Flux law

Uphill diffusion occurs in binary systems because, strictly speaking, diffusion brings mass from high chemical potential to low chemical potential (De Groot and Mazur, 1962), or from high activity to low activity. Hence, in a binary system, a more rigorous flux law is (Zhang, 1993) ... 

Two Basic Descriptions of Transport by Random Motion Mass Transfer Model and Gradient-Flux Law... 

The second model, the so-called gradient-flux law, is considered to be more fundamental, although it is based on a more restrictive physical picture. In contrast to the mass transfer model, in which no assumption is made regarding the spatial separation of subsystems A and B, in the gradient-flux law it is assumed that the subsystems and the distance between them, Axa/b, become infinitely small. For very small subsystems the term occupation number loses its meaning and must be replaced by occupation density or concentration. Obviously, the difference in occupation density tends toward zero, as well. Yet the ratio of the two differences, Aoccupa-tion density Axa/b, is equal to the spatial gradient of the occupation density and usually different from zero ... 

One well-known example of the gradient-flux law is Fick s first law, which relates the diffusive flux of a chemical to its concentration gradient and to the molecular diffusion coefficient ... 

Manifestations of the gradient-flux law are not due to a random process but due the equilibrium between external force and internal friction. The positive sign results from the special sign convention used for electric currents and fields. 

The relation between length and time scales of diffusion, calculated from the Einstein-Smoluchowski law (Eq. 18-8), are shown in Fig. 18.11 for diffusivities between 10 10 cm2s 1 (helium in solid KC1) and 108 cm2s (horizontal turbulent diffusion in the atmosphere). Note that the relevant time scales extend from less than a millisecond to more than a million years while the spatial scales vary between 1 micrometer and a hundred kilometers. The fact that all these situations can be described by the same gradient-flux law (Eq. 18-6) demonstrates the great power of this concept. 

In fight of this analogy, we anticipate that the effect of turbulence may be dealt with in a similar manner like the random motion of molecules for which die gradient-flux law of diffusion (Eq. 18-6) has been developed. In addition, the mass transfer model (Eq. 18-4) may provide an alternative tool for describing the effect of turbulence on transport... 

Table 2.1 presents corresponding well-known empirical force-flux laws that apply under certain conditions. These are Fourier s law of heat flow, a modified version of Fick s law for mass diffusion at constant temperature, and Ohm s law for the electric current density at constant temperature.5 The mobility, Mj, is defined as the velocity of component i induced by a unit force. 

Force—Flux Laws for Systems with Unconstrained Components, i. 

Extensive Quantity Flux Conjugate Force Empirical Force—Flux Law ... 

Using the empirical laws displayed in Table 2.1, the entropy production can be identified for a few special cases. For instance, if only heat flow is occurring, then, using Eq. 2.15 and Fourier s heat-flux law,... 

The connection between the direct coefficients in Eq. 2.21 and the empirical force-flux laws discussed in Section 2.1.2 can be illustrated for heat flow. If a bar of pure material that is an electrical insulator has a constant thermal gradient imposed along it, and no other fields are present and no fluxes but heat exist, then according to Eq. 2.21 and Table 2.1,... 

Relation Between Levels of Description. It is c ur intention here to make the relation between the macroflus J and the individual cell membrane flux law JM more explicit. The diffusion-like coefficients of (52) may be written, using ( 9), as... 

The mass transfer flux law is analogous to the laws for heat and momentum transport. The constitutive equation for Ja, the diffusional flux of A resulting from a concentration difference, is related to the concentration gradient by Pick s first law ... 

Next, for evaluating the composed polarizability and total energy in the electrostatic AC-complex one should relay on the basic principles of electrostatic, starting from the Gauss electric flux law linking the total (source) charge with the electrostatic field created through a closed surface... 

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