Condensation and evaporation mass flux

From the kinetic theory of gases, an expression for the net-mass flux at the interphase can be derived based on the works of Hertz [223] and Knudsen [224]. From a statistical consideration under the assumption of a Maxwell-Boltzmann distribution for the velocity of the gas molecules, the maximum condensation mass flux can be calculated. The evaporation mass flux has to equal the condensation mass flux at equilibrium. The resulting Hertz-Knudsen equation for calculating the area specific net-mass flux is given below ... 

The water transport in OMD is a simultaneous heat and mass transfer process. Evaporation cools the feed and condensation warms the brine solution. This results in a temperature gradient across the membrane, which adversely affects the driving force and in turn the mass flux. 

The calculation of the resistance coefficients can be accomplished in the frame of the Monin-Obukhov similarity theory (Monin and Yaglom, 1971). The genuine flux quantities are the friction velocity u and the scale functions 0 and referring to temperature and humidity. The turbulent momentum flux f, the sensible heat flux the mass flux from evaporation and condensation and the corresponding latent heat flux are... 

Sitarski-Nowakowski Approach None of the approaches given above describes the dependence of the transition regime mass flux on the molecular mass ratio z of the condensing/evaporating species and the surrounding gas. Sitarski and Nowakowski (1979) applied the 13-moment method of Grad (Hirschfelder et al. 1954) to solve the Boltzmann equation to obtain... 

Equation (13.7) is called the condensation equation and describes mathematically the rate of change of a particle size distribution n(v,t) due to the condensation or evaporation flux / ( , /), neglecting other processes that may influence the distribution shape (sources, removal, coagulation, nucleation, etc). A series of alternative forms of the condensation equation can be written depending on the form of the size distribution used or the expression for the condensation flux. For example, if the mass of a particle is used as the independent variable, one can show that the condensation equation takes the form... 

It is important to stress again that MD is not purely a mass transfer operation in the way that, for example, direct osmosis is, because heat transfer is also a very important element of the process due to the water evaporation at the feed side and water condensation at the extract side. In this case, a simultaneous heat and mass transfer takes place through the membrane. Simultaneously here means that the heat transfer and mass transfer are intimately connected the heat transfer rate depends on mass flux and vice versa. 

Here we do not consider in detail the modeling of the mass and heat transfer processes from the droplet surface into the surrounding gas. The evaporation or condensation of droplets has been addressed in detail by Kukkonen et al. (1989), Kulmala and Vesala (1991), Vesala and Kukkonen (1992), and Vesala and Kulmala (1993) see also Kulmala et al. (1993). Vesala (1991) has discussed the validation of various mass flux and droplet temperature equations against laboratory-scale experimental data. 

The VBS provides a convenient framework for organic dynamics in addition to equilibrium partitioning because equilibrium is a balance between condensation (the molecular flux from the gas to the particle phase) and evaporation (the molecular flux from the particle phase to the gas). The difference between the vapor concentrations at the particle surface and far away from it serves as a driving force for net condensation or evaporation. Because the particle surface is usually assumed to be in equilibrium with the gas phase adjacent to it, evaporation depends explicitly on volatility. Condensation on the other hand depends only on the collision rate of molecules with the surface and so it is first order independent of volatility. The volatility of organic compounds thus affects the aerosol growth dynamics specifically through its influence on the evaporation term in the driving force for mass transport. 

Figure 16. Schematic illustration of envelopes of gas species i, in this case Mg, surrounding a volatilizing molten chondrule in space. The size of the gas envelope is a function of ambient background pressure P by virtue of the effect that pressure has on the gas molecule diffusivity D,. The diffusion coefficient can be calculated from the kinetic theory of gases, as shown. The level of isotopic fractionation associated with volatilization of the molten chondrule depends upon the balance between the evaporative flux J vap and the condensation flux Tom When the fluxes are equal (i.e., when = 0), there is no mass-dependent isotope fractionation associated with volatilization. This will be the case when the local partial pressure P, approaches the saturation partial pressure P,...

The mass balances of the species in the diffusion media can be deduced from eq 23. Furthermore, the fluxes of the various species are often already known at steady state. For example, any inert gases (e.g., nitrogen) have a zero flux, and the fluxes of reactant gases are related to the current density by Faraday s law (eq 24). Although water generation is given by Faraday s law, water can evaporate or condense in the diffusion media. These reactions are often modeled by an expression similar to... 

An important problem is the research of change of the initial drop spectrum described by distribution (21.3) under the influence of mass-exchange (evaporation of methanol, condensation of water vapor), coagulation, breakup and deposition of drops at the pipe wall. As of now, it is not possible to take into account the flux of drops from the wall (ablation), because at the present time there are no reliable relevant data in literature. 

---