Buoyancy factor

With this relationship for all samples was calculated from ninh This M is used for evaluating the reaction data. The ultracen rifuge (u.c measurements were carried out in a Spinco model E analytical ultracentrifuge, with 0.4% solutions in 90% formic acid containing 2.3 M KCl. By means of the sedimenta- ion diffusion equilibrium method of Scholte (13) we determine M, M and M. The buoyancy factor (1- vd = -0.086) necessary for tSe calculation of these molecular weights from ultracentrifugation data was measured by means of a PEER DMA/50 digital density meter. 

The rate of sedimentation is defined by the sedimentation constant 5, which is directly proportional to the polymer mass m, solution density p, and specific volume of the polymer V, and inversely proportional to the square of the angular velocity of rotation o), the distance from the center of rotation to the point of observation in the cell r, and the fractional coefficient /, which is inversely related to the diffusion coefficient D extrapolated to infinite dilution. These relationships are shown in the following equations in which (1 — Vp) is called the buoyancy factor since it determines the direction of macromolecular transport in the cell. 

We introduce the buoyancy factor as the relative influence of the natural convection over forced convection... 

It is instructive to compare the predictions of Eqs. (83) and (72) with the numerical solution obtained by Lloyd and Sparrow [24]. Table III shows that for large Prandtl numbers the difference is within 10%. The approximate equation is, unexpectedly, satisfactory even for low values of the Prandtl number if the buoyancy factor Bx is sufficiently small. Even though the error increases for larger values of Bx, this can be corrected by using the appropriate limiting values for Nux N and NuXiF. The first column in Table III for Pr = 0.72 is based on NuxN and Nux F for Pr - oo. The appropriate expressions for Prandtl numbers around unity are, however,... 

There is no point in using the very accurate density for water from Table 7-1 because the other densities are given only to two significant figures furthermore, the slight correction has almost no effect on the value of the factor or the true weight. If we used d0 = 0.9982 g/ml, the buoyancy factor would be 1.001052 and the true weight would be 99.9415 g. The error is only two parts in a million. 

Stockman (1997) considered dispersion in fractures using a lattice gas simulation incorporating sorption kinetics and buoyancy factors. He advocated the use of solute slugs over step changes in concentration because moment calculations are simplified and noise in the computation of second moments is reduced. 

When the buoyancy factor is constant, s is proportional to m/f (equation on page 88) oc m/m oc Note that this says that the sedimentation coefficient is proportional to the two-thirds root of the mass. 

Cellular plastics are used extensively in flotation applications because of their ability to maintain a low buoyancy factor. The buoyancy factor is directly affected by the amount of water a particular foam plastic will absorb. The test method developed to determine water absorption of rigid cellular plastics is fully described in the ASTM Standards Manual. Basically, the test consists of determining the volume of initial dry weight of the object and calculating the initial buoyancy force. The object is then immersed in water and, at the end of the immersion period, the final buoyancy force is measured with an underwater weighing assembly. The difference between the initial and final buoyancy force is the weight of water absorbed. This difference is expressed in terms of water absorbed per unit of specimen volume. The test results are seriously affected if proper steps are not followed closely and variables are not controlled carefully. 

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