Mathematik-Gebäude, Seminarraum M614/616

Consider a rigid ball B partially immersed in equilibrium, in an unlimited liquid bath with surface S symmetric and horizontal at infinity and subject to surface tension in a downward gravity field g. B will create a local disturbance in S, which vanishes rapidly with distance from its center. Moving B vertically a small distance h leads to no substantive change in the configuration, and similar behavior will be observed. If gravity is removed, the problem changes basically. The only liquid surface under the conditions becomes a horizontal plane meeting the ball in a contact angle determined entirely by the materials. Thus if B is now moved vertically the distance h, S must move rigidly with it; consequently the entire liquid must also move, which conceivably would require an infinite amount of work, a seemingly absurd conclusion.
This talk will be devoted to my attempts to reformulate the conditions of the problem in terms of mathematically precise and physically reasonable statements, and to continuing efforts to obtain correct predictions as to what actually would occur under such circumstances.

Prof. em. Robert Finn

Stanford University (USA)