Abstract
In this note the authors consider the motion of a cylinder through a block of ice. The cylinder is pushed laterally through the ice block. The ice melts over the leading portion of the cylinder, the water films acts as lubricant (flows around the cylinder), and refreezes over the trailing portion of the cylinder. A cross section through the embedded cylinder is shown. The same problem was solved first by Nye, who proceeded from the assumption that the thickness of the water proceeded from the assumption that the thickness of the water film is constant. The objective in this note is to present a general and formal treatment, in which the film thickness is allowed to vary around the cylinder. In this way they arrive not only at Nye's constant-thickness results but also at the limiting conditions under which those results are valid. The authors then extend the analysis to a cylinder with an elliptical cross section, and report also the shape of the cylindrical cable that moves through a block of ice.
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