# Classification of Evaporation

Figure 1 Comparison of (a) heterogeneous and (b) direct contact evaporation.

The latent heat of vaporization acts as a heat sink during phase change. It is supplied either by migration through the liquid, as in heterogeneous evaporation, or directly to the interface, as in direct contact evaporation. In the former, the heat must migrate by conduction (and in some cases convection) through the liquid to the interface. Figure 1 illustrates the difference between heterogeneous and direct contact evaporation. When a beaker of water is placed on a hot plate, as shown in Fig. 1(a), only heterogeneous evaporation can occur, because heat must migrate from the bottom of the beaker to the surface of the water in order for evaporation to take place. The liquid’s temperature is highest at its point of contact with the bottom of the beaker. Adjacent to the bottom is a layer through which heat passes only by conduction. Convection takes place throughout most of the depth, causing the temperature to decrease slightly. Just below the surface, a thin layer exists in which the temperature drops abruptly as the interface is approached. The surface temperature of the liquid can be assumed to equal the saturation temperature corresponding to the partial pressure of the vapor at the surface. Evaporation from a liquid film or a droplet attached to a heated wall is heterogeneous evaporation.

Figure 1(b) shows an example of direct contact evaporation, where a beaker of water sits on a table in a room of temperature ${{T}_{\infty }}$ with a relative humidity < 100%. Since the heat required for the evaporation is supplied at the surface, there is no temperature gradient through the depth of the liquid except just below the interface. Evaporation of a liquid droplet suspended in a hot gas mixture is another example of direct contact evaporation, because the latent heat of evaporation is supplied to the surface of the droplet by the surrounding hot gas mixture.

Evaporation of a liquid film or droplet attached to an adiabatic wall is direct evaporation because the latent heat is provided by the gas mixture, not the wall. Evaporation from a liquid surface is a mass transfer process, where the rate at which the molecules leave the liquid exceeds the rate at which the molecules move back into the liquid from the vapor. Therefore, the vapor pressure at the interface, which is the saturation pressure corresponding to the liquid surface temperature, psat(TI)

– if the effects of capillary and disjoining pressures are negligible – must exceed the vapor pressure, pv. The difference between the saturation pressure and the vapor pressure is negligibly small when a liquid is evaporating to its pure vapor. Consequently, the temperature at the interface is equal to the saturation temperature corresponding to the local vapor pressure.

If evaporation is from a liquid to a mixture of vapor and noncondensable gas, the vapor generated at the interface must be diffused to the main stream of the mixture. In this case, evaporation will be further limited by the mass diffusion process. However, if the effect of vapor diffusion is negligible, the temperature at the interface equals the saturation temperature corresponding to the partial pressure of the vapor in the mixture. In this case, evaporation can occur only if saturation pressure corresponding to the interfacial temperature exceeds the partial pressure in the vapor. For example, a beaker of water is in thermal equilibrium with its surroundings at 20 °C and 50% relative humidity. The saturation pressure of water at 20 °C is 2.3 kPa, and the vapor partial pressure in air at 50% humidity is half of that, 1.15 kPa. Since the liquid saturation pressure exceeds the vapor partial pressure, evaporation occurs.

Therefore, heterogeneous evaporation requires that the liquid is superheated to a temperature above the saturation temperature corresponding to the partial pressure of the vapor, ${{T}_{\ell }}>{{T}_{sat}}({{p}_{v}})$. For direct contact evaporation, the temperature of the vapor-gas mixture in contact with the liquid must exceed the saturation temperature corresponding to the partial pressure of the vapor. Let us reuse the example of a beaker of water in thermal equilibrium with its surroundings at 20 °C and 50% relative humidity. Since the gas temperature of 20 °C is greater than the saturation temperature of 8.8 °C, corresponding to the partial pressure of the vapor, evaporation occurs.

Figure 2 Evaporation domains for a vapor-gas mixture.

The conditions under which evaporation to a mixture of vapor and noncondensable gas can occur are demonstrated in a T-s diagram, as shown in Fig. 2. The saturated liquid and vapor lines represent the temperature and entropy conditions necessary for equilibrium between liquid and vapor phases. The saturated vapor line and the isotherm T = TI intersect at a point I from which the interface saturation pressure isobar p = pI is drawn. For evaporation to occur, the interface saturation pressure pI must be greater than the vapor partial pressure pv. If the temperature of the vapor is above the interfacial temperature (see point a), the latent heat of evaporation is supplied by the gas; evaporation under this condition is referred to as hot evaporation. The liquid for hot evaporation can be either saturated or subcooled, as represented by curve a'b' in Fig. 2. The above example with the beaker of water, shown in Fig. 1(b), occurs at point a because the vapor temperature (20 °C) is greater than the interfacial temperature, which is at the saturation temperature corresponding to the partial pressure of the vapor (8.8 °C). At point b, which represents a case where the relative humidity is 100%, the gas temperature equals the saturation temperature and hot evaporation ceases.

At point c, the temperature of the gas is below the saturation temperature, so the gas cannot provide the latent heat of vaporization. For evaporation occur at point c, heat must be supplied by a superheated liquid, represented by curve b'f' in Fig. 2. As discussed in phase equilibrium, the superheated liquid is in a metastable state. If the temperature of the liquid is higher than that of point f', vapor bubbles will appear in the liquid. Evaporation occurring under this condition is referred to as cool evaporation because the interface is warmer than the gas. At the intersection of isobar p = pv and the saturated liquid line (point d) the vapor is saturated. As a result, cool evaporation does not occur under equilibrium condition. Practically speaking, evaporation is still possible, but it will result in supersaturated vapor, which is in a metastable state as discussed phase equilibrium. If the vapor-gas mixture is already supersaturated, as represented by point e, evaporation is possible provided that sufficient superheat exists in the liquid. Evaporation to the vapor-gas mixture at point f will be impossible, because it represents the maximum possible supersaturation of the vapor-gas mixture.

## References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Burlington, MA.

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.