Macroscale Thermodynamics and the Chemical Potential for Swelling Porous Media

The thermodynamical relations for a two-phase, N-constituent, swelling porous medium are derived using a hybridization of averaging and the mixture-theoretic approach of Bowen. Examples of such media include 2-1 lattice clays and lyophilic polymers. A novel, scalar definition for the macroscale chemical potential for porous media is introduced, and it is shown how the properties of this chemical potential can be derived by slightly expanding the usual Coleman and Noll approach for exploiting the entropy inequality to obtain near-equilibrium results. The relationship between this novel scalar chemical potential and the tensorial chemical potential of Bowen is discussed. The tensorial chemical potential may be discontinuous between the solid and fluid phases at equilibrium; a result in clear contrast to Gibbsian theories. It is shown that the macroscopic scalar chemical potential is completely analogous with the Gibbsian chemical potential. The relation between the two potentials is illustrated in three examples.     

Coupled Solvent and Heat Transport of a Mixture of Swelling Porous Particles and Fluids: Single Time-Scale Problem

A three-spatial scale, single time-scale model for both moisture and heat transport is developed for an unsaturated swelling porous media from first principles within a mixture theoretic framework. On the smallest (micro) scale, the system consists of macromolecules (clay particles, polymers, etc.) and a solvating liquid (vicinal fluid), each of which are viewed as individual phases or nonoverlapping continua occupying distinct regions of space and satisfying the classical field equations. These equations are homogenized forming overlaying continua on the intermediate (meso) scale via hybrid mixture theory (HMT). On the mesoscale the homogenized swelling particles consisting of the homogenized vicinal fluid and colloid are then mixed with two bulk phase fluids: the bulk solvent and its vapor. At this scale, there exists three nonoverlapping continua occupying distinct regions of space. On the largest (macro) scale the saturated homogenized particles, bulk liquid and vapor solvent, are again homogenized forming four overlaying continua: doubly homogenized vicinal fluid, doubly homogenized macromolecules, and singly homogenized bulk liquid and vapor phases. Two constitutive theories are developed, one at the mesoscale and the other at the macroscale. Both are developed via the Coleman and Noll method of exploiting the entropy inequality coupled with linearization about equilibrium. The macroscale constitutive theory does not rely upon the mesoscale theory as is common in other upscaling methods. The energy equation on either the mesoscale or macroscale generalizes de Vries classical theory of heat and moisture transport. The momentum balance allows for flow of fluid via volume fraction gradients, pressure gradients, external force fields, and temperature gradients.     

Mechanische Relaxationserscheinungen bei Acrylgläsern — Beziehungen zur Struktur,Eigenschaften und Verarbeitbarkeit

Ohne ZusammenfassungVorgetragen auf der Jahrestagung der Deutschen Rheologen vom 11.–13. Mai 1964 in Berlin-Dahlem.     

Evidence for an anisotropy-induced non-collinear spin state in exchange-coupled Co/Cu(001)

The magnetization behaviour of a Co/Cu/Co(001) sandwich has been studied by magneto-optical Kerr effect measurements. The sample was grown by molecular beam epitaxy onto a sapphire (1 .2) substrate with a Cu/Cr/Nb(001) buffer system. The copper layer had the form of a wedge with the thickness range chosen to be around the second region of antiferromagnetic exchange coupling. The hysteresis loops in the regime of weak antiferromagnetic coupling show characteristic steps, which can be explained by an anisotropy-induced non-collinear spin state. Indication for a similar behaviour is also found in the regime of strong antiferromagnetic coupling. This behaviour is explained by taking into account the competition between anisotropy, interlayer exchange coupling and external field energy. The nature of this metastable non-collinear magnetization state is in marked contrast to the biquadratic (90°) exchange coupling which was discovered in Fe/Cr(001).