CYLINDRICAL LIQUID BRIDGES SQUEEZED BETWEEN PARALLEL PLATES - EXACT STOKES-FLOW SOLUTIONS AND HYDRODYNAMIC-FORCES

The problem of a dynamic liquid bridge between moving parallel plates is introduced. For the case of the Stokes flow in a cylindrical bridge driven by a slow change of the distance between the plates, an exact infinite-series solution is constructed, without invoking the lubrication approximation which was never surmounted in previous theories of dynamic liquid bridges. The boundary conditions at the free surface are fully satisfied, and the singularities of physical quantities at the moving contact line are avoided by allowing a minute but nonzero slip velocity. It is shown that, for narrower bridges, the "nonlubricative" contribution to hydrodynamic forces may become comparable with the force associated with the lubrication approximation.