On The Physical Interpretation of Fluid Interfacial Concepts and Fields

Abstract

A fluid-fluid interfacial region is in general very thin. In such case its macroscopic behaviour is well-modelled in terms of a bidimensional continuum which can exchange matter with its contiguous bulk phases. In particular, balance relations for mass, linear and rotational momentum, and energy can be ascribed to a surface which models the instantaneous location of the region. Delineation of the interfacial region, selection of a model surface and appropriate velocity fields, and motivation of the appropriate balance relations, are here effected on the basis of molecular considerations. A further balance relation (redundant for bulk continua), that of moment of mass, is also developed. This furnishes a relationship between the geometrical (‘normal’) velocity of the model surface, the velocity field associated with interfacial matter, and mass transport across the interface. All fields are identified with local averages of molecular quantities in both space and time. The analysis is based upon very weak assumptions concerning the nature of molecular interactions and the random character of molecular thermal motions. Such assumptions are made explicitly and their physical basis is discussed. The notation employed is coordinate-free: relevant explanation is summarised in an Appendix.