickel thermogravi-tational column for polymer fractionation [3]. Langhammer [4] and recently Ecenarro [5, 6] utilized the same experimental technique, in which separation results from the interplay between thermal diffusion and convection. This results in a rather complicated experimental situation, which has been analyzed in detail by Tyrrell [7]. 

The convective diffusion equation is analogous to equations commonly used in dealing with heat and mass transfer. Similarly, if migration can be neglected in a multicomponent solution, then the convective diffusion equation can be applied to each species,... 

The DGM by Mason and Malinauskas (1983) is the frequently used alternative to effective Fick s diffusion for the calculation of the multicomponent diffusion and convection in the porous media. A number of special features of multicomponent diffusion and convection in the pore space have been outlined by Krishna (1993). 

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

Moreover, the convection of the vapors in the pores was considered and the condensation in the pores was described by the multicomponent Kelvin equation (Shapiro and Stenby, 1977). 

His treatment includes natural convection but is limited to mass transfer controlled deposition and equilibrium distributions in the gas phase. Pollard and Newman (20) detail Si deposition on a rotating disk treating the multicomponent mass and heat transfer... 

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