Chemical potential field, flow

To understand fully the chemical reaction processes that take place in rock assemblages, it is necessary to introduce the concept of chemical potential Much the same as in a gravitational potential, in which an object tends to fall from a high to a low altitude, in a chemical potential field the reaction or flow direction of components always tends to proceed from a high to a low chemical potential region. 

Let now consider a system where in addition to the diffusion flux due to the chemical potential differences, there is also a certain flow field v(r, t). The equation for the temporal change of the order parameter field in this case is [1,4,157]... 

Fluxes of chemical components may arise from several different types of driving forces. For example, a charged species tends to flow in response to an applied electrostatic field a solute atom induces a local volume dilation and tends to flow toward regions of lower hydrostatic compression. Chemical components tend to flow toward regions with lower chemical potential. The last case—flux in response to a chemical potential gradient—leads to Fick s first law, which is an empirical relation between the flux of a chemical species, J, and its concentration gradient, Vcj in the form J, = —DVcj, where the quantity D is termed the mass diffusivity. 

It is evident from the last equation that the effects of the gradient and the electric field can be either additive or subtractive, because each term on the right-hand side can be of either sign. In fact, a flow of charged particles produced by a chemical potential difference across a diffusion medium can lead to charge flow and the creation of an electric potential which effectively cancels the effects of the chemical potential difference... 

The classification of separations should reflect the patterns of component transport and equilibrium that develop in the physical space of the system. The transport equations show that we have two broad manipulative controls that can be structured variously in space to affect separative transport. First is the chemical potential which controls both relative transport and the state of equilibrium. Chemical potential, of course, can be varied as desired in space by placing different phases, membrane barriers, and applied fields in appropriate locations. A second means of transport control is flow, which can be variously oriented with respect to the phase boundaries, membranes, and applied fields—that is, with respect to the structure of the chemical potential profile. 

Viewed in this way, chemical potential profiles (along with flow) govern separation different phases, membranes, and applied fields are simply convenient media for imposing the desired profiles. The media are selected on pragmatic grounds chemical compatibility with the components and the system, selectivity between components, noninterference with detectability, ease of solvent removal (another separation process), facilitation of rapid transport, and so on. 

Anywhere a chemical potential increment or gradient exists, an elementary separation step can occur. Anywhere random flow currents exist, separation is dissipated. Thus random flow currents are parasitic in regions where incremental chemical potential is used for separation. These currents should thus be eliminated, insofar as possible, in regions where electrical, sedimentation, and other continuous (c) fields are generating separations. Likewise, they should not be allowed to transport matter over discontinuous (d) separative interfaces such as phase boundaries or membrane surfaces. However, they are nonparasitic in bulk phases (removed from the separative interface) where only diffusion occurs. Here, in fact, they aid diffusion and speed the approach to equilibrium. This positive role is recognized in the following category of flow. 

Table 1. Relationship between X and the physical solute properties using different FFF techniques [27,109] with R=gas constant, p=solvent density, ps=solute density, co2r=centrifugal acceleration, V0=volume of the fractionation channel, Vc=cross-flow rate, E=electrical field strength, dT/dx=temperature gradient, M=molecular mass, dH=hydrodynamic diameter, DT=thermal diffusion coefficient, pe=electrophoretic mobility, %M=molar magnetic susceptibility, Hm=intensity of magnetic field, AHm=gradient of the intensity of the magnetic field, Ap = total increment of the chemical potential across the channel...

Chemical behaviour depends on chemical potential and electromagnetic interaction. Both of these factors depend on the local curvature of space-time, commonly identified with the vacuum. Any chemical or phase transformation is caused by an interaction that changes the symmetry of the gauge field. It is convenient to describe such events in terms of a Lagrangian density which is invariant under gauge transformation and reveals the details of the interaction as a function of the symmetry. The chemically important examples of crystal nucleation and the generation of entropy by time flow will be discussed next. The important conclusion is that in all cases, the gauge field arises from a symmetry of space-time and the nature of chemical matter and interaction reduces to a function of space-time structure. 

In the absence of an external force field, the system at stable thermody namic equilibrium must be fully uniform (isotropic) in respect of such para meters as temperature, pressure and chemical potentials of all the involved components. In other words, there are zero gradients of these parameters through the inner space of the system at the thermodynamic equilibrium. As a result, any matter or energy flows are not observed in these systems. 

X HERMAL FIELD-FLOW FRACTIONATION (ThFFF) separates polymers according to their molecular weight and chemical composition. The molecular weight dependence is well understood and is routinely used to characterize molecular weight distributions (1-4). However, the dependence of retention on composition is tied to differences in the thermal diffusion of polymers, which is poorly understood. As a result, the compositional selectivity of ThFFF has not realized its full potential. How-... 

The entropy flow is based on a heat or material flow, the entropy generation on a heat flow in a temperature field, diffusion by mass forces and differences in the chemical potential, mechanical dissipation and chemical reactions. 

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