Continuum regime

For a pure component droplet evaporating into a stagnant gaseous medium in the continuum regime, the quasi-steady rate of change of droplet radius a with time is given by an equation attributed to Maxwell (1890),... 

For the data in the continuum regime they wrote the approximation... 

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. 

In the continuum regime the flux through the orifice, Fc, can be expressed as... 

When Kn < 0.2, the particles are described as being in the continuum regime. A theoretical description of particle motion in this flow regime... 

Experimental investigations on convective heat transfer in liquid flows in microchannels have been in the continuum regime. Hence, the conventional Navier-Stokes equations are applicable. 

Isobaric applications in the continuum regime, making use of molecular bulk diffusion and/or some viscous flow are found in catalytic membrane reactors. The membrane is used here as an intermediating wall or as a system of microreactors [29,46]. For this reason some attention will be paid to the general description of mass transport, which will also be used in Sections 9.4 and 9.5. 

The viscous flow of a binary mixture which is fully in the continuum regime does not affect the concentration of both gases and relation (9.2) applies for the mixture as for a single gas with the mixture viscosity ti(x) of the mixture with a constant mole fraction x. 

If the pressure at the downstream (permeate) side is in the transition or continuum regime and is not negligible, there is a back-diffusional flux into the membrane decreasing the value of a. Equation 9.38 gives the effect of back diffusion on the actual separation factor [23,24]. 

The accommodation coefficient or represents the fraction of the gas molecules that leave the surface in equilibrium with the surface. The fraction I — cr is specularly reflected such that the velocity normal to the surface is reversed. As in the case of Stokes law, the drag is proportional to the velocity of the spheres. However, for the free molecule range, the friction coefficient is proportional to dj whereas in the continuum regime dp ip), it is proportional to dp. The coefficient a must, in general, be evaluated experimentally but is usually near 0.9 for momentum transfer (values differ for heat and mass transfer). The friction coefficient calculated from (2.19) is only 1% of that from Stokes law for a 20-A particle. 

Figure 2.3 Cjkulaied dilTusiitn cueflictcms for power-law fractai-l ike) agglomerates normalized by the Sioke.s-Ein.<>tcin diffusion coefiidem for a primary particle. The total number of primary parttdes in the aggregate is and Df is the fractal dimetision. The results hold for the continuum regime, Op, ip. (After Tandon and Rasner, 1995.)...

In the continuum regime dp 0.1 /xm), the ion fluxes ft and ft can be estimated from steady-state solutions to the ion diffusion equation (2.43) in the presence of a Coulomb force field. surrounding the particles image forces are neglected (Fuchs and Sutugin, 1971) ... 

Figure 7.] Varialicin of collision frequency function (i(a. 02) with particle size ratio a ju2 for air at 23°C and 1 atm based on Fuchs (1964, p. 294). The value of f i, 2) is. smallest for particles of equal size (01/02 = I) and the spread in value with particle size is smallesl. Forrii/o =. P go< s through a weak maximum for Knudsen number near 5. The value of (0. 03) highest for interacting panicles of very different sizes (large 01/02). The lowest curves correspond to the continuum regime.

In the continuum regime, the collision kernel for agglomerates is based on the Smolu-chowski expression derived in Chapter 7 ... 

Example Derive an expression for the change in the number density with time for the self-preserving distribution in the continuum regime. 

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.)...

Simultaneous Coagulation and Diffusional Growth Similarity Solution for Continuum Regime 313... 

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