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The viscous drag on solids moving through solids



An extension of the theory of Ornstein (1906) and Nye (1967) for the drag force on circular wires and other solid bodies creeping through ice by means of pressure-melting and regelation is provided. Nye's theory leads to a form of Stokes law, with rates controlled by heat conduction and lubrication flow in a thin water layer between ice and solid body. New analytical solutions are given for the corresponding drag force and torque on elliptical cylinders and spheroids for the special case of thermally thin water layers and for certain special forms of uncoupled translation and rotation that allow for single-harmonic temperature fields. The present results differ from those proposed by Nye for general body shapes in the limit of negligible thermal resistance of the water layer. Also, the present results for the drag force on elliptic cylinders do not agree with the formulae derived by Tyvand and Bejan (1992) for small ellipticity. A brief review is given for various effects that might account for certain departures of the Nye theory from experiment on circular wires, in the hope that the present results may suggest simpler experiments aimed at systematic modification of the theory to account for such anomalies. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1488–1498, 2014