Noncontinuum effects corrections

Stokes Law and Noncontinuum Effects Slip Correction Factor... 

FIGURE 17.13 Water vapor diffusivity corrected for noncontinuum effects and imperfect accommodation as a function of the droplet diameter at T = 283 K and p = 1 atm. 

C Repeat Problem 17.7 neglecting the correction to the diffusion coefficients and thermal conductivities for noncontinuum effects (assume that D v = Dv, k a = ka). Compare with Problem 17.7 and discuss your observations. 

Stokes law is based on the solution of equations of continuum fluid mechanics and therefore is applicable to the limit Kn -> 0. The nonslip conditions used as a boundary condition are not applicable for high Kn values. When the particle diameter Dp approaches the same magnitude as the mean free path X of the suspending fluid (e.g., air), the drag force exerted by the fluid is smaller than predicted by Stokes law. To account for noncontinuum effects that become important as Dp becomes smaller and smaller, the slip correction fac-... 

The correction factor Pend in Eq. (65) is dimensionless and accounts for noncontinuum effects. The mobility of solute molecules in the metastable gas phase is expressed by the gas-phase diffusion coefficient 2 g, and the driving force for condensation is the difference in mole fraction between the metastable phase (yj) and a gas phase that is in equilibrium with the precipitated phase (y ). Nucleation and condensation are mechanisms of precipitation that compete with each other. Condensation depends on the availability of the outer surface area of particles that have been generated by nucleation. Both processes lower the actual solute mole fraction yj and therefore diminish the driving force for either process. 

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