Free molecule regime

For data obtained in the free-molecule regime the procedure is somewhat different. In this case da/dt is given by... 

If the vapor pressure is determined by measurements in the free-molecule regime, then evaporation rate measurements in the continuum regime permit the diffusion coefficient to be determined from a single experiment in the carrier gas of interest and at the temperature of interest. 

Richardson, Hightower and Pigg (1986) used a quadrupole mounted in a vacuum chamber to measure the vapor pressure of sulfuric acid as a function of temperature in the range 263 T < 303 K. They operated well into the free-molecule regime and assumed an evaporation coefficient of unity. Richardson et al. correlated their data by means of the equation... 

This review of the chemistry and physics of microparticles and their characterization is by no means comprehensive, for the very large range of masses that can be studied with the electrodynamic balance makes it possible to explore the spectroscopy of atomic ions. This field is a large one, and Nobel laureates Hans Dehmelt and Wolfgang Paul have labored long in that fruitful scientific garden. The application of particle levitation to atmospheric aerosols, to studies of Knudsen aerosol phenomena, and to heat and mass transfer in the free-molecule regime would require as much space as this survey. 

At high Re and Ma in the free-molecule regime, transfer rates for spheres have been calculated by Sauer (S4). These results, together with others for cylinders and plates, have been summarized by Schaaf and Chambre (Sll). The particles are subject to aerodynamic heating and the heat transfer coefficients are based upon the difference between the particle surface temperature and the recovery temperature (see standard aerodynamics texts). In the transitional region, the semiempirical result of Kavanau (K2),... 

An interpolation formula is often used to cover the entire range of values of the Knudsen number 2ip/dp) from the continuum to the free molecule regimes. It is introduced as a correction to the Stokes friction coefficient ... 

Values of the Self-Preserving Size Distribution for the Continuum ((trr) and Free Molecule ( /) Regimes Calculated by a Discrete Sectional Method (Vemury and Pratsinis, 1995)... 

To evaluate a it is necessary to solve for the SPD, which depends on Df. Values of a for the free molecule regime vary little with Df in the range 2 to 3 as shown in Table 8.1. along with the 1/0/ moment of the size distribution function. Mi/Of For Df 3, ctsa function of the size of the primary particle, ctpo. 

Figure 8.5 Self-preserving size distributions of agglomerates of various D/ in the free molecule regime. Values of ij/, and tj are tabulated in the original reference. (After Vemury and Pratsinis, 1995.)...

Fig. 8.S The dependence of the exponent q on Df for agglomeration in the free molecule regime is much more sensitive than in the continuum regime. (After Matsoukas and Friedlander, 1991.)...

Figure 8.9 shows mass distributions for various values of Df, based on the selfpreserving size distributions in the free molecule regime. For the same conditions and residence time, a low value of Df produces a broad distribution with a high proportion of mass at large particle sizes, The growth in the mass median diameters with time are shown in Fig. 8.10 with Df as the parameter. 

Derive an expression for the change in total panicle concentration dN /dt for a cloud of monodisperse agglomerates in the free molecule regime. 

Thu.s for panicle volume-controlled growth, the final particle diameter is proportional to the initial diameter. For volume-controlled growth, the initial polydispersity is carried through to the hnal size distribution. This result is quite different from that of diffusion in the free molecule regime for which the Rnal panicle diameter is independent of the initial diameter. 

As shown by (12.19) the behavior of the system depends on the relative values of the collision and coalescence times which are determined by the process conditions and material properties. If the size distribution remains nearly self-preserving throughout the time of interest, the fractional change in average particle volume with time in the free molecule regime (Chapter 7), i.s... 

Finally, the reader is reminded that the analysis is based on the use of the linear approximation (12,4) for the decay with time of the area of a doublet. The characteristic collision time used in the calculations was based on the free molecule regime. 

Marlow (1981) has extended this development to the transition and free-molecule regimes and determined that the effect of van der Waals forces on aerosol coagulation rates can be considerably more pronounced in these size ranges than in the continuum regime. 

Keywords Accommodation coefficients Condensation Evaporation Free-molecule regime Gas phase transport Knudsen regime Non-continnum regime... 

In the limit of large Knudsen number Kn 7I> 1) the kinetic theory of gases is applied to determine the molecular flux. This is the free-molecule regime. 

---