Arrhenius-type law

The Butler-Volmer (BV) approximation is the simplest approach to model and capture the essential features of the empirical Tafel equation. It considers an electrochemical half-cell reaction as an activated process, with the forward and backward reaction rates following an Arrhenius type law according to... 

A physisorbed molecule vibrates in a shallow potential well. Since the binding energy is low, it may readily break free. The rate of escape is considered to follow an Arrhenius-type law ... 

The sorption kinetics of n-hexane in MFI-type zeolites of different sizes have been measured by means of micro-FTIR spectroscopy. To check for an influence of the Si/Al ratio, nsj/Ai, on the sorption characteristics, a sample of silicalite was also investigated. The measured transport diffiisivities show ndther a dependence on the crystal size nor on the Si/Al ratio. The temperature dependence is shown to follow an Arrhenius-type law. The results of this study compare well with literature data obtained by different techniques. 

An alternative (very popular) approach is based on the very simple idea of calculating the growth rate of particles with the following empirical expression Gp = kg S - 1), where g is derived from experiments, as well as kg, which is in turn very often described with an Arrhenius-type law ... 

In the first place it can be assumed that the amount of the fission products in the gap between the fuel and the cladding is the same as that which was there when the fuel was discharged from the reactor, except for the effects of radioactive decay. Indeed, the phenomenon of diffusion from the fuel to the gap is governed by a diffusion coefficient, D cs, which depends on the temperature (in kelvin) according to an Arrhenius type law (ANS, 1984) ... 

The mass flow through the membrane is strongly dependent on the temperature. Thus, for a pure compound, flow can be described with Arrhenius-type law taking into account the temperature polarization ... 

Diffusion is a thermally activated process so diffusion rates increase with increasing temperature. For many types of diffusion, this temperature effect is modeled by fitting the diffusion coefficient to an Arrhenius type law. 

The flux is also affected by the temperature an Arrhenius type law is very often a good representation of this dependence with an activation energy in the range of 17-63 kJ/mol (Huang and Rhim, 1991). As a rule of thumb, a twofold increase of the flux is often assumed for a 10°C temperature rise. On the contrary, the selectivity generally decreases as the temperature... 

Besides a normal activated proton jump mechanism with a rate which obeys an Arrhenius type law... 

As was already presented in Sections 2.4.1 and 2.4.2, in all liquid metals (Pb, Pb-Bi, Na), and for both corrosion mechanisms dissolution or oxidation, increasing the temperature leads to an increase of the corrosion rate. This is expressed in all the correlations already presented, in which it can be observed that the corrosion rate depends on the inverse of the temperature according to an Arrhenius-type law. 

Assuming that n is invariant with the temperature, the permeability can be described by an Arrhenius-type law as follows ... 

D, W. Blair, CombustFlame 20 (1), 105—9 (1973) CA 78, 113515 (1973) A simple heat-transfer model is coupled with an Arrhenius-type pyrolysis law to study the effect of solid-state heat-transfer losses on burning rates of solid rocket-proplnt strands. Such heat-transfer losses materially affect the burning rates and also cause extinction phenomena similar to some that had been observed exptly. Strand diam and compn, adiabatic burning rate, and the heat-transfer film coeff at the strand surface are important variables. Results of theoretical analysis are applied to AP-based composite solid proplnts... 

The polymer rheology is modeled by extending the usual power-law equation to include second-order shear-rate effects and temperature dependence assuming Arrhenius type relationship. 

Since the burning surface temperature, T, is dependent on the regression rate of the propellant, it should be determined by the decomposition mechanism of the double-base propellant. An Arrhenius-type pyrolysis law represented by Eq. (3.61) is used to determine the relationship between the burning rate and the burning surface temperature. 

Another way to induce precipitation without needing a homogeneous nucleation step is the seeding of the solution. Best results are usually obtained if seeding is done with the desired phase. If the solution is seeded, usually no nucleation takes place, since the precursor concentration never exceeds a critical threshold. The precipitation rates in seeded systems normally follow Arrhenius-type rate laws. Precipitation of Al(OH)3 in the Bayer process is described by [7]... 

Nevertheless, the reliability of the assessment of the drop in titer by accelerated aging is disputable. The whole calculation principle relies on the fact that the kinetics follow laws of the Arrhenius type throughout the whole studied temperature domain. It so happens that this particular point is not that obvious if the dehydrated product contains an amorphous phase, which is quite frequently the case. As a matter of fact, a freeze-dried vaccine whose substrate contains sugars and proteins often has a vitreous transition temperature (Tg Lyo) greater than zero [12,25]. 

Thermal effects constitute a significant portion of the study devoted to catalysis. This is true of electrochemical reactions as well. In general the reaction rate constants, diffusion coefficients, and conductivities all exhibit Arrhenius-type dependence on temperature, and as a rule of the thumb, for every 10°C rise in temperature, most reaction rates are doubled. Hence, temperature effects must be incorporated into the parameter values. Fourier s law governs the distribution of temperature. For the example with the cylindrical catalyst pellet described in the previous section, the equation corresponding to the energy balance can be written in the dimensionless form as follows ... 

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