Engineering models for synthetic microvascular materials with interphase mass, momentum and energy transfer

New materials are being developed that consist of a solid matrix with pores or vessels through which a functional fluid phase may pass. The fluid can provide expanded functionality such as healing and remodeling, damage disclosure, enhanced heat transfer, and controlled deformation, stiffness and damping. This paper presents a class of engineering models for synthetic microvascular materials that have fluid passages much smaller than a characteristic structural length such as panel thickness. The materials are idealized as two-phase continua with a solid phase and a fluid phase occupying every volume. The model permits the solid and fluid phases to exchange mass, momentum and energy. Balance equations and the entropy inequality for general mixtures are taken from existing continuum mixture theory. These are augmented with certain definite types of solid–fluid interactions in order to enable adequately general, but workable, engineering analysis. The thermomechanical characteristics of this restricted class of materials are delineated. By demanding that the law of increase of entropy be satisfied for all processes, much is deduced about the acceptable forms of constitutive equations and internal state variable evolution equations. The paper concludes with a study of the uniaxial tension behavior of an idealized vascular material.