Evaporation of a Multi-component Drop Into an Inert Gas

Evaporation of a Multi-component Drop Into an Inert Gas 

Evaporation of drops of multi-component solution into an inert gas, plays an important role in such processes as dehydration and humidifying of gas by the method of jet spraying, combustion of liquid fuel injected into the combustion chamber of engines and heating systems, etc. 

Consider a spherical drop consisting of n components that can evaporate into the ambient inert (neutral) gas [19]. Neutral gas is defined as a gas that does not participate in mass exchange processes in other words, it does not condense (though the term inert means chemically inactive we use it also for neutral gas) and does not evaporate at a drop s surface. The main problem is to study the drop-gas dynamics changes of temperatures, drop size, and component concentrations in the drop and the gas. As demonstrated in the previous section, the general treatment that would lead to exact formulas for temperature and concentrations as functions of position and time presents an extremely complex problem. Therefore, we should make a few simplifying assumptions, some of which are similar to the assumptions made in the previous section. 

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. 

Denote by Xi and yi the molar fractions of components in the liquid and gaseous phases. In this case, i= l..n so that y +i is the molar fraction of neutral component in the gas. By virtue of the above assumptions and in view of spherical symmetry of the problem, we now have X = Xi(t) and yi = yi(r). 

---