Fractional error, particle

Fig. 1. Approximate behavior of the fractional error as a function of the mean size parameter a, = ir D,/ and the fractional standard deviation o. Where D, is the mean particle diameter.

Selected results on number concentrations are presented on Figure 1. Wersborg s results were obtained at = 3.0 and o = 50 cm/sec. The soot particles (curve a) refer to particles larger than about 15 A diameter, measured by electron microscopy. The charged fraction of particles (curve b) was determined by measuring particle number with and without an electric field applied across the beam to remove all charged particles. Measurement error was estimated to be below 20%. 

The fractional error C/Co, where C is the measured particle concentration when the true gas concentration is Co can be shown (9) to be equal to ... 

Since m is the mass of solid remaining at time t, the quantity m/m0 is the fraction undissolved at time t. The time to total dissolution (m/m0 = 0) of all the particles is easily derived. Equation (49) is the classic cube root law still presented in most pharmaceutics textbooks. The reader should note that the cube root law derivation begins with misapplication of the expression for flux from a slab (Cartesian coordinates) to describe flux from a sphere. The error that results is insignificant as long as r0 8. 

Salamone and Newman (SI) recently studied heat transfer to suspensions of copper, carbon, silica, and chalk in water over the concentration range of 2.75 to 11.0% solids by weight. These authors calculated effective thermal conductivities from the heat transfer data and reached conclusions which not only contradicted Eqs. (35) and (36), but also indicated a large effect of particle size. However, if one compares the conductivities of their suspensions at a constant volume fraction of solids, the assumed importance of particle size is no longer present. It should also be noted that their calculational procedure was a difficult one in that it placed all undefined errors present in the heat transfer data into the thermal conductivity term. For example, six of the seven-... 

Equation (8.3.14) is not an asymptotically exact result for the black sphere model due to the superposition approximation used. When deriving (8.3.14), we neglected in (8.3.11) small terms containing functionals I[Z], i.e., those terms which came due to Kirkwood s approximation. However, the study of the immobile particle accumulation under permanent source (Chapter 7) has demonstrated that direct use of the superposition approximation does not reproduce the exact expression for the volume fraction covered by the reaction spheres around B s. The error arises due to the incorrect estimate of the order of three-point density p2,i for a large parameter op at some relative distances ( f — f[ < tq, [r 2 - r[ > ro) the superposition approximation is correct, p2,i oc ct 1, however, it gives a wrong order of magnitude fn, oc Oq2 instead of the exact p2,i oc <7q 1 (if n — r[ < ro, fi — f[ < ro). It was... 

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