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A singularity method for calculating hydrodynamic forces and particle velocities in low-Reynolds-number flows

Published online by Cambridge University Press:  20 April 2006

T. Dabroś
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Abstract

A numerical technique is presented which allows one to estimate hydrodynamic forces and torques or translational and angular velocities of particles in a general flow field. Particle–solid wall interactions can be readily included. The base functions used in the technique presented are singular fundamental solutions of the Stokes equation for a point force and a point force and a point source. The least-square approach is used preferentially in order to find the intensities of these singularities. Test calculations show that the results are self-consistent and in fairly good agreement with the exact solutions in a wide range of conditions. For example, for a spherical particle moving with no slip towards the solid wall, it has been shown that the method can provide good estimates of the resistance coefficient up to separations of the order of 5% of the particle radius. We believe that better agreement, for smaller separations, is within reach at the expense of increased computer costs. For spheroidal particles good results were obtained for aspect ratio in the range 0.5–2.0.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 156 , July 1985 , pp. 1 - 21
Copyright
© 1985 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Washington.
Aderogba, K. 1976 J. Engng Maths 10, 143.
Barrodale, I. & Phillips, C. 1975 A.C.M. Trans. Math. Softw. 1, 264.
Barrodale, I. & Roberts, F. D. K. 1980 A.C.M. Trans. Math. Softw. 6, 231.
Batchelor, G. K. 1970 J. Fluid Mech. 44, 419.
Blake, J. R. 1971 Proc. Camb. Phil. Soc. 70, 303.
Blake, J. R. & Chwang, A. T. 1974 J. Engng Maths 8, 23.
Brenner, H. 1961 Chem. Engng Sci. 16, 242.
Burgers, J. M. 1938 Second Report on Viscosity and Plasticity. North Holland.
Chwang, A. T. 1975 J. Fluid Mech. 72, 17.
Chwang, A. T. & Wu, T. Y. 1974 J. Fluid Mech. 63, 607.
Chwang, A. T. & Wu, T. Y. 1975 J. Fluid Mech. 67, 787.
Cox, R. G. 1970 J. Fluid Mech. 44, 791.
Cox, R. G. & Brenner, H. 1967 J. Fluid Mech. 28, 391.
Dagan, Z., Weinbaum, S. & Pfeffer, R. 1982a J. Fluid Mech. 115, 505.
Dagan, Z., Weinbaum, S. & Pfeffer, R. 1982b J. Fluid Mech. 117, 143.
Gantos, P., Pfeffer, R. & Weinbaum, S. 1978 J. Fluid Mech. 84, 79.
Gantos, P., Weinbaum, S. & Pfeffer, R. 1980 J. Fluid Mech. 99, 739.
Gluckman, M. J., Pfeffer, R. & Weinbaum, S. 1971 J. Fluid Mech. 50, 705.
Gluckman, M. J., Weinbaum, S. & Pfeffer, R. 1972 J. Fluid Mech. 55, 677.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 Chem. Engng Sci. 22, 653.
Goren, S. L. & O'Neill, M. E.1971 Chem. Engng Sci. 26, 325.
Horvath, H. 1974 Staub 34, 251.
Lamb, H. 1953 Hydrodynamics (6th edn). Cambridge University Press.
Lawson, C. L. & Hanson, R. J. 1974 Solving Least Squares Problems. Prentice-Hall.
Leichtberg, S., Weinbaum, S. & Pfeffer, R. 1976 Biorheology 13, 165.
Liron, N. 1978 J. Fluid Mech. 86, 705.
Liron, N. & Mochon, S. 1976a J. Engng Maths 10, 287.
Liron, N. & Mochon, S. 1976b J. Fluid Mech. 75, 593.
Maude, A. D. 1961 Brit. J. Appl. Phys. 12, 293.
Rallison, J. M. & Acrivos, A. 1978 J. Fluid Mech. 89, 191.
Russell, W. B., Hinch, E. J., Leal, L. G. & Tieffenbruck, G. 1977 J. Fluid Mech. 83, 273.
Stimson, M. & Jeffery, G. B. 1926 Proc. R. Soc. Lond. A 111, 110.
Stokes, G. G. 1851 Trans. Camb. Phil. Soc. 9, 8.
Tam, C. K. W. 1969 J. Fluid Mech. 38, 537.
Youngren, G. K. & Acrivos, A. 1975 J. Fluid Mech. 69, 377.