- Access by Xinjiang University
Aggregation of frictional particles due to capillary attraction
Phys. Rev. E 83, 051403 – Published 23 May, 2011
DOI: https://doi.org/10.1103/PhysRevE.83.051403
Abstract
Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster—the lowest-energy state—depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.
Article Text
References (22)
- M. M. Nicolson, Proc. Cambridge Philos. Soc. 45, 288 (1949).
- D. Vella and L. Mahadevan, Am. J. Phys. 98, 817 (2005).
- P. Singh, D. Joseph, and N. Aubry, Soft Matter 6, 4310 (2010).
- S. Gart, D. Vella, and S. Jung, Soft Matter 7, 2444 (2011).
- N. Bowden, A. Terfort, J. Carbeck, and G. Whitesides, Science 276, 233 (1997).
- C. Allain and M. Cloitre, Fractals in Physics (Elsevier/North-Holland, Amsterdam, 1986), pp. 283–285.
- M. Berhanu and A. Kudrolli, Phys. Rev. Lett. 105, 098002 (2010).
- J. H. Poynting and J. J. Thompson, A Text-book of Physics: Vol. 1, Properties of Matter (Griffith & Co., London, 1913).
- D. Y. C. Chan, J. J. D. Henry, and L. R. White, J. Colloid Interface Sci. 49, 410 (1981).
- P. Kralchevsky, V. Paunov, I. Ivanov, and K. Nagayama, J. Colloid Interface Sci. 151, 79 (1991).
- P. Kralchevsky, N. Denkov, V. Paunov, O. Velev, I. Ivanov, H. Yoshimura, and K. Nagayama, J. Phys.: Condens. Matter 6, A395 (1994).
- V. Paunov, P. Kralchevsky, N. Denkov, and K. Nagayama, J. Colloid Interface Sci. 157, 100 (1993).
- P. Singh and D. Joseph, J. Fluid Mech. 530, 31 (2005).
- O. Velev, N. Denkov, V. Paunov, P. Kralchevsky, and K. Nagayama, Langmuir 9, 3702 (1993).
- C. Dushkin, P. Kralchevsky, V. Paunov, H. Yoshimura, and K. Nagayama, Langmuir 12, 641 (1996).
- F. M. N. Vassileva, D. van den Ende, and J. Mellema, Langmuir 21, 11190 (2005).
- C. Camoin, J. F. Roussel, R. Faure, and R. Blanc, Europhys. Lett. 3, 449 (1987).
- C. Allain and M. Cloitre, J. Colloid Interface Sci. 157, 261 (1992).
- G. K. Batchelor, J. Fluid Mech. 74, 1 (1976).
- G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375 (1972).
- G. P. Association, Physical Properties of Glycerine and Its Solutions (G. P. Association, New York, 1963).
- K. Ludema, Friction, Wear, Lubrication: A Textbook in Tribology (CRC Press, Boca Raton, FL, 1996).