Noncontinuum

Table 5.2 gives a new correlation, based on a critical examination of available data for spheres (N6). Results in which wall effects, compressibility effects, noncontinuum effects, support interference, etc. are significant have been excluded. The whole range of Re has been divided into 10 sub intervals, with a distinct correlation for each interval. Adjacent equations for match within 1% at the boundaries between sub intervals, but the piecewise fit shows slight gradient discontinuities there. The Re = 20 boundary corresponds to onset of wake formation as discussed above, the remaining boundaries being chosen for convenience. 

Compressibility and noncontinuum effects are related. For an ideal gas, kinetic theory leads to the relationship (Sll) ... 

Analogous to the slip velocity between gas and particle at Kn above the continuum flow range discussed in Section A above, a temperature discontinuity exists close to the surface at high Kn. Such a discontinuity represents an additional resistance to transfer. Hence, transfer rates are generally lowered by compressibility and noncontinuum effects. The temperature jump occurs over a distance 1.996kl 2 — a )/Fva k + 1) (K2, Sll) where is the thermal accommodation coefficient, interpreted as the extent to which the thermal energy of reflected molecules has adjusted to the surface temperature. 

For small particles, subject to noncontinuum effects but not to compressibility, Re is very low see Eq. (10-52). In this case, nonradiative heat transfer occurs purely by conduction. This situation has been examined theoretically in the near-free-molecule limit (SI4) and in the near-continuum limit (T8). The following equation interpolates between these limits for a sphere in a motionless gas ... 

Solution (by example) Consider a point particle a minimum distance z from a "rod" of similar point particles spaced at intervals a along straight line. To see the effect of noncontinuum structure in the rod, calculate the difference in the particle-rod interaction (1) when the isolated particle is at opposite one of the particles on the rod or (2) when the particle sits opposite the midpoint between two particles in the rod. That is, case (2) is case (1), but the rod is shifted over by a distance a/2. 

Figure 4. Electrospray of the LO active site peptide (sample 1). The electrospray ionization mass spectrometer was scanned in noncontinuum mode over a range of m/z of 350 to 2000 at 5 s/scan (see text for details).

Actual construction of such a device presents a number of technical challenges. When electrodes are synthesized at 10- to 100-nm diameters, with the anode and cathode separated by similar distances, problems in hard wiring and assembly are to be expected. In addition, there currently is no three-dimensional architecture for an electrochemical cell that would achieve uniform current density. Also, at the nanometer scale, noncontinuum effects, especially mass transport, become a concern. Other issues of concern include ensuring that there is enough territory for phase nucleation to occur and quantized charging when the electrode material approaches nanoscale dimensions. 

CONTINUUM AND NONCONTINUUM DYNAMICS THE MEAN FREE PATH 397... 

Stokes Law and Noncontinuum Effects Slip Correction Factor... 

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