Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T09:55:44.690Z Has data issue: false hasContentIssue false
  • English
  • Français

The elastohydrodynamic collision of two spheres

Published online by Cambridge University Press:  21 April 2006

Robert H. Davis ,
Jean-Marc Serayssol  and
E. J. Hinch
Robert H. Davis
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80309
Jean-Marc Serayssol
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80309
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamic deformation of a solid elastic sphere which is immersed in a viscous fluid and in close motion toward another sphere or a plane solid surface is presented. The deformed shape of the solid surfaces and the pressure profile in the fluid layer separating these surfaces are determined simultaneously via asymptotic and numerical techniques. This research provides the first steps in establishing rational criteria for predicting whether a solid particle will stick or rebound subsequent to impact during filtration or coagulation when viscous forces are important.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 479 - 497
Copyright
© 1986 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

Abramowitz, M. & Stegun, I. A., (eds) 1964 Handbook of Mathematical Functions. US Govt. Printing Office, Washington.
Chen, J.-D. 1984 Effects of London van der Waals and electric double-layer forces on the thinning of a dimpled film between a small drop or bubble and a horizontal solid plane. J. Colloid Interface Sci. 98, 329.Google Scholar
Cooley, M. D. A. & O'Neill, M. E.1969 On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or a stationary sphere. Mathematika 16, 37.Google Scholar
Cox, R. E. & Brenner, H. 1967 The slow motion of a sphere through a viscous fluid towards a plane surface — II. Small gap widths, including inertial effects. Chem. Engng Sci. 22, 1753.Google Scholar
Dahneke, B. 1971 The capture of aerosol particles by surfaces. J. Colloid Interface Sci. 37, 342.Google Scholar
Dahneke, B. 1972 The influence of flattening on the adhesion of particles. J. Colloid Interface Sci. 40, 1.Google Scholar
Dahneke, B. 1973 Measurements of bouncing of small latex spheres. J. Colloid Interface Sci. 45, 584.Google Scholar
Davis, R. H. 1984 The rate of coagulation of a dilute polydisperse system of sedimenting spheres. J. Fluid Mech. 145, 179.Google Scholar
D'Ottavio, T. & Goren, S.1983 Aerosol capture in granular beds in the impaction dominated regime. Aerosol Sci. & Tech. 2, 91.Google Scholar
Ellenbecker, M. J., Lewith, D. & Price, J. M. 1980 Impaction and particle bounce at high Stokes numbers. J. Air Poll. Control Assoc. 30, 1224.Google Scholar
Esmen, N. A., Zeioler, P. & Whitfield, R. 1978 The adhesion of particles upon impact. J. Aerosol Sci. 9, 547.Google Scholar
Gal, E., Tardos, G. & Pfeffer, R. 1985 A study of inertial effects in granular bed filtration. AIChEJ J. 31, 1093.Google Scholar
Goldsmith, W. 1960 Impact. Edward Arnold.
Hocking, L. M. 1973 The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres. J. Engng Maths 7, 207.Google Scholar
Hughes, B. D. & White, L. R. 1979 Soft contact problems in linear elasticity. Q. J. Mech. Appl. Maths 32, 445.Google Scholar
Jain, R. K. & Ivanov, I. B. 1980 Thinning and rupture of shaped films. J. Chem. Soc. Faraday Trans. II 76, 250.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Theory of Elasticity, 1st English edn. Pergamon.
Lawrence, C. J., Kuang, Y. & Weinbaum, S. 1985 The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 2. Boundary layer and exact numerical solutions. J. Fluid Mech. 156, 479.Google Scholar
Lawrence, C. J. & Weinbaum, S. 1985 Hydrodynamic arrest of a flat body moving towards a paralel surface of arbitrary Reynolds number. J. Fluid Mech. (submitted).Google Scholar
LoUffler, F. 1980 Problems and recent advances in aerosol filtration. Sep. Sci. Technol. 15, 297.Google Scholar
Love, A. E. H. 1927 A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover.
Melik, D. S. & Fogler, H. S. 1984 Gravity-induced flocculation. J. Colloid Interface Sci. 101, 72.Google Scholar
Muller, V. M., Yushchenko, V. S. & Derjaguin, B. V. 1983 General theoretical consideration of the influence of surface forces on contact deformations and the reciprocal adhesion of elastic spherical particles. J. Colloid Interface Sci. 92, 92.Google Scholar
Payatakes, A. C. & Gradon, L. 1980 Dendritic deposition of aerosol particles in fibrous media by inertial impaction and interception. Chem. Engng Sci. 35, 1083.Google Scholar
Prodi, F. & Tampieri, F. 1982 The removal of particulate matter from the atmosphere: the physical mechanisms. PAOEOPH 120, 286.Google Scholar
Pruppacher, H. R. & Klett, J. D. 1978 Microphysics of Clouds and Precipitation. Reidel.
Schowalter, W. R. 1984 Stability and coagulation of colloids in shear fields. Ann. Rev. Fluid Mech. 16, 245.Google Scholar
Serayssol, J.-M. 1985 Dynamic deformation and rebound of particles during filtration and coagulation. M.S. thesis, University of Colorado, Boulder, Colorado.
Serayssol, J.-M. & Davis, R. H. 1985 The influence of surface interactions on the elastohydro- dynamic collision of two spheres. J. Colloid Interface Sci. (submitted).Google Scholar
Tabdos, G. I., Yu, E., Pfeffer, R. & Squires, A. M. 1979 Experiments on aerosol filtration in granular sand beds. J. Colloid Interface Sci. 71, 616.Google Scholar
Tien, C. & Payatakes, A. C. 1979 Advances in deep bed filtration. AIChE J. 25, 737.Google Scholar
Tsiang, R. C., Wang, C.-S. & Tien, C. 1982 Dynamics of particle deposition in model filter fibers. Chem. Engng Sci. 37, 1661.Google Scholar
Weinbaum, S., Lawrence, C. J. & Kuang, Y. 1985 The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 1. Analytic solutions; inviscid and small– but finite-Reynolds-number limits. J. Fluid Mech. 156, 463.Google Scholar