Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T07:35:07.694Z Has data issue: false hasContentIssue false

The motion of a deformable drop in a second-order fluid

Published online by Cambridge University Press:  19 April 2006

P. C.-H. Chan
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, 91125
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, 91125

Abstract

The cross-stream migration of a deformable drop in a unidirectional shear flow of a second-order fluid is considered. Expressions for the particle velocity due to the separate effects of deformation and viscoelastic rheology are obtained. The direction and magnitude of migration are calculated for the particular cases of Poiseuille flow and simple shear flow and compared with experimental data.

Type
Research Article
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beavers, G. S. & Joseph, D. D. 1975 J. Fluid Mech. 69, 475.
Bretherton, F. P. 1962 J. Fluid Mech. 14, 284.
Brodnyan, J. G., Gaskins, F. H. & Philippoff, W. 1957 Trans. Soc. Rheol. 1, 109.
Brunn, P. 1976 Rheol. Acta 15, 589.
Chaffey, C. E., Brenner, H. & Mason, S. G. 1965 Rheol. Acta 4, 64.
Chaffey, C. E., Brenner, H. & Mason, S. G. 1967 Rheol. Acta 6, 100.
Chan, P. C.-H. 1979 Ph.D. thesis, California Institute of Technology.
Chan, P. C.-H. & Leal, L. G. 1977 J. Fluid Mech. 82, 549.
Cox, R. G. & Brenner, H. 1968 Chem. Engng Sci. 23, 147.
Frankel, N. A. & Acrivos, A. 1970 J. Fluid Mech. 44, 65.
Gauthier, F., Goldsmith, H. L. & Mason, S. G. 1971a Rheol. Acta 10, 344.
Gauthier, F., Goldsmith, H. L. & Mason, S. G. 1971b Trans. Soc. Rheol. 15, 297.
Goldsmith, H. L. & Mason, S. G. 1962 J. Colloid Sci. 17, 448.
Haber, S. & Hetsroni, G. 1971 J. Fluid Mech. 49, 257.
Hadamard, J. 1911 C. R. Acad. Sci. Paris 152, 1735.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.
Ho, B. P. & Leal, L. G. 1974 J. Fluid Mech. 65, 365.
Ho, B. P. & Leal, L. G. 1976 J. Fluid Mech. 76, 783.
Karnis, A. & Mason, S. G. 1966 Trans. Soc. Rheol. 10, 571.
Karnis, A. & Mason, S. G. 1967 J. Colloid Sci. 24, 164.
Leal, L. G. 1975 J. Fluid Mech. 69, 305.
Peery, J. H. 1966 Ph.D. thesis, Princeton University.
Rybczynski, W. 1911 Bull. Akad. Sci. de Cracovie, A 40.
Taylor, G. I. 1932 Proc. Roy. Soc. (London) A 138, 41.
Taylor, G. I. 1934 Proc. Roy. Soc. (London) A 146, 501.
Wohl, P. R. 1976 Adv. Engng Sci., N.A.S.A. CP-2001. 4, 1493.
Wohl, P. R. & Rubinow, S. I. 1974 J. Fluid Mech. 62, 185.