Foundations of Transport Theory

Abstract

The transport theory of multicomponent and multiphase mixtures of elastic and inelastic materials is the only well-established physical theory of matter capable of modeling a wide variety of physicochemical processes taking place within the volcanic system. These processes include melt segregation and transport toward the surface of the Earth, magma mixing and differentiation, crystal growth, exsolution and bubble growth in magma, magma fragmentation and interaction with water, thermomechanical deformation of the volcanic edifice, distribution of pyroclasts in the atmosphere, and pyroclastic, lava, and mudflows. This phenomenological theory includes the basic physical laws expressing the transport of mass, momentum, energy, and entropy for a continuum and is assumed to be valid for all bodies irrespective of their molecular or atomic structure. Such laws are, however, underdetermined and additional relations or constitutive equations are required to model the behavior of real materials subjected to pressure, temperature, and composition gradients. The latter equations are most often determined from the macroscopic behavior of matter and are necessarily restricted to those materials and conditions for which they have been developed. The basic laws of the transport theory represent one of our greatest achievements and cannot be a priori derived from the more fundamental laws governing the molecular behavior of matter without invoking additional assumptions.

Nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning.

—Lord Kelvin (William Thomson), 1849