Incorporation of line quantities in the continuum description for multiphase, multicomponent bodies

Abstract

In this thesis the continuum description for dynamic, multiphase, multicomponent systems with intersecting dividing surfaces, is developed. In this development, the contribution of line excess quantities (line mass density, line velocity, $...$) associated with the common line, is taken into account. Starting with the standard postulates of mechanics, the governing equations for a common line (the species mass balance at the common line, the momentum balance at the common line, $...$) are derived.The material behavior of common lines is discussed. A constitutive equation for the line stress tensor is introduced. It is shown that the inclusion of curvature terms in the equations of state for the surface and line internal energies is a violation of the entropy inequality. With the correct equation of state for the surface and line internal energies, the results for a static problem derived using minimization of the total internal energy, are shown to be identical to the results derived using the differential momentum balance, the jump momentum balance and the momentum balance at the common line. Finally, the sessile drop problem is analyzed, starting from the governing equations for a static problem. A singular perturbation solution is developed, where the perturbation parameter characterizes the strength of the long-range intermolecular forces. This solution is used to develop a new method to determine line tension and solid-fluid surface tensions, using small sessile drops.