Apparent --- coefficient linear

F/=real volume of liquid at F/ =apparent volume of liquid at t°C. as measured by the graduation on the vessel, a =apparent coefficient of cubical expansion of the liquid, a=true coefficient of cubical expansion of the liquid ( l.VIII C), g=coefficient of cubical expansion of the glass of the vessel (taken as three times the coefficient of linear expansion). Then ... 

Eq. (4.179) contains (1) the kinetic apparent coefficient k+ (2) the potential term, or driving force related to the thermodynamics of the net reaction (3) the term of resistance, ie, the denominator, which reflects the complexity of reaction, both its multi-step character and its non-hnearity finally, (4) the non-linear term (N k,c)), a polynomial in concentrations and kinetic parameters, which is caused exclusively by nonlinear steps. In the case of a linear mechanism, this term vanishes. In classical kinetics of heterogeneous catalysis (LHHW equations), such term is absent. 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

Sorption curves obtained at activity and temperature conditions which have been experienced to be not able to alter the polymer morphology during the test, i.e. a = 0.60 and T = 75 °C, for as cast (A) and for samples previously equilibrated in more severe conditions, a = 0.99 and T = 75 °C (B), are shown in Fig. 13. According to the previous discussion, the diffusion coefficient, calculated by using the time at the intersection points between the initial linear behaviour and the equilibrium asymptote (a and b), for the damaged sample is lower than that of the undamaged one, since b > a. The morphological modification which increases the apparent solubility lowers, in fact, the effective diffusion coefficient. 

The growth current is characterized by the coefficient lG. Figure 46 is a log-log plot of lG vs. NaCl concentration, which yields a linear relation with the slope of 2.02 lG is proportional to the second order of NaCl concentration. However, in Eq. (112), lG is apparently in proportion to the first order of NaCl concentration. This apparent discrepancy can be solved by assuming that the coefficient B is a function of the coverage 0, which depends on NaCl concentration as shown in Fig. 44. So, including the... 

Reynolds number. It should be stressed that the heat transfer coefficient depends on the character of the wall temperature and the bulk fluid temperature variation along the heated tube wall. It is well known that under certain conditions the use of mean wall and fluid temperatures to calculate the heat transfer coefficient may lead to peculiar behavior of the Nusselt number (see Eckert and Weise 1941 Petukhov 1967 Kays and Crawford 1993). The experimental results of Hetsroni et al. (2004) showed that the use of the heat transfer model based on the assumption of constant heat flux, and linear variation of the bulk temperature of the fluid at low Reynolds number, yield an apparent growth of the Nusselt number with an increase in the Reynolds number, as well as underestimation of this number. 

Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8-50°C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, D ic, was approximated by the measured self-dilfusion coefficient for AOT below 28°C, and by the linear extrapolation of these AOT data above 28°C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for... 

The permeability coefficient Kpcr is just the flux divided by Cw. It is apparent that the permeability coefficient is linear with P for small distribution coefficients and constant for large P. Thus, for small P the epithelium is the barrier, and for large P the stroma is the barrier. A fit for steroid permeability is shown in Fig. 12, where the regression analysis gave De = 1.4 x 10 9cm2/s and Ds = 2.0 x 10 6cm2/s for 4 = 4 x 10 3 cm and 4 = 3.6 x 10 2 cm [205]. These values for the diffusion coefficients are reasonable compared with those of aqueous gels and lipid membranes. 

Equation 23.7 is based on the actual change in steam enthalpy across the turbine. Although both Equations 23.6 and 23.7 have the same form, their coefficients have completely different meanings. Comparing Equations 23.6 and 23.7, it becomes apparent that the slope of the linear Willans Line (Equation 23.6) is related to the isentropic enthalpy change and turbine isentropic efficiency9. 

To overcome the problem of non-ideality the work be carried out at the Q temperature because in nonideal solutions the apparent Molecular weight is a linear function of concentration at temperatures near Q and the slope depending primarily on the second virial coefficient. 

Other dilute solution properties depend also on LCB. For example, the second virial coefficient (A2) is reduced due to LCB. However, near the Flory 0 temperature, where A2 = 0 for linear polymers, branched polymers are observed to have apparent positive values of A2 [35]. This is now understood to be due to a more important contribution of the third virial coefficient near the 0 point in branched than in linear polymers. As a consequence, the experimental 0 temperature, defined as the temperature where A2 = 0 is lower in branched than in linear polymers [36, 37]. Branched polymers have also been found to have a wider miscibility range than linear polymers [38], As a consequence, high MW highly branched polymers will tend to coprecipitate with lower MW more lightly branched or linear polymers in solvent/non-solvent fractionation experiments. This makes fractionation according to the extent of branching less effective. 

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