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 Knudsen equation for vaporization, expressed in the form Ga = pa(Ma/2jiRT) -gives the expression for die flux... 

The vapor pressure of a molten metal can be measured with a device called a Knudsen cell. This is a container closed across the top by a thin foil pierced by a small, measured hole. The cell is heated in a vacuum, until the vapor above the melt streams from the small hole (it effuses). The weight of the material escaping per second tells the rate at which gaseous atoms leave. 

Kinetics, chemical, 124 Knudsen cell, 63 Kroll process, 368 Krypton, 91 atomic volume, 410 boiling point, 307 heat of vaporization, 105... 

Vapor pressures of phases in these systems were measured by the Knudsen effusion technique. Use of mass spectrometer-target collection apparatus to perform thermodynamic studies is discussed. The prominent sublimation reactions for these phases below 2000 K was shown to involve formation of elemental plutonium vapor. Thermodynamic properties determined in this study were correlated with corresponding values obtained from theoretical predictions and from previous measurements on analogous intermetallics. 

Vapor pressures were determined by using the Knudsen effusion technique. Effusion rates through and orifice contained in each sample cell were measured as a function of temperature by use of a mass spectrometer/target collection... 

Total vapor pressures associated with each of the above reactions were calculated by use of the Knudsen equation... 

Knudsen effusion technique and equation, vapor pressure determination. 100-101... 

Consider the mass, thermal and momentum balance equations. The key assumption of the present analysis is that the Knudsen number of the flow in the capillary is sufficiently small. This allows one to use the continuum model for each phase. Due to the moderate flow velocity, the effects of compressibility of the phases, as well as mechanical energy, dissipation in the phases are negligible. Assuming that thermal conductivity and viscosity of vapor and liquid are independent of temperature and pressure, we arrive at the following equations ... 

Knudsen effusion will be involved later as we discuss free molecular flow in channels and tubes. Knudsen effusion also finds application in the measurement of the vapor pressure of materials of low vapor pressure, typically in the... 

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... 

Samples were analyzed by gas chromatography (GC). Water solubility was determined by equilibration of analytical grade material with water at constant temperature. Equilibrium was approached from both under and super saturation conditions and samples were analyzed by GC. Vapor pressures were determined by the Knudsen effusion method. 

Malaspina, L., Bardi, G., Gigli, R. (1974) Simultaneous determination by Knudsen-effusion microcalorimetric technique of the vapor pressure and enthalpy of vaporization of pyrene and 1,3,5-triphenylbenzene. J. Chem. Thermodyn. 6, 1053-1064. 

The heat transfer across the vapor layer and the temperature distribution in the solid, liquid, and vapor phases are shown in Fig. 13. In the subcooled impact, especially for a droplet of water, which has a larger latent heat, it has been reported that the thickness of the vapor layer can be very small and in some cases, the transient direct contact of the liquid and the solid surface may occur (Chen and Hsu, 1995). When the length scale of the vapor gap is comparable with the free path of the gas molecules, the kinetic slip treatment of the boundary condition needs to be undertaken to modify the continuum system. Consider the Knudsen number defined as the ratio of the average mean free path of the vapor to the thickness of the vapor layer ... 

The vapor-layer model developed in Section IV.A.2 is based on the continuum assumption of the vapor flow. This assumption, however, needs to be modified by considering the kinetic slip at the boundary when the Knudsen number of the vapor is larger than 0.01 (Bird, 1976). With the assumption that the thickness of the vapor layer is much smaller than the radius of the droplet, the reduced continuity and momentum equations for incompressible vapor flows in the symmetrical coordinates ( ,2) are given as Eqs. (43) and (47). When the Knudsen number of the vapor flow is between 0.01 and 0.1, the flow is in the slip regime. In this regime, the flow can still be considered as a continuum at several mean free paths distance from the boundary, but an effective slip velocity needs to be used to describe the molecular interaction between the gas molecules and the boundary. Based on the simple kinetic analysis of vapor molecules near the interface (Harvie and Fletcher, 2001c), the boundary conditions of the vapor flow at the solid surface can be given by... 

Peck D-H, Miller M, and Hilpert K. Vaporization and thermodynamics of La j Ca,Cr03 investigated by Knudsen effusion mass spectrometry. Solid State Ionics 2001 143 391 400. 

Knudsen cells (effusion cells) are exclusively used for vapor pressure measurements (see vapor pressure) in the pressure range from 1 torr to 10-6 torr. In the low temperature range (—20° — +400 °C) pyrex glass cells are applicable. Especially the vapor pressures of dyes, organic compounds can be measured in such cells, because metal cells may sometimes cause catalytic decompositions of the investigated materials. 

Another high-temperature cell (Fig. 8 g, up to 2400 °C, can be produced from tungsten. Tungsten Knudsen cells are used primarily for high-temperature vapor pressure measurements, e.g. for metal oxides. They are suitable also for metals when graphite linings are applied to the inner surface. The vapor pressure can be determined... 

Langmuir cells (Fig. 8 h) are very similar to Knudsen cells. Here the vaporization of a solid from its uncovered surface can be measured in a similar way by thermo-gravimetric methods. 

Fig. 22. Thermobalance for vapor pressure measurements. Schematic drawing of experimental equipment. A-Knudsen cell B-cold trap C-Ionization gauge D-Balance and housing E-Diffusion pumps F-Thermostatically controlled reaction chamber...

Fig. 34. Vapor pressure of benzoic acid measured on a thermobalance with Knudsen effusion cell...

REGRESSION ANALYSIS OF VAPOR PRESSURE DATA CALCULATED WITH KNUDSEN EQUATION... 

For measuring low vapor pressures within the range from 1 to 10-6 torr, the well-known Knudsen effusion method was applied (see Section 2.2.). The alumina Knudsen cell was used for vapor pressure measurements of gold and of sodium chloride. The orifice is located in the center of the lid. 

Fig. 66. Stepwise, isothermal vaporization of gold in a thermobalance with Knudsen ceil...

The optimum data are selected in step l by using a precalculated standard deviation, which is directly related to the constancy of temperature. These selected sets of data are used in step 2 for calculation of equilibrium vapor pressures by means of the Knudsen equation. A regression analysis of these vapor pressure data is then carried out in step 3. 

An important requirement for such vapor pressure measurements with Knudsen cells is the temperature distribution in and around the cell. If the temperature is not homogeneous within the cell, condensation and crystallization of the vaporized species may occur in the colder regions. This was observed e.g. with gold. In other cases the orifice was reduced in diameter up to complete blockage when vaporized metals like aluminium where oxidized due to the partial pressure of oxygen. To prevent these deposits, ultra high vacuum is necessary or the use of graphite cells instead of alumina cells. 

Ideally, the Knudsen effusion method can be applied for determination of vapor pressures if molecular flow is verified (p < 10 3 torr). Precise measurement of vapor... 

For this purpose a special Knudsen cell with exchangeable orifice plates has been designed. When the equilibrium pressure, which corresponds to the saturation pressure ps is reached, effusion of a part of the vaporizing substance takes place through the orifice. The amount depends strongly on the shape and length of the orifice (Fig. 68). From the substance which vaporizes in all directions, only a partial beam can pass freely through the orifice. 

The effusion rate Am/At at identical orifice diameter and temperatures was slowest for the cylindrical hole with long effusion channel and fastest for a cylindrical orifice with very short effusion channel. This means that the back scattering of the vapor molecules is strongly reduced if the ratio L/D between length L of the effusion channel and diameter D of the orifice is small, which is in agreement with theoretical calculations by Clausing66,67. There are three contributions to the Knudsen cell current which originate from the cell interior, from the channel wall, and the cell lid. 

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