Physical and thermodynamic quantities at the interface

In this chapter, the assumption wdl he made that the material interface is in a state which can he characterized, locally, hy physical and thermodynamic quantities, as can the media in contact with that interface. Thus, in the absence of fields, we had, for the internal surface energy e =eg[ Sg, lper unit mass (see Chapter 3 of [PRU 12])  

These equations remain valid for non-polarized conductive media. In the case of polarized conductors, we propose thermodynamic laws of the following type (in Chapter 3, 

For the moment, we shall not go into great detail about the compatibility conditions which the vectorial quantities must satisfy. In the above equations, the interface is considered to be a two-dimensional fluid medium. This consideration is by no means obligatory, though. We could also envisage interfaces with the behavior of an elastic surface, for example. This exploits the product j d /pj, which is transformed into a product of the pressure tensor by the strain rate tensor (see Chapter 3 of [PRU 12]). We retain the option of bringing these tensors into play in applications when it becomes necessary to do so. However, in the demonstrations given below, so as not to complicate the discussion, we shall suppose that the interface behaves like a fluid. 

The motion of the material at the interface is characterized by physical quantities particiilarly the fields, the momentum and the energy. These quantities will be characterized by 0, or 2 i-order tensors. However, most of the time, in addition to these physical quantities, we need to take account of the fluxes of those quantities across the surfaces in the 3-dimensional space. In the Minkowski space, these notions of quantities and fluxes associated therewith are replaced by a simpler concept that of the flux across a 

4 The electric and magnetic polarizations per rmit mass p and m are defined by equations [3.3] and [3.4], Here, we see the appearance of the corresponding interfacial quantities and.  

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