Molecular theory of surface tension
Abstract
The calculus of variations is used for determination of the equilibrium distribution of the molecular density in a twophase, one component system. The total Helmholtz free energy, to be minimized, is thus expressed as a definite integral. From analysis of the EulerLagrange differential equation general expressions are obtained for pressure and surface tension. Gravitational effects are obtained from the differential equation when an appropriate term is incorporated into the original Helmholtz free energy density. In a three dimensional treatment the stress tensor formula is obtained from the corresponding partial differential equation. A (differential) generalization of the YoungLaplace equation for the spherical interface is derived. In addition metastable regions are described and interpreted. The stress tensor for the system in the presence of any kind of conservative force field can also be obtained.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 1975
 Bibcode:
 1975PhDT.........9Y
 Keywords:

 Interfacial Tension;
 Molecular Theory;
 Pressure;
 Calculus Of Variations;
 Differential Equations;
 EulerLagrange Equation;
 Gravitational Effects;
 Stress Tensors;
 Atomic and Molecular Physics