Radius quotient

The growth rate, characterized by the change of the radius with time, is proportional to the driving force for the phase separation, given by the differences between 2 > the chemical composition of the second phase in the continuous phase at any time, and, its equihbrium composition given by the binodal line. The proportionahty factor, given by the quotient of the diffusion constant, D, and the radius, r, is called mass transfer coefficient. Furthermore the difference between the initial amount of solvent, (])o, and c]) must be considered. The growth rate is mathematically expressed by [101]... 

If the amplitude scattering matrix elements (5.4) for a homogeneous, isotropic sphere of radius a are divided by the volume v, the resulting quotients approach finite limits as the sphere radius tends to zero ... 

At any radius r, the rate of reaction per unit area can be calculated from the quotient, (dn/dt)r/Sr. Consequently, the specific rate of reaction and calculated carbon dioxide concentration (both taken at the same value of r) can be plotted to determine the true order of reaction, independent of diffusion control. Figure 19 presents such data for the carbon rod reacted at 1200°, assuming the relative concentrations for Case 3 in Table VI to be applicable. From an auxiliary plot similar to Fig. 19, a finite reaction rate at zero carbon dioxide concentration is found. Since the concentrations of carbon dioxide were calculated assuming Co to be zero, it is clear that this reaction rate is due to a finite Co concentration at the center of the rod. The actual values of concentration at values of r were estimated by extrapolat-... 

Suppose that you have optimized a gradient on a 0.46 X 25 cm column and you want to transfer it to a 0.21 X 10 cm column. The quotient V2/V is ( nr2L)2/( nr1L), where r is column radius and L is column length. For these columns, V2/Vj = 0.083. Equation 25-8 tells us to decrease the volume flow rate, the sample mass, and the delay time to 0.083 times the values used for the large column. The gradient time should not be changed. 

Let us examine the experimental results. Daoud et al.,20 and thereafter Wiltzius, Haller, Cannell, and Schaeffer2 made systematic measurements of as a function of p for semi-dilute solutions of polystyrene (neutron and X-ray scattering). Figure 15.27 shows the results of Wiltzius et al. The quotients JRg,z are brought on the vertical axis, where RG z is the radius of gyration in the limit p -> 0. The overlap ratios are brought on the horizontal axis. These ratios are determined by the measurement of the second virial coefficient [see (15.4.3)]... 

The radius of gyration of a column section with respect to a given axis is equal to the square root of the quotient of the moment of inertia with respect to that axis, divided by the area of the section, that is ... 

Furthermore there is a relation between geometry and speeds The quotient of the tool radius... 

Figure 2.1 Temperature increase ATn as a function of the quotient and the radius of the tubular reactor.

For large particles, for which the double layer thickness is small in comparison to the particle radius, these equations must approach the corresponding equations (7) and (13) for small potentials for the flat double layer. Actually, if a is very large, in the idiffuse layer the quotient afr will be almost 1, and xa 1, so that eq. (16) will pass into the form... 

Apparent viscosity n. At any point in a fluid undergoing laminar shear, the nominal shear stress divided by apparent shear rate. In simple fluids, viscosity is a state property, depending only on composition, temperature, and pressure. In polymer melts and solutions, it is, nearly always, also dependent on the shear rate (or stress), hence the term apparent viscosity. The term is also applied to the quotient of the shear rate at the wall, which reduces to nR -API (SQL), where R and L are the radius and length of the tube, AP is the pressure drop through the tube, and Q is the volumetric flow rate. Elias HG (1977) Macromolecules, vols 1-2. Plenum Press, New York. Staudinger H, Heuer W (1930) A relationship between the viscosity and the molecular weight of polystyrene (German). Ber 63B 222-234. 

The individual resistances presented in Table 35.1 can be combined into a total resistance, which must be provided by the propulsion system at the propelled wheels. These forces can also be illustrated by the quotient of the driving torques at the front and rear axles and the dynamic radius of the wheels ... 

The correct size for the equivalent sphere etc. is then got by working out an appropriate mean radius or half-width of the real body. Semenov s route would lead us to consider simply the quotient (volume/ surface area). A more reliable route is to work out the square root of the harmonic mean-square radius. That is, narrow dimensions are to be emphasized. A compromise, probably entirely adequate for work involving factors of safety, is often the sphere of equal volume. This will inevitably be more explosive than, and inferior in stability to, the non-spherical system. The presumed superior stability of the inscribed sphere sets the other bound. 

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