Hertz-Knudsen vaporization

A material vaporizes freely from a surface when the vaporized material leaves the surface with no collisions above the surface. The free surface vaporization rate is proportional to the vapor pressure and is given by the Hertz-Knudsen vaporization equation (Eq. 6.1) ... 

The assumptions inherent in the derivation of the Hertz-Knudsen equation are (1) the vapor phase does not have a net motion (2) the bulk liquid temperature and corresponding vapor pressure determine the absolute rate of vaporization (3) the bulk vapor phase temperature and pressure determine the absolute rate of condensation (4) the gas-liquid interface is stationary and (5) the vapor phase acts as an ideal gas. The first assumption is rigorously valid only at equilibrium. For nonequilibrium conditions there will be a net motion of the vapor phase due to mass transfer across the vapor-liquid interface. The derivation of the expression for the absolute rate of condensation has been modified by Schrage (S2) to account for net motion in the vapor phase. The modified expression is... 

LVov [85], from published measurements of the rates of volatilization of many oxides, has proposed a mechanism of sublimation based on the Hertz-Knudsen-Langmuir model of vaporization (see Section 2.4.5.). This approach is similar in some respects to that developed by Searcy [86]. 

The L vov sublimation model. The applications (outlined in Sections 2.4.5. and 2.4.6.) of the Hertz-Knudsen-Langmuir vaporization model to decompositions by L vov et al. [94] are based on the assumption that decomposition involves an initial sublimation step, followed by condensation of the less volatile products. Because sublimation is an endothermic process, the condensation process would need to make a significant energetic contribution for the decomposition to be exothermic overall. 

The method of quantitative vaporization is based on the Hertz Knudsen equation [87]. The mass loss rate dm/dt of a substance A, vaporized at the temperature T in the Knudsen cell, is determined by weighing, in addition to the ion intensity measurement, k is obtained by the equatiop... 

The maximum theoretical rate of vaporization V (kgm s ) from the surface of a pure liquid or solid under its own vapour pressure is given by the Hertz-Knudsen equation, which can be derived from the kinetic theory of gases ... 

For the Hertz-Knudsen model and the definition of the condensation coefficient we follow Hill [4]. The bombardment of small droplets by vapor molecules is described by the impingement rate... 

Figure 48.1 illustrates a typical Knudsen cell. The Knudsen cell provides a way to probe the vapor in equilibrium with the condensed sample of interest plus cell material. Under the low-pressure conditions used (<10 bar), the fugacities of real gases are equal to their partial pressure, and the behavior of the vapor phase is readily described by the kinetic theory of gases. There are several excellent texts on this subject [19,20]. The key relationship derived from kinetic theory to this technique is the Hertz-Knudsen-Langmuir (HKL) expression, which relates the flux of a molecular species striking a surface, Ja (mol area s ), to its equilibrium vapor pressure in a closed container ... 

According to the Hertz-Knudsen theory, the drop of vapor pressure depends on the rate of evaporation v (cm/s) ... 

In the calculations of partial pressures (Hastie et al., 1968), ionization of dimeric molecules accompanied by loss of more than one atom (especially in reaction steps that can interfere with ionization of monomers) was assumed to be improbable. This assumption was experimentally confirmed in studies of the congruent evaporation of SmCl3 (Chervoimyi et al., 1974). Isothermal evaporation of a sample of known weight was carried out at several temperatures, and the saturated vapor pressure was determined by the Hertz-Knudsen equation. In each experiment, the state of an imsaturated vapor caused by the presence of an nonvolatile species ( 1.5% SmCl2) was determined in the end of... 

The investigations of Hertz were given a new impetus only a few decades later in the studies of Knudsen [20] and Langmuir [21]. The interest of Knudsen in vaporization was prompted by his studies of thermal conductivity and rarefied gas flow, as well as by the possibility of development of the effusion... 

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