Relation phenomenological

Disordering energy versus disorder in minerals a phenomenological relation and application to orthopyroxene. /. Phys. Chem. Solids 47, 417-420. 

In addition, the simple phenomenological relation (6.1.4), with a constant electro-osmotic coefficient lc, was replaced by a more elaborate one, accounting for the w dependence on the flow rate and the concentrations Ci, C2 via a stationary electro-osmotic calculation. This approach was further adopted by Meares and Page [7] [9] who undertook an accurate experimental study of the electro-osmotic oscillations at a Nuclepore filter with a well-defined pore structure. They compared their experimental findings with the numerically found predictions of a theoretical model essentially identical to that of [5], [6]. It was observed that the actual numerical magnitude of the inertial terms practically did not affect the observable features of the system concerned. 

Ninomiya,K., Ferry,J.D. Phenomenological relation for viscoelastic properties of polymer diluent systems the relative dissipation index N21. J. Macromol. ScL-Phys. B 3.237-258 (1969). 

To find a principle which so narrows down the statistics (e.g., to a subclass of probability densities S ) that 9 relations in addition to the 5 transport equations will hold between our macroscopic quantities, so that the initial value problem for (p, ua, E), with the basic boundary conditions, will become determinate. In actuality, this will amount to finding a principle from which the various phenomenological relations of two paragraphs back are (approximate) deductions. 

This is identical with the phenomenological relation of Equation (9) if one formally identifies S with SU with V and 9 with kT. In this way. contact widi the phenomenological theory has been established, and die quantities characteristic of the one theory have been correlated with that of the other. With this correlation, or interpretation.

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In the linear-response region the fluxes Jt of matter and heat are related to the thermodynamic forces Fk by linear phenomenological relations... 

An experimental approach to analyze the resulting sweep-rate dependence of the coercivity is to exploit the phenomenological relation [159]... 

Stucki (1980, 1984) applied the linear nonequilibrium thermodynamics theory to oxidative phosphorylation within the practical range of phosphate potentials. The nonvanishing cross-phenomenological coefficients Ly(i v /) reflect the coupling effect. This approach enables one to assess the oxidative phosphorylation with H+pumps as a process driven by respiration by assuming the steady-state transport of ions. A set of representative linear phenomenological relations are given by... 

This equation is independent of the type of phenomenological relations between fluxes and forces. In contrast, linear phenomenological equations and the Onsager reciprocal relations yield... 

Linear nonequilibrium thermodynamics has some fundamental limitations (i) it does not incorporate mechanisms into its formulation, nor does it provide values for the phenomenological coefficients, and (ii) it is based on the local equilibrium hypothesis, and therefore it is confined to systems in the vicinity of equilibrium. Also, properties not needed or defined in equilibrium may influence the thermodynamic relations in nonequilibrium situations. For example, the density may depend on the shearing rate in addition to temperature and pressure. The local equilibrium hypothesis holds only for linear phenomenological relations, low frequencies, and long wavelengths, which makes the application of the linear nonequilibrium thermodynamics theory limited for chemical reactions. In the following sections, some of the attempts that have been made to overcome these limitations are summarized. 

Equations (14.13) and (14.14) represent the nonlinear phenomenological relations between the external driving forces of permeation flows AnA and AfiB and the conjugate flows. /A and JB. 

These reciprocity relations are derived in Section 6.5. It should be clearly recognized that Eq. (6.3.6) holds only if the phenomenological relations involve conjugate fluxes and forces. If nonconjugate quantities are used, and Lji are... 

The preceding phenomenological relations may be rendered symmetric by considering instead of J0 and J+ the total volume flow Jv V0J0 + V+J+ and total current density 1+ ZFJ+ ... 

Another set of circumstances frequently encountered is specified by (d) J7 — J — Jg - 0. Here, no currents are allowed to flow, and adiabatic conditions are imposed along the y-direction. Then the phenomenological relations (6.10.1) can be reduced to... 

The transport processes that we study in this work are linear transport processes [1]. They arise when one has a linear phenomenological relation. 

Inserting Eq. (3.11) into the linear response relation (2.17) and comparing with the phenomenological relation (2.3) we obtain a relation for the shear viscosity of an isotropic fluid. 

In a uniaxially symmetric system the linear phenomenological relations between the forces and the fluxes become [27]... 

The authors of ref. 51, where nonthermal critical effects typical of the low-temperature limit region were found, assumed that acceleration of reactions was determined by the energy barrier lowering due to the excess free energy of structurally nonequilibrium medium G and suggested a phenomenological relation ... 

Develop phenomenological relations for the set of conditions Jy = VyT = 7/ = 0 and prove that a temperature gradient is set up along x as a consequence of current flow along that direction. What is the resultant heat flux along y Express the resistivity and Hall coefficients in terms of the various Lij. 

This section will set out the thermodynamic framework underlying the properties of Langmuir monolayers. Typicedly. we look for phenomenological relations (i.e. relations that are not based upon a molecular model) between thermodynamic functions characterizing the monolayer. More crudely, what thermodynamic information is available and what can be derived from it ... 

The adsorption of heavy metals onto amorphous or crystalline forms of iron oxide and clays occurs in nature and is phenomenologically related to the binding of contaminant to the superhcial ferric and/or aluminium ions. Although, this behavior explains the concentration of metal contaminants in soils, it does not constitute a viable method for trapping low concentrations of contaminants from aqueous streams because of its limited adsorption capacity. 

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