Modeling of the microwave drying process of aqueous dielectrics

Abstract

We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.

On Implicit Constitutive Theories

“…In the above remarks (3.1) stands for (38). The model (37) has been advanced by many as a possible representation for the inelastic response exhibited by some bodies. I do not share this point of view.…”

“…While both Galilean and Lorentz invariance seem to be appropriate restrictions in that they are consistent with one another, frame-indifference that allows for rotations that are time dependent between frames is not consistent with Lorentz invariance. It has been shown in [37] that frame-indifference cannot be required amongst all observers and that the rotation of the earth is sufficient to create problems as time goes on. In fact, it is easy to see that if Q(t) is not zero velocities can exceed the speed of light for sufficiently large |x|.…”

“…While the radiation is not subject to any restrictions, it is required to be whatever it takes to meet the balance of energy. While ignoring the radiation completely might be reasonable for certain processes, it is completely untenable for many other processes (a case in point is problems involving microwave radiation or any problem concerning electromagnetic radiation, see Rajagopal and Tao [37]). There are yet other difficulties associated with the use of the Clausius-Duhem inequality (or for that matter any form of the second law) such as, whether it ought to be enforced locally or whether it ought only to be enforced globally, etc., but we shall not get into a discussion of such issues here.…”

A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood

“…More importantly, our models arise in a thermodynamic setting that involves specifying the manner of the rate of dissipation and the manner in which energy is stored by the material in question. The procedure also guarantees constitutive relations that automatically meet the second law of thermodynamics and in order to ensure this we do not appeal to a procedure that is often used to place restrictions on allowable constitutive relations that presumes that the body can be subjected to arbitrary processes (see Rajagopal and Tao, 2002 for a detailed discussion of these issues). We ensure that the rate of dissipation is non-negative and we maximize the rate of dissipation to select the final constitutive equation (see Rajagopal and Srinivasa, 2000).…”

A thermodynamical framework for chemically reacting systems

“…(4.2) is insufficient because specific radiant heating does not show up explicitly (see §1 of Rajagopal and Tao [33]). Now, we will assume the existence of sufficiently smooth, specific Gibbs potential, which is introduced through the Legendre transform: 2…”