Time-dependent drop deformation in a rotating high viscosity fluid
Authors:
H. A. Stone and J. W. M. Bush
Journal:
Quart. Appl. Math. 54 (1996), 551-556
MSC:
Primary 76U05; Secondary 76D45
DOI:
https://doi.org/10.1090/qam/1402409
MathSciNet review:
MR1402409
Full-text PDF Free Access
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Abstract: An exact solution is presented which describes the time-dependent deformation of a nearly spherical drop suspended on the rotation axis of a more dense rotating viscous fluid. The solution is demonstrated to be similar, though not identical, to that derived from the commonly invoked assumption that the external flow field is purely extensional.
R. G. Cox, The deformation of a drop in a general time-dependent fluid flow, J. Fluid Mech. 37, 601–623 (1969)
D. A. Edwards, H. Brenner, and D. T. Wasan, Interfacial Transport Processes and Rheology, Butterworth-Heinemann, Boston, 1991
H. P. Greenspan, The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1968
E. J. Hinch, Hydrodynamics at low Reynolds numbers, in A Brief and Elementary Introduction: Disorder and Mixing (Eds. E. Guyon, J. P. Nadal and Y. Pomeau), NATO ASI Series, Series E, 152: 43–55 (1988)
J. C. Hsu and R. W. Flumerfelt, Rheological applications of a drop elongation experiment, Trans. Soc. Rheol. 19, 523–540 (1975)
H. H. Hu and D. D. Joseph, Evolution of a liquid drop in a spinning drop tensiometer, J. Colloid and Interface Sci. 162, 331–339 (1994)
D. D. Joseph, M. S. Arney, G. Gillberg, H. Hu, D. Hultman, C. Verdier, and T. M. Vinagre, A spinning drop tensioextensometer, J. Rheology 36, 621–662 (1992)
L. G. Leal, Laminar Flow and Convective Transport Processes, Butterworth-Heinemann, Boston, 1990
A. Nadim and H. A. Stone, The motion of small particles and droplets in quadratic flows, Stud. Appl. Math. 85, 53–73 (1991)
J. M. Rallison, The deformation of small viscous drops and bubbles in shear flows, Ann. Rev. Fluid Mech. 16, 45–66 (1984)
D. K. Rosenthal, The shape and stability of a bubble at the axis of a rotating liquid, J. Fluid Mech. 12, 358–366 (1962)
B. Vonnegut, Rotating bubble method for the determination of surface and interfacial tension, Rev. Sci. Instr. 13, 6–9 (1942)
R. G. Cox, The deformation of a drop in a general time-dependent fluid flow, J. Fluid Mech. 37, 601–623 (1969)
D. A. Edwards, H. Brenner, and D. T. Wasan, Interfacial Transport Processes and Rheology, Butterworth-Heinemann, Boston, 1991
H. P. Greenspan, The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1968
E. J. Hinch, Hydrodynamics at low Reynolds numbers, in A Brief and Elementary Introduction: Disorder and Mixing (Eds. E. Guyon, J. P. Nadal and Y. Pomeau), NATO ASI Series, Series E, 152: 43–55 (1988)
J. C. Hsu and R. W. Flumerfelt, Rheological applications of a drop elongation experiment, Trans. Soc. Rheol. 19, 523–540 (1975)
H. H. Hu and D. D. Joseph, Evolution of a liquid drop in a spinning drop tensiometer, J. Colloid and Interface Sci. 162, 331–339 (1994)
D. D. Joseph, M. S. Arney, G. Gillberg, H. Hu, D. Hultman, C. Verdier, and T. M. Vinagre, A spinning drop tensioextensometer, J. Rheology 36, 621–662 (1992)
L. G. Leal, Laminar Flow and Convective Transport Processes, Butterworth-Heinemann, Boston, 1990
A. Nadim and H. A. Stone, The motion of small particles and droplets in quadratic flows, Stud. Appl. Math. 85, 53–73 (1991)
J. M. Rallison, The deformation of small viscous drops and bubbles in shear flows, Ann. Rev. Fluid Mech. 16, 45–66 (1984)
D. K. Rosenthal, The shape and stability of a bubble at the axis of a rotating liquid, J. Fluid Mech. 12, 358–366 (1962)
B. Vonnegut, Rotating bubble method for the determination of surface and interfacial tension, Rev. Sci. Instr. 13, 6–9 (1942)
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Article copyright:
© Copyright 1996
American Mathematical Society
