Determination of the Kelvin equation in the presence of an arbitrary gravitational/inertial field

摘要

The validity of the Kelvin equation in the presence of an arbitrary stationary field due to gravity or an accelerated reference frame is determined by a fluid-dynamical argument. In this approach capillary rise and the Kelvin effect appear to be different aspects of the same phenomenon. A general form of the Kelvin equation is obtained that does not depend on the applied field. A higher-order approximation than the usual Kelvin equation is derived by using Lagrange's expansion method. The fluid-dynamical approach is proved to be equivalent to a purely thermodynamical approach provided that the surface free energy in the presence of the external field is appropriately defined. Both the fluid-dynamical and the thermodynamic approach lead to the conclusion that the generalized form of Kelvin equation does not depend on the applied field. (C) 2006 American Association of Physics Teachers.