constants do not vary over the volume of the bodies. Spe-Distributed forces resulting from molecular interactions between cifically, the interaction energy E between two bodies demacroscopic bodies are usually concentrated near surfaces. A new fined by the volumes V 1 and V 2 is given by the doubleformulation has been developed that replaces these distributed volume integral 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 intersurwhere r 1 and r 2 are the number densities of molecules in face stress tensor. It is a symmetric tensor defined for any body the two bodies. Similarly, the total force of interaction bein terms of the intermolecular potential and the shape of the body.
tween two bodies, A, is
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
รwdV 1 dV 2 .
[2]
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. แญง 1997
Because the double-volume integrations are difficult to exe-
Academic Press
cute analytically, the application of this theory has been