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Keywords:
numerical modeling; rigid particle; viscous flow; equations of motion; elliptic integrals
numerical modeling; rigid particle; viscous flow; equations of motion; elliptic integrals
Summary:
Modeling the movement of a rigid particle in viscous fluid is a problem physicists and mathematicians have tried to solve since the beginning of this century. A general model for an ellipsoidal particle was first published by Jeffery in the twenties. We exploit the fact that Jeffery was concerned with formulae which can be used to compute numerically the velocity field in the neighborhood of the particle during his derivation of equations of motion of the particle. This is our principal contribution to the subject. After a thorough check of Jeffery’s formulae, we coded software for modeling the flow around a rigid particle based on these equations. Examples of its applications are given in conclusion. A practical example is concerned with the simulation of sigmoidal inclusion trails in porphyroblast.
References:
[1] A. Einstein: Eine neue Bestimmung der Moleküldimensionen. Ann. Physik 19 (1906), 289–306, errata 34 (1911), 591–592.
[2] N. C. Gay: The motion of rigid particles embedded in a viscous fluid during pure shear deformation of the fluid. Tectonophysics 5 (1968), 81–88. DOI 10.1016/0040-1951(68)90082-6
[3] S. K. Ghosh, H. Ramberg: Reorientation of inclusions by combination of pure shear and simple shear. Tectonophysics 34 (1976), 1–70. DOI 10.1016/0040-1951(76)90176-1
[4] I. S. Gradshtein, I. M. Ryzhik: Table of Integrals, Series, and Products. 5th ed. Boston, Academic Press 1994. MR 1243179
[5] G. B. Jeffery: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. Roy. Soc. London Ser. A 102 (1922), 161–179.
[6] J. Ježek: Software for modeling the motion of rigid triaxial particles in viscous flow. Computers and Geosciences 20 (1994), 409–424. DOI 10.1016/0098-3004(94)90049-3
[7] J. Ježek, S. Saic, K. Segeth, K. Schulmann: Three-dimensional hydrodynamical modelling of viscous flow around a rotating ellipsoidal inclusion. Computers and Geosciences 25 (1999), 547–558. DOI 10.1016/S0098-3004(98)00165-4
[8] J. Ježek, K. Schulmann, K. Segeth: Fabric evolution of rigid inclusions during mixed coaxial and simple shear flows. Tectonophysics 257 (1996), 203–221. DOI 10.1016/0040-1951(95)00133-6
[9] T. Masuda, S. Mochizuki: Development of snowball structure: numerical simulation of inclusion trails during synkinematic porphyroblast growth in metamorphic rocks. Tectonophysics 170 (1989), 141–150. DOI 10.1016/0040-1951(89)90108-X
[10] W. H. Press et al.: Numerical Recipes. The Art of Scientific Computing. Cambridge, Cambridge University Press 1986. MR 0833288 | Zbl 1132.65001
[11] L. J. Reed, E. Tryggvason: Preferred orientations of rigid particles in a viscous matrix deformed by pure shear and simple shear. Tectonophysics 24 (1974), 85–98. DOI 10.1016/0040-1951(74)90131-0
[12] S. Wolfram: Mathematica. A System for Doing Mathematics by Computer. Reading, MA, Addison-Wesley 1993. Zbl 0925.65002
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