Theory of regelation

The steady motion of a wire or other object through a block of ice by regelation is analysed theoretically. The solutions of the heat flow problem and the associated water flow problem are not independent, in general, because they both involve the thickness of the water film surrounding the moving object. Where the controlling thermal resistance is that of the object, however, the velocity under a given force may be calculated independently of the water film thickness. In this case the velocity of an object of given thermal resistivity, under a given force, depends only on its volume and not on its shape; the velocity is thus independent of the attitude of the object. For a sphere or a circular cylindrical wire the thickness of the water film is always uniform and is independent of the velocity of the object, regardless of whether the controlling thermal resistance is that of the object, the water film or the ice. Some of the theoretical expectations are in conflict with recent experiments and possible explanations are suggested. The mere fact that the object moves at all by regelation seems to contradict the Verhoogen theory of pressure melting under non-hydrostatic stress. In a supplementary note to the paper Professor F. C. Frank argues that the geometry of the water film described is usually unstable, and that this may explain the experimental results.