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Published in Raj Deo Tewari, Abhijit Y. Dandekar, Jaime Moreno Ortiz, Petroleum Fluid Phase Behavior, 2019
Raj Deo Tewari, Abhijit Y. Dandekar, Jaime Moreno Ortiz
The relationship between a Newtonian liquid viscosity and temperature is modeled by the Eyring equation. Crude oil above WAT behaves as a Newtonian fluid where viscosity remains the same at all shear rates. However, below WAT, precipitated wax solids cause viscosity to change according to shear rates. By definition, shear rate is the rate of change of velocity at which one layer of fluid passes over an adjacent layer. It is dependent on volumetric flowrate and the spacing between the layers. For a Newtonian fluid flowing within a pipe, the shear rate is given by γ˙=4Qπr3⋅
Reaction Kinetics in Food Systems
Published in Dennis R. Heldman, Daryl B. Lund, Cristina M. Sabliov, Handbook of Food Engineering, 2018
Ricardo Villota, James G. Hawkes
The overall reaction rate is therefore controlled by the rate of formation of the activated complex which is a function of the change in “Gibbs free energy” (ΔG) going from the normal to the activated state, similar to the previous discussion (Section 2.3.4.1.). In the case with the effect of changing temperature, the relationship was given by the Arrhenius equation, assuming pressure was held constant. The influence of pressure on reaction rate, however, may be described by the basic thermodynamic relationship, as shown in Equation (3.36) as applied to the Eyring Equation (3.37): (dΔGodP)T=ΔVo
Computational Fluid Dynamics Analysis of High Pressure Processing of Food
Published in Mohammed M. Farid, Mathematical Modeling of Food Processing, 2010
A.G. Abdul Ghani, Mohammed M. Farid
A mathematical model describing the variation of the inactivation rate constant of soybean LOX as a function of pressure and temperature was studied by Ludikhuyze et al. [2]. Temperature dependence of the inactivation rate constants of LOX cannot be described by Arrhenius equation over the entire temperature range, therefore development of another kinetic model was attempted. Hence, Eyring equation which was valid over the entire temperature domain was used. The temperature dependant parameters (krefP, Va) in the Eyring equation below were replaced by mathematical expressions reflecting temperature dependence of the latter parameters.
Theoretical understanding the effects of external electric field on the hydrolysis of anticancer drug titanocene dichloride
Published in Molecular Physics, 2020
The Gaussian 09 suite programme was used for the calculations [43]. The calculations of systems including H, C, O and Cl were done using the standard 6-311G (d,p) basis set [44–47]. For Ti element, standard Def2-TZVPPD basis set [48] has been applied. Optimisation calculations were performed using BP86 functional [49–51]. This functional composed of the exchange functional of Becke and the correlation functional of Perdew. Harmonic vibrational frequencies were calculated to verify that the optimised structures have no imaginary frequency. Moreover, all the transition state (TS) structures were verified by IRC (Intrinsic reaction coordinate) analysis [52–55]. The rate constants (k) were calculated within the transition state theory according to the Eyring equation [56]: where kB is the Boltzmann constant, R is gas constant, T the absolute temperature and h the Planck constant. is the activation free energy for each step. The standard concentration (c0 = 1 mol/dm3) was considered.
The role of 8-quinolinyl moieties in tuning the reactivity of palladium(II) complexes: a kinetic and mechanistic study
Published in Journal of Coordination Chemistry, 2019
Daniel O. Onunga, Deogratius Jaganyi, Allen Mambanda
From the temperature dependence of k2, Eyring plots of lnversus were constructed. The enthalpy of activation (ΔH≠) and entropy of activation (ΔS≠) were calculated from the slopes and y-intercepts, respectively, from the plots according to Eyring Equation (2) [59], where T and R represent temperature and gas constant, respectively. Representative Eyring plots for the reactions of 4 are presented in Figure 3; similar plots for the reactions of other complexes are shown in Figures S19–S21 while the values of with their respective are summarized in Tables S6–S9 in the Supporting Information (ESI‡). In addition, the calculated activation parameter values are summarized in Table 3.
Effect of high pressure pretreatment on drying kinetics and oleoresin extraction from ginger
Published in Drying Technology, 2018
Jincy M. George, Halagur B. Sowbhagya, Navin K. Rastogi
The values of the effective moisture diffusion coefficients were determined by plotting experimental drying data in terms of (MR) against drying time t as per Eq. (7). The plot results in a straight line with the slope equal to and De values were calculated from the slope of Figure 2a,b. The relevant values of moisture diffusion coefficients for different drying temperatures and pretreatment pressures are inferred from the slopes and presented in Table 1. To present the effect of temperature and pressure on diffusion coefficients values (De), the plotted values were as per relation similar to Arrhenius and Eyring equation (Eqs. 8 and 9) against temperature (l/T) and pressure (P), respectively (Figure 3b):where T refers to drying temperature in K and P refers to treatment pressure in MPa.