Three-dimensional computations of solution hydrodynamics during the growth of potassium dihydrogen phosphate I. Spin up and steady rotation

Journal of Crystal Growth

Volumn 180, Issue 3-4, 1997, Pages 497-509

  Zhou, Yuming ^a   Derby, Jeffrey J ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Fluid flow; Solution growth; Three dimensional modeling

Indexed keywords

COMPUTATIONAL METHODS; CRYSTAL STRUCTURE; FINITE ELEMENT METHOD; FLOW PATTERNS; HYDRODYNAMICS; PHOSPHATES; POTASSIUM COMPOUNDS; SALTS;

GALERKIN METHOD; POTASSIUM DIHYDROGEN PHOSPHATE; TIME DEPENDENT SIMULATION;

CRYSTAL GROWTH;

EID: 0031244750     PISSN: 00220248     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0248(97)00251-0     Document Type: Article

References (67)

1. D. Elwell, H.J. Scheel, Crystal Growth from High-Temperature Solutions, Academic Press, London, 1975.
2. P.E. Hillner, A.J. Gratz, S. Manne, P.K. Hansma, Geology 20 (1992) 359.
3. J.J. DeYoreo, T.A. Land, B. Dair, Phys. Rev. Lett. 73 (6) (1994) 838.
4. C.M. Yip, M.D. Ward, Biophys. J. 71 (1996) 1071.
5. A.A. Chernov, J. Crystal Growth 24/25 (1974) 31.
6. W.R. Wilcox, J. Crystal Growth 65 (1983) 133.
7. A.A. Chernov, J. Crystal Growth 118 (1992) 333.
8. A.A. Chernov, S.R. Coriell, B.T. Murray, J. Crystal Growth 132 (1993) 405.
9. S.Y. Potapenko, J. Crystal Growth 158 (1996) 346.
10. H. Lin, P.G. Vekilov, F. Rosenberger, J. Crystal Growth 158 (1996) 552.
11. P.G. Vekilov, H. Lin, F. Rosenberger, Phys. Rev. B, 1996, submitted.
12. G.H. Westphal, F. Rosenberger, J. Crystal Growth 43 (1978) 687.
13. L.C. Liu, W.R. Wilcox, R.L. Kroes, B.R. Lal, in: G.E. Rindone (Ed.), Materials Processing in the Reduced Gravity Environment of Space, Elsevier, Amsterdam, 1983, p. 389.
14. H. Yoo, W.R. Wilcox, R. Lal, J.D. Trolinger, J. Crystal Growth 92 (1988) 101.
15. A. Nadarajah, F. Rosenberger, J.L Alexander, J. Crystal Growth 104 (1990) 218.
16. C. Huo, P. Ge, Z. Xu, Z. Zhu, J. Crystal Growth 114 (1991) 486.
17. Z. Xu, C. Huo, P. Ge, Z. Zhu, J. Crystal Growth 125 (1992) 135.
18. Z. Xu, P. Ge, C. Huo, Z. Zhu, J. Crystal Growth 129 (1993) 506.
19. S.Y. Potapenko, J. Crystal Growth 133 (1996) 132.
20. H. Lin, F. Rosenberger, J.I.D. Alexander, A. Nadarajah, J. Crystal Growth 151 (1995) 153.
21. R. Janssen-van Rosmalen, W.H. van der Linden, E. Dobbinga, D. Visser, Kristall und Technik 13 (1) (3978) 17.
22. P.P. Bordui, S. Motakef, J. Crystal Growth 96 (1989) 405.
23. L.N. Rashkovich, B.Yu. Shekunov, J. Crystal Growth 100 (1990) 133.
24. T.E. Tezduyar, M. Behr, S. Mittal, A.A. Johnson, in: P. Smolinski, W.K. Liu, G. Hulbert, K. Tamma (Eds.), New Methods in Transient Analysis, AMD, vol. 143, ASME, New York, 1992, p. 7.
25. Z. Johan, T.J.R. Hughes, K.K. Mathur, S.L. Johnsson, Comput. Meth. Appl. Mech. Eng. 99 (1992) 113.
26. M. Behr, A. Johnson, J. Kennedy, S. Mittal, T.E. Tezduyar, Comput. Methods Appl. Mech. Eng. 108 (1993) 99.
27. A.G. Salinger, Q. Xiao, Y. Zhou, J.J. Derby, Comput. Methods Appl. Mech. Eng. 119 (1994) 139.
28. Q. Xiao, A.G. Salinger, Y. Zhou, J.J. Derby, Int. J. Numer. Meth. Fluids 21 (1995) 1007.
29. A. Yeckel, J.W. Smith, J.J. Derby Int. J. Numer. Meth. Fluids 24 (1997) 1.
30. A. Yeckel, J.J. Derby, Parallel Computing, 1997, accepted.
31. J. Derby, S. Kuppurao, Q. Xiao, A. Yeckel, Y. Zhou, in: J.P. van der Eerden, O.S.L. Bruinsma (Eds.), Science and Technology of Crystal Growth, Kluwer, Dordecht, 1995, p. 111.
32. Q. Xiao, J.J. Derby, J. Crystal Growth 152 (1995) 169.
33. Q. Xiao, S. Kuppurao, A. Yeckel, J.J. Derby, J. Crystal Growth 167 (1996) 292.
34. J.J. DeYoreo, J. Britten, K. Montgomery, N.P. Zaitseva, B.W, Woods, L.J. Atherton, C.A. Ebbers, Z.U. Rek, ICF Quarterly Report 3(1993) 103. Also available as report UCRL-LR-105821-93-3, 1993, Lawrence Livermore National Laboratory, Livermore, CA.
35. J.J. DeYoreo, N.P. Zaitseva, K. Montgomery, R. Vitale, L.J. Atherton, presentation at AACG West-13, Fallen Leaf Lake, CA, June 7-10, 1994.
36. N. Zaitseva, L.N. Rashkovich, S.V. Bogatyreva, J. Crystal Growth 148 (1995) 276.
37. J.J. De Yoreo, Z.U. Rek, N.P. Zaitseva, B.W. Woods, J. Crystal Growth, in press.
38. T.G. Petrov, E.B. Treivus, A.P. Kasatkin, Growing Crystals from Solution, translated by A. Tybulewicz, Consultants Bureau, New York, 1969.
39. J.C. Brice, The Growth of Crystals from Liquid, North-Holland, Amsterdam, 1973.
40. F. Rosenberger, Fundamentals of Crystal Growth, I, Springer, Berlin, 1979.
41. C. Belouet, M. Monnier, J.C. Verplanke, J. Crystal Growth 29 (1975) 109.
42. C. Belouet, Progr. Crystal Growth Characterization 3 (1981) 121.
43. R. Janssen-van Rosmalen, P. Bennema, J. Crystal Growth 42 (1977) 224.
44. W.J.P. van Enckevort, R. Janssen-van Rosmalen, H. Klapper, W.H. van der Linden, J. Crystal Growth 60 (1982) 67.
45. P.F. Bordui, J.C. Jacco, G.M. Loiacono, R.A. Stolzenberger, J.J. Zola, J. Crystal Growth 84 (1987) 403.
46. A. Yeckel, Y. Zhou, J.J. Derby, J. Crystal Growth, 1997, submitted.
47. H.P. Greenspan, The Theory of Rotating Fluids, Cambridge University Press, London, 1968.
48. G. Strang, G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973.
49. T.J.R. Hughes, The Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1987.
50. C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Methods, Cambridge University Press, Cambridge, 1987.
51. J.J. Derby, S. Brandon, A.G. Salinger, Q. Xiao, Comput. Meth. Appl. Mech. Eng. 112 (1994) 69.
52. FIDAP Users Manual Fluid Dynamics International, Inc., Revision 6.0, Evanston, IL (1991).
53. P.M. Gresho, UCRL-92275, Lawrence Livermore National Laboratory, Livermore, CA, 1985.
54. G. Dahlquist, A. Björck, Numerical Methods, translated by N. Anderson, Prentice-Hall, Englewood Cliffs, NJ, 1974.
55. C.W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
56. Y. Zhou, PhD Thesis, Department of Chemical Engineering and Materials Science, University of Minnesota, 1995.
57. Y. Saad, M.H. Schultz, SIAM J. Sci. Statist. Comput. 7 (3) (1986) 856.
58. Y. Saad, Highly parallel preconditioners for general sparse matrices, in: G. Golub, M. Luskin, A. Greenbaum, (Eds.) Recent Advances in Iterative Methods, IMA Volumes in Mathematics and Its Applications, vol. 60, Springer, Berlin, 1994, pp.387-402.
59. A. Pothen, H.D. Simon, L. Wang, Technical Report RNR-92-003, NASA Ames Research Center, Moffet Field, CA, 1992.
60. G. Karypis, V. Kumar, Tech. Report, TR 95-035, Department of Computer Science, University of Minnesota, 1995.
61. T. von Karman, Z. Agnew. Mat. Mech. 1 (1921) 233.
62. D.D. Joseph, Stability of Fluid Motions, I, Springer, Berlin, 1976.
63. D.D. Joseph, Stability of Fluid Motions, II, Springer, Berlin, 1976.
64. S.N. Brown, K. Stewartson, Ann. Rev. Fluid Mech. 1 (1969) 45.
65. J.C Williams III, Ann. Rev. Fluid Mech. 9 (1977) 113.
66. H. Schlichting, in: Boundary Layer Theory, 7th ed. McGraw-Hill, New York, 1979.
67. J.J. DeYoreo, N.P. Zaitseva, L.J. Atherton, Lawrence Livermore National Laboratory, Livermore, CA, 1994, private communication.