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)... 

A diffusion pump needs a forepump (usually a rotary pump). Oil can also migrate from the forepump into the vacuum chamber through the diffusion pump, when the rotary pump works in the molecular regime ( 10 2torr). 

The MO theory differs greatly from the VB approach and the basic MO theory is an extension of the atomic structure theory to molecular regime. MOs are delocalized over the nuclear framework and have led to equations, which are computationally tractable. At the heart of the MO approach lies the linear combination of atomic orbitals (LCAO) formahsm... 

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... 

Effective diffusivity in Knudsen regime Effective diffusivity in molecular regime Knudsen diffusion coefficient Diffusion coefficient for forced flow Effective diffusivity based on concentration expressed as Y Dispersion coefficient in longitudinal direction based on concentration expressed as Y Radial dispersion coefficient based on concentration expressed as Y Tube diameter Particle diameter... 

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 ... 

The inter-molecular scattering dominates the scattering function at wave-vectors q smaller than the reciprocal distance between chains (c /AO, where c is the number density of monomers in solution. The inter-molecular regime is controlled by concentration fluctuations arising from the difference in the number of chains in volumes j(. Assuming there are no interactions between chains (strictly valid only in very dilute solutions), the mean-square fluctuation in the number of chains in the volume jq is of the order of the average number nJNi c l Nq ). The fluctuation in the... 

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. 

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