A note on the kinematic boundary condition with historical perspective

The kinematic boundary condition results from the application of conservation of mass at the bounding surface of a fluid. For a material interface, this condition reduces to the requirement that there is no flux of fluid across the boundary. As demonstrated, this can be satisfied by fluid particles which remain on the interface. However, following Kelvin, it is highlighted that this commonly referenced scenario is a special case of a more general result. The mathematical expression of the kinematic boundary condition is more complex when there is a transfer of mass across the interface. Conservation of mass is still applicable across interfaces of this type, and the resulting condition is shown to collapse to that for a material surface when the mass flux across the interface is zero.