The viscous drag on solids moving through solids

AIChE Journal

Volumn 60, Issue 4, 2014, Pages 1488-1498

  Goddard, Joe D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Basal melting; Glaciers; Harmonic functions; Hydrodynamic lubrication; Ice regelation; Pressure melting

Indexed keywords

BASAL MELTING; DRAG FORCE AND TORQUE; ELLIPTIC CYLINDER; ELLIPTICAL CYLINDER; HYDRODYNAMIC LUBRICATION; LUBRICATION FLOWS; PRESSURE MELTING; THIN WATER LAYERS;

CYLINDERS (SHAPES); EXPERIMENTS; GLACIERS; HARMONIC FUNCTIONS; ICE; LUBRICATION; MELTING;

DRAG;

EID: 84897600518     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.14334     Document Type: Article

References (41)

1. Thomson J. Theoretical considerations on the effect of pressure in lowering the freezing point of water. Trans Roy Soc Edin. 1848;16(5):575-580.
2. Thomson W. XII. The effect of pressure in lowering the freezing-point of water experimentally demonstrated. Philos Mag Ser 3. 1850;37(248):123-127.
3. Thomson J. On crystallization and liquefaction, as influenced by stresses tending to change of form in the crystals. Proc R Soc London. 1860;11:472-481.
4. Faraday M. Experimental Researches in Chemistry and Physics. London: Taylor & Francis, 1859.
5. Faraday M. Note on regelation. Proc R Soc London. 1859;10:440-450.
6. Ornstein LS. Motion of a wire through a lump of ice. Proc Kon Ned Akad Wet. 1906;14:629-635. (in Dutch).
7. Nye JF. Theory of regelation. Philos Mag. 1967;16:1249-1266.
8. Frank FC. Regelation: a supplementary note. Philos Mag. 1967;16(144):1267-1274.
9. Mullins WW, Sekerka RF. Stability of a planar interface during solidification of a dilute binary alloy. J Appl Phys. 1964;35(2):444-451.
10. Davis SH. Theory of Solidification. Cambridge, New York: Cambridge University Press, 2001.
11. Worster MG. Convection in mushy layers. Annu Rev Fluid Mech. 1997;29(1):91-122.
12. Drake LD, Shreve RL. Pressure melting and regelation of ice by round wires. Proc R Soc London A. 1973;332(1588):51-83.
13. Taylor GI. Cavitation of a viscous fluid in narrow passages. J Fluid Mech. 1963;16(4):595-619.
14. Nye JF. A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation. Proc R Soc London A. 1969;311(1506):445-467.
15. Nye JF. Glacier sliding without cavitation in a linear viscous approximation. Proc R Soc London A. 1970;315(1522):381-403.
16. Evans DCB, Nye JF, Cheeseman KJ. The kinetic friction of ice. Proc R Soc London A. 1976;347(1651):493-512.
17. Colbeck SC, Najarian L, Smith HB. Sliding temperatures of ice skates. Am J Phys. 1997;65(6):488-492.
18. Dash JG, Fu H, Wettlaufer JS. The premelting of ice and its environmental consequences. Rep Prog Phys. 1995;58(1):115-167.
19. Rosenberg R. Why is ice slippery? Phys Today. 2005;58(12):50-55.
20. Wettlaufer JS, Worster MG. Premelting dynamics. Annu Rev Fluid Mech. 2006;38(1):427-452.
21. Hynninen T, Heinonen V, Dias C, Kartunnen M, Foster A, Ala-Nissila T. Cutting ice: nanowire regelation. Phys Rev Lett. 2010;105(8):086102.
22. Pinkus O, Sternlicht B. Theory of Hydrodynamic Lubrication. McGraw-Hill: New York, 1961.
23. Tyvand P, Bejan A. The pressure melting of ice due to an embedded cylinder. J Heat Trans (ASME). 1992;114(2):532-535.
24. Lamb H. Hydrodynamics. Cambridge, UK: Cambridge University Press, 1916.
25. Miloh T, Benveniste Y. On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces. Proc R Soc A. 1999;455(1987):2687-2706.
26. Moon P, Spencer DE. Recent investigations of the separation of Laplace's equation. Proc Am Math Soc. 1953;4(2):302-307.
27. Hobson EW. The Theory of Spherical and Ellipsoidal Harmonics. Cambridge, UK: Cambridge University Press, 1931.
28. Abramowitz M, Stegun I. Handbook of Mathematical Functions, Volume 55 of Applied Mathematics Series. New York: U.S. National Bureau of Standards, 1965.
29. Olver F, Lozier D, Bolsvert R, Clark C, editors. NIST Handbook of Mathematical Functions. U.S. National Institute of Standards and Technology & Cambridge University Press: New York, 2010. Available at http://dlmf.nist.gov/14.3. Last accessed on May 6, 2013.
30. Stishov SM. The thermodynamics of melting of simple substances. Sov Phys Usp. 1975;17(5):625.
31. Tallon JL. The entropy change on melting of simple substances. Phys Lett A. 1980;76(2):139-142.
32. Stillinger FH, Debenedetti PG. Phase transitions, Kauzmann curves, and inverse melting. Biophys Chem. 2003;105(23):211-220.
33. Feeney MR, Debenedetti PG, Stillinger FH. A statistical mechanical model for inverse melting. J Chem Phys. 2003;119(8):4582-4591.
34. Lu HM, Jiang Q. Melting volume change of different crystalline lattices. Phys Stat Solidi B. 2004;241(11):2472-2476.
35. Wittenberg LJ, DeWitt R. Volume contraction during melting; emphasis on lanthanide and actinide metals. J Chem Phys. 1972;56(9):4526-4533.
36. Sangster RC, Carman JN. Contraction of germanium on melting. J Chem Phys. 1955;23(1):206-207.
37. Vaidya SN, Akella J, Kennedy GC. Melting of germanium to 65 kbar. J Phys Chem Solids. 1969;30(6):1411-1416.
38. Cusack N, Kendall P. A note on the viscosity and resistivity of liquid gallium. Proc Phys Soc. 1960;75(2):309.
39. Singh A, Tsai AP. Melting behaviour of lead and bismuth nano-particles in quasicrystalline matrix-the role of interfaces. Sadhana. 2003;28(1-2):63-80.
40. Owens BB. Melting properties of the alkali nitrates to 10 000 atmospheres. J Chem Phys. 1965;42(7):2259-2262.
41. Brygoo S, Henry E, Loubeyre P, Eggert J, Koenig M, Loupias B, Benuzzi-Mounaix A, Rabec Le Gloahec M. Laser-shock compression of diamond and evidence of a negative-slope melting curve. Nat Mater. 2007;6(4):274-277.