An Intersurface Stress Tensor

Distributed forces resulting from molecular interactions between macroscopic bodies are usually concentrated near surfaces. A new formulation has been developed that replaces these distributed body forces by effective surface tractions and is not limited by the geometrical restrictions of Derjaguin's approximation. It offers great computational simplification over the use of the body-force distribution. The body-force distribution is integrated and partitioned to various surface elements. The resulting expressions for surface traction involve a second-order tensor termed the intersurface stress tensor. It is a symmetric tensor defined for any body in terms of the intermolecular potential and the shape of the body. It acts much like the internal stress tensor; the surface traction vector on a surface introduced into its field is the inner product of the tensor and the surface normal. The new surface formulation reduces to Derjaguin's approximation for the case of a half-space with a plane surface. Properties of the new tensor are explored. Actual components are derived for several geometries.