On the derivation of boundary conditions from the global principles of continuum mechanics

Gerald G. Kleinstein, Northeastern University

Abstract

We consider the motion of a fluid exterior to a moving rigid obstacle, or interior to a moving rigid shell. The boundary conditions, such as the no-slip condition and the condition of an isothermal wall, applied in the solution of the system of differential equations describing these motions, are currently assumed to be an approximation derived from experimental observation rather than an exact law. It is the purpose of this paper to show that the boundary conditions at a material interface between a fluid and a solid are derivable from the global principles of balance of continuum mechanics and the Clausius-Duhem inequality.