Pitts equation

M. Okamoto, T. Sakai, and K. Hayashi, Biochemical switching device realizing McCulloch-Pitts type equation, Biol Cybern., 58, 295-299 (1988). 

Pitt et al.73 showed that DL-polylactic acid undergoes first-order degradation with respect to initial molecular weight, according to the equation... 

If the quantum yield is not known, which is often the case, it can be set equal to 1 and GC-SOLAR or Equation (11) with Zx becomes a useful screening tool for estimating the maximum (solar noon) value of kPE. If other transformation processes for the same chemical have rate constants larger than the value calculated for kPE with 0 = 1, then photolysis is not likely to be important, because actual values of O are generally less than one and usually less than 0.1 (Calvert and Pitts 1967 Mill and Mabey, 1985 Mill, 1995). 

Sidebottom et al., 1969, 1970 Winton and Tedder, 1976). Instead of ejecting the newly added radical, the adduct radical may eject an alternative group (Johari et al., 1971 Allen and Pitts, 1966). Equations (4) and (5) illustrate this. 

In order to determine the rate equation for hydrodesulfurization, a semi-logarithmic plot of the total sulfur content with time was made (Figure 2). The plot indicated two independent first-order reactions with greatly different rate constants. This is in agreement with the findings of Gates, et al. (7) and Pitts (3). A procedure similar to that of Pitts (3 ) was used to describe the hydrodesulfurization kinetics. The rate expression is given below ... 

Huggins and colleagues proposed the PITT in 1979 [17]. This technique also aims to determine the diffusion coefficient of diffusing species from Fick s equations. The solid particles are supposed to have initially a homogeneous concentration [18]. 

While Cook and Oblad showed that structural adsorption causes AF for activated adsorption to increase linearly with 0 and thereby accounts for the equation for the rate of activated adsorption (Equation 9), Pitt and Wadsworth demonstrated that desorption of C02 from thoria followed the equation of Becker (2) for desorption—namely,... 

Pitt s energy allocation model, in the form of Equation 36.2, is somewhat restricted for application in wastewater treatment. The value of jjL, the specific growth rate, is difficult to determine due to the variety of physiological states in the biomass, the variety of microbial species, each with different growth rates and substrate affinities. 

Use of this equation presupposes that the tablet is circular in cross-section and of uniform thickness, i.e., it is cylindrical. Pitt et al. have attempted to extend the concept of tensile strength to tablets which are not cylindrical. ... 

This reaction is of interest because current models underestimate the production of HONO, which is an important photolytic source of hydroxyl radical (Ammann et al. 1998 Finlayson-Pitts and Pitts 2000). This reaction could also be important as a reductive pathway for nitrogen species in the atmosphere, which is in contrast to most atmospheric reactions which tend to oxidize trace gases (e g., the conversion of SO2 to H2SO4). Molar yields of HONO via Equation (31) (relative to the moles of NO2 lost) typically range from 50 to 100%, while yields of NO are 4 to 30% (Gerecke et al. 1998 Stadler and Rossi 2000). It appears that the formation of NO results from the secondary reaction of HONO at the surface of the soot (Stadler and Rossi 2000). The mechanism of... 

The stresses developed in convex tablets tested undergoing the diametral compression test have been examined by Pitt et al. (1989), who proposed the following equation for the calculation of the tensile strength ... 

Both treatments make use of the same general equations for transport processes in fluids and of the same model to represent the electrolyte solution. However, they lead to somewhat different results due to the manner in which the problem is approached and because of the different boundary conditions employed to evaluate the constants which appear upon integration of the differential equations. We shall give here an account of the conductance theory based on the mathematical approach used by Pitts and shall point out the differences and agreements between his treatment and that of Fuoss and Onsager. The mathematical technique used by the latter authors has been given in detail by Fuoss... 

This expression was obtained by Leist and gives the first order correction to the limiting law 5.2.1 due to the finite size of the ions. Equation 5.2.21 appears as the first order correction in both the Pitts and Fuoss-Onsager treatments. 

The first two terms plus the first one inside the square brackets give Leist s expression 5.2.21. The third term in eqn. 5.2.26 gives the high order effect of the local velocity which arose from the perturbation of the ionic electrostatic potential. The second term in the brackets represents the higher order contribution of the asymmetric potentials and distribution functions from the continuity equation. The last term in eqn. 5.2.26 arises from in eqn. 5.2.25, which is due to the introduction of the first order term in U y into the continuity eqn. 5.2.12 and is equal to ajSc/(l + j) (V(2) + y The functions Si and Ti have been tabulated by Pitts for values of Ka in the range 0.02-0.50. 

The alternative approach to the conductance equation for electrolytic solutions followed by Fuoss and Onsager has many points in common to the one employed by Pitts. Some differences are, however, worth mentioning. 

The expressions for the A terms are given in Table 5.2.1 according to the Pitts (P) and Fuoss and Hsia (F-H) treatments. Another theoretical treatment of conductances has been given by Kremp and by Kremp, Kraeft and Ebeling. Their result has been approximated by Kraeft to an equation of the form 5.2.31 with = 0 the expression for /i has been included in Table 5.2.1. 

J2 = 0 is in some cases capable of representing the experimental data for ku < 0.2, but obviously the value of the a parameter must be different. Comparing the Pitts and the Fuoss and Hsia expanded conductance equations, it is clear that for a given electrol)rte Pitt s equation predicts a larger molar conductance, i.e., smaller interionic effects. 

Table 5.2.2 illustrates the performance of the Pitts and the Fuoss and Hsia equations for some dissociated electrolytes in organic solvents at 25 C. The values of the fitting parameters for salts in DMF and in... 

Comparison of Pitts (P) and Fuoss and Hsia (F-H) Expanded Conductance Equations... 

Equation 5.127 can be applied to some of the situations we have already analyzed, such as gravitationally produced instability of superposed fluids and capillary instability of a fluid cylinder. It has also been applied to more complex simations, such as stability of a pendant drop (Huh, 1969 Pitts, 1974). We remark that the expression in braces in Equation 5.127 is the local force acting in the normal direction on the deformed interface to restore it to its initial configuration. Hence application of the force method amoimts to a requirement that this expression be positive for stability. 

The strategies for including these higher order contributions in the conductance equation have been analyzed in detail in the literature (Fem dez-Prini, 1973). At the end of the 1970s there were several alternative equations to the original treatment by Fuoss and Onsager (1957) to account for the effect of concentration on electrolyte conductances the Pitts (1953) equation (P), the Fuoss-Hsia (Fuoss and Hsia, 1967) equation (FH) later modified by Femandez-Prini (1969) (FHFP) and valid only for dilute, binary, symmetrical electrolytes, and the Lee and Wheaton (1978) equation (LW) valid for unsymmetrical electrolytes. 

In terms of the relative weight W defined above, an expression for has been derived [58] which is formally analogous to the expression for Wo in the Pitts-Giovanelli treatment (Equation (3.58)), that is,... 

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