Free Molecular Regime

Landgrebe, J. D., and Pratsinis, S. E., Gas Phase Manufacture of Particulates Interplay of Chemical Reaction and Aerosol Coagulation in the Free-Molecular Regime." Ind. Eng. Chem. Res., 28 1474-1481 (1989)... 

For the other extreme of the free molecular regime where Kn - oc, the particle radius is small compared to the mean free path. In this case, the thermal velocity distribution of the gas is not distorted by uptake at the surface. In effect, the gas molecules do not see the small particles. For this case, Fuchs and Sutugin (1970, 1971) show that for diffusion to a spherical particle of radius a... 

When dp is mnch smaller than A(Kn 1, free molecular regime), it is given by... 

The limiting behavior of the coagulation coefficient /3, in the continuum and the free molecular regimes can now be examined. In the continuum limit, where Krt — 0, one has... 

For free molecular regime the mathematical model of evaporative cooling of multicomponent droplet with two volatile components has been described in [3]. We use this mathematical model as the background. Additionally, the equation describing the change of a nanoparticle radius R due to diffusion transfer of a soluble impurity is ... 

Vacuum Aerodynamic Diameter Calculate the ratio of the aerodynamic to the physical diameter of a spherical particle of density pp in the continuum and the free molecular regimes. 

If the particle is in the free molecular regime, then 2k Dp and the second term dominates the RHS of (9.34), which simplifies to... 

Combining this and simplifying, we find that in the free molecular regime ... 

Transition and Free Molecular Regime When the mean free path Xp of the diffusing aerosol particle is comparable to the radius of the absorbing particle, the boundary... 

On the other hand, in free molecular regime coagulation with DpX = Dp2, using (13.51), one can show that... 

In the free molecular regime if Dp2 3> Dpi, the coagulation coefficient has the following asymptotic behavior ... 

By comparing (13.54) and (13.55) we see that, with Dp fixed, K 2 increases more rapidly with Dp2 for free molecular regime than for continuum regime coagulation. 

Deposition of nanoparticles was investigated in the free molecular regime approximation for thermophoretic force and the Brownian motion. The analytical solution was obtained by the Galerkin method for the heat transfer between gas flow and substrates and convective diffusion. Relative roles of two channels of nanoparticle deposition are discussed. 

Transition and Free Molecular Regime When the mean free path of the diffusing aerosol particle is comparable to the radius of the absorbing particle, the boundary condition at the absorbing particle surface must be corrected to account for the nature of the diffusion process in the vicinity of the surface. The correction is appreciable when the apparent free path of the aerosol particles kp is of the same order of magnitude as the radius Rp as we will see this occurs for Rp <0. /im. 

In this section, the rarefied flow in step flows at different Knudsen numbers is considered [11]. Nitrogen flow in a channel with sudden expansion step geometry is considered. Pressure ratio along the channel is equal to 2, and wall and inlet gas temperature is 300 K. A grid with 100 X 60 structured meshes is used, and 25 particles are set in each cell. The simulations are performed for different Kn numbers in slip, transition, and free molecular regimes. Figure 8 shows the Mach number contours for different inlet Knudsen numbers. The step height is equal... 

Free-molecular regime Internal rarefied gas flows Slip flow regime Transitional regime... 

However, in the transitional regime, i.e., when the rarefaction parameter is intermediate (8 1), the slip solution is not valid. Such a situation is realized when the channel/tube size a is less than 2 X 10 m. In this case, the kinetic Boltzmaiui equation is applied to calculate the coefficients Gp and Gt- hi the free-molecular regime, i.e., when the rarefaction parameter is... 

In the free-molecular regime (8 0) assuming the diffuse gas-smf ace interaction on the channel/ tube wall, the coefficients Gp and Gt can be calculated directly without numerical solution of the kinetic equation. In the case of the channel, the Poiseuille coefficient Gp is given by the following double integral ... 

As pointed out earlier in Sect.2.2 outside the free molecular regime, there is no general microscopic kinetic equation for description of the evolution of ufp aerosols in nonequilibrium host gas. There are macroscopic equations such as (2.6) or the generalized Langevin equation [2.6] ... 

---