Local mass exchange

Non-local mass exchange The effective mass flow is non-local (Case A) when atoms at a step edge can directly exchange with a vapor reservoir (through evaporation-condensation) or with an overall terrace reservoir that forms by fast direct adatom hops between different terraces. In such cases, we assume that step velocity is proportional to the chemical potential difference between the step and the reservoir ... 

Local Radiative Exchange The interchange rate Q between an isothermal gas mass at Tq and its isothermal black bounding surface of area Ai is given by... 

A common feature of all models for the upper part of circulating fluidized beds is the description of the mass exchange between dense phase and dilute phase. Analogously to low-velocity fluidized beds, the product of the local specific mass-transfer area a and the mass-transfer coefficient k may be used for this purpose. Many different methods for determining values for these important variables have been reported, such as tracer gas backmixing experiments [112], non-steady-state tracer gas experiments [117], model reactions [115], and theoretical calculations [114],... 

The results of the numerical solution of the conjugation boundary-value problem for the mass exchange (3.106), (3.107) are shown in Fig. 3.20. The initially homogeneously cold air gets the latent heat from the droplet layer and becomes warmer and warmer from cross section 1 to 5, etc. (family (I) of curves in Fig. 3.20,A). In turn, the droplets become cooler their temperature is reduced especially intensively at the EPR entrance (the dashed curve 0) but less and less intensively in subsequent cross sections (the family of curves (II)). The curves TE(z) and t(z) attract each other and meet at the theoretical infinity z —> -oo. The complex relation between the two profiles is testified by the local maxima on TE(z) at early cross sections (curves 1 and 2) and by negative values of the mass flow (3.97) presented in Fig. 3.20,B. A dilative thermal boundary layer grows over the droplet EPR. Its width dE(x) grows theoretically to infinity over the EPR, but the internal portions of all the variables tend to a certain final position within the EPR, 0 < z < 1. 

The heat and mass exchange coefficients aH and aH were taken constant in ( 3.50). However, they often depend on local flow circumstances. Their simplified description is given in what follows. 

Some complex compact heat exchanger surfaces have been studied using mass transfer methods, for example, naphthalene sublimation [109] and chemical reaction between a surface coating and ammonia added to the air stream [110]. These elegant but tedious methods yield local mass transfer coefficients that can be used to infer heat transfer coefficients by the usual analogy. This detailed information, in turn, should aid in the development of more efficient surfaces. Numerical studies have also yielded useful predictions for laminar flows [111, 112]. 

A Lagrangian modeling framework is one that moves with the local wind so that there is no mass exchange between the air parcel and its surroundings, with the exception of species emissions that are allowed to enter the parcel through its base (Figure 25.2). The... 

Besides, small subsystems of the solution relax, i.e., reach equilibrium much sooner than the entire solution. As a result, chemical equilibrium in separate parts of the solution is reached at different times. Equilibrium, reached in a separate part of the solution, is called local chemical equilibrium. The local equilibrium principle maintains that each small (but macroscopic) element of volume in a nonequilibrium overall system at any moment in time is in the state of equilibrium. Special significance is attributed to local equilibrium at the boxmdary of different media, which determines the nature and rate of the mass exchange between them. 

Note that r > 0 in reactions with the formation of i-th component, and r < 0 in case of its absorption. The values r are determined by the kinetics of chemical reactions, local thermodynamic state and the stoichiometric coefficients characteristic for given chemical reactions. According to chemical thermodynamics [5], the rate of mass exchange in a chemical reaction for the i-th component is determined by... 

First, we shall use a quasi-stationary approach already mentioned earlier, based on the assumption that characteristic times of heat and mass transfer in the gaseous phase are much shorter than in the liquid phase, since the coefficients of diffusion and thermal conductivity are much greater in the gas than in the liquid. Therefore the distribution of parameters in the gas may be considered as stationary, while they are non-stationary in the liquid. On the other hand, small volume of the drop allows us to assume that the temperature and concentration distributions are constant within the drop, while in the gas they depend on coordinates. Another assumption is that the drop s center does not move relative to the gas. Actually, this assumption is too strong, because in real processes, for example, when a liquid is sprayed in a combustion chamber, drops move relative to the gas due to inertia and the gravity force. However, if the size of drops is small (less than 1 pm) and the processes of heat and mass exchange are fast enough, then this assumption is permissible. As usual, we assume the existence of local thermodynamic equilibrium at the drop s surface, as well as equal pressures in both phases. The last condition was formulated at the end of Section 6.7. 

Abzalimov, R.R., Kaltashov, I.A. (2006) Extraction of local hydrogen exchange data from HDX CAD MS measurements by deconvolution of isotopic distributions of fragment ions. J Am Soc Mass Spectrom, 17(11), 1543-1451. 

We first illustrate the time lag procedure on a simple adsorption system where the partition between molecules in the gas phase and those on the surface is linear (linear isotherm). We also consider at any local point within the medium, the mass exchange between the two phases is so rapid that local equilibrium is instantaneously established, that is ... 

If the rate of mass exchange between the two phases is faster than the diffusion rate, we can invoke the local equilibrium between the two phases, that is ... 

Given below is the model of a subdivided mass exchanger that was developed in Example 1.2. Determine the local solute concentration profile, Ca(, r) on the tube side using the method of separation of variables discussed in Chapter 6. As part of your solution, you will need to define the relationship that will yield the eigenvalues. Also, use... 

Equation (28.3)) is obtained from the total mass balance in combination with the ideal gas law and the isobaric assumption. The result shown here is obtained after several manipulation steps that also require the enthalpy balance. This equation is an ordinary differential equation with respect to the spatial coordinate. It describes the change of the gas velocity due to a local change in temperature (second term on the right-hand side) and due to changes in the total mole number due to mass exchange with the electrode (third term) or the reforming process (last term). 

In a gas—sohd CFB with heterogeneous reactions and mass transfer, in Hne with the structural characteristics of the SFM model (Hong et al, 2012), as shown in Fig. 12, the mass transfer and reaction in any local space can be divided into components of the dense cluster (denoted by subscript c), the dilute broth (denoted by subscript f), and in-between (denoted by subscript i), respectively. And these terms can be represented by Ri (1 = gc, gf, gi, sc, sf, si). Both the dense and dilute phases are assumed homogenous and continuous inside, and the dense phase is fiarther assumed suspended uniformly in the dilute phase in forms of clusters of particles. Then the mass transfer terms can be described with Ranz-Marshall-hke relations for uniform suspension of particles (Haider and Basu, 1988). In particular, the mesoscale interaction over the cluster will be treated as is for a big particle with hydrodynamic equivalent diameter of d. Due to dynamic nature of clusters, there are mass exchanges between the dilute and dense phases with rate ofTk (k = g, s), pointing outward from the dilute to the dense phase. 

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