Power—law equation

Here /, r and, v are unequal integers in the set 1, 2, 3. As already mentioned, in the thin-layer approach the fluid is assumed to be non-elastic and hence the stress tensor here is given in ternis of the rate of deforaiation tensor as r(p) = riD(ij), where, in the present analysis, viscosity p is defined using the power law equation. The model equations are non-dimensionalized using... 

Another complication arises when not all of the internal surface of a porous catalyst is accessed. Then a factor called the effectiveness T is apphed, making the power law equation, for instance,... 

The ASME Dispersion Parameters. The horizonal and vertical dispersion parameters are represented by the following empirical power law equation... 

Since the power law equations are going to be used rather than the flow curves, it is necessary to use the true shear rates. 

We attempted to describe the integral dependences in Fig. 7 also by the power-law equations... 

The kinetics of a coupled catalytic reaction can be well described by equations of the Langmuir-Hinshelwood type, since these are able to express mutual influencing of single reactions. Power-law equations are not suitable for this purpose. 

Gamer and Hailes [462] postulated a chain branching reaction in the decomposition of mercury fulminate, since the values of n( 10—20) were larger than could be considered consistent with power law equation [eqn. (2)] obedience. If the rate of nucleation is constant (0 = 1 for the generation of a new nuclei at a large number of sites, N0) and there is a constant rate of branching of existing nuclei (ftB), the nucleation law is... 

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. 

Rate constant. It is easiest to estimate the value of the rate constant if it is the only unknown in the kinetic expression. Typically these expressions are the power law equations ... 

A simple estimate of the diffusion coefficients can be approximated from examining the effects of molecular size on transport through a continuum for which there is an energy cost of displacing solvent. Since the molecular weight dependence of the diffusion coefficients for polymers obeys a power law equation [206], a similar form was chosen for the corneal barriers. That is, the molecular weight (M) dependence of the diffusion coefficients was written as ... 

Data for the reaction between hydrogen (A) and bromine (B) with equal concentrations are tabulated. Time is in minutes and concentrations in mols/liter. A complex mechanism has been established (see problem P2.03.15) but here a power law equation will be fitted,... 

Dolomite is dissolved by hydrochloric acid. Data at initial conditions give the concentration of acid, gmol/liter, and its rate of reaction, gmol/liter-sqcm-sec, when exposed to 30 sqcm of solid in one liter of solution (Lund et al, Chem Eng Sci 28 691,1973). Find the constants of a power law equation. 

Solutions for with several power law equations are developed in P7.03.14 and for an L-H rate equation in P7.03.15. 

Time-temperature superposition is frequently applied to the creep of thermoplastics. As mentioned above, a simple power law equation has proved to be useful in the modelling of the creep of thermoplastics. However, for many polymers the early stages of creep are associated with a physical relaxation process in which the compliance (D t)) changes progressively from a lower limit (Du) to an upper limit (DR). The rate of change in compliance is related to a characteristic relaxation time (x) by the equation ... 

In general it is fair to say that rheologists have been conservative in their use of non-exponential kernels. One particular form clearly stands out as a candidate for describing experimental data, at least for a limited range of relaxation times. This is the power law equation, often applied to... 

The term S represents the strength of the network. The power law exponent m was found to depend on the stochiometric ratio r of crosslinker to sites. When they were in balance, i.e. r = 1, then m - 1/2. From Equations (5.140) and (5.141) this is the only condition where G (co) = G (cd) over all frequencies where the power law equation applies. If the stochiometry was varied the gel point was frequency dependent. This was also found to be the case for poly(urethane) networks. A microstructural origin has been suggested by both Cates and Muthumkumar38 in terms of a fractal cluster with dimension D (Section 6.3.5). The complex viscosity was found to depend as ... 

In addition to temperature, the viscosity of these mixtures can change dramatically over time, or even with applied shear. Liquids or solutions whose viscosity changes with time or shear rate are said to be non-Newtonian, that is, viscosity can no longer be considered a proportionality constant between the shear stress and the shear rate. In solutions containing large molecules and suspensions contain nonattracting aniso-metric particles, flow can orient the molecules or particles. This orientation reduces the resistance to shear, and the stress required to increase the shear rate diminishes with increasing shear rate. This behavior is often described by an empirical power law equation that is simply a variation of Eq. (4.3), and the fluid is said to be a power law fluid ... 

Various reports can be found in the relevant literature in connection with the kinetics of sintering of supported metal catalysts. A power-law equation used is (Forzatti and Lietti, 1999)... 

To illustrate some of the structural features of the aggregates formed, we can make use of an empirical relationship between Mw and Re, which takes the form of a power-law equation (Burchard, 1994) ... 

Work by the USBuMines in ground motion transmission (Ref 2) produced two particularly significant results for the typical charge weights and distances found in surface blasting 1) the constant m is equal to one-half of the constant n the power law equation then has only two unknowns and assumes the following form ... 

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