Effects of viscosity ratio and three dimensional positioning on hydrodynamic interactions between two viscous drops in a shear flow at finite inertia
Drops driven toward each other by shear at finite inertia follow two distinct types of trajectories. Type I trajectory is similar to the one in Stokes flow where drops slide past each other. However, ...
Drops driven toward each other by shear at finite inertia follow two distinct types of trajectories. Type I trajectory is similar to the one in Stokes flow where drops slide past each other. However, ...
Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency
A sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor. A plate oscillating in the normal direction to...
A sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor. A plate oscillating in the normal direction to...
Sedimentation of a sphere in a fluid channel
Phys. Fluids 21, 103304 (2009); doi:10.1063/1.3253408
Published 26 October 2009
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We studied both experimentally and numerically the sedimentation velocity of small solid particles through liquid channels merging at the intersection of three soap films. The wall mobility induces a nontrivial behavior for the particle drag coefficient, providing particular transport properties that are not observed for channels with rigid walls. It is shown that for sufficiently small particles, slow and fast motions are observed for the particle along the channel, depending on the particle position within the channel cross section and the sphere/channel size ratio. The velocity corresponding to fast motions can be as high as twice the Stokes velocity in an unbounded fluid. Moreover, the fast motions are not observed anymore when the size ratio exceeds a critical value, which has been found to be approximately equal to 0.5. As another major difference with the solid wall channel, the sphere velocity does not vanish when the size ratio reaches unity. Instead, the smallest value is found to be 
of the Stokes velocity.
©2009 American Institute of Physics
| History: | Received 11 March 2009; accepted 21 September 2009; published 26 October 2009 |
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http://link.aip.org/link/?PHFLE6/21/103304/1 |
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- G. G. Stokes, “On the effect of the internal friction of fluids on the motion of pendulums,” Trans. Cambridge Philos. Soc. 9, 8 (1851).
- J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics, 2nd ed. (Noordhoof, Leiden, 1973).
- A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall. I. Motion through a quiescent fluid,”
Chem. Eng. Sci. 22, 637 (1967) . - M. E. Staben, A. Z. Zinchenko, and R. H. Davis, “Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow,” Phys. Fluids 15, 1711 (2003)
- M. E. Staben and R. H. Davis, “Particle transport in Poiseuille flow in narrow channels,”
Int. J. Multiphase Flow 31, 529 (2005) . - A. Miyamura, S. Iwasaki, and T. Ishii, “Experimental wall correction factors of single solid spheres in triangular and square cylinders and parallel plates,”
Int. J. Multiphase Flow 7, 41 (1981) . - R. P. Chhabra, “Wall effect on free-settling velocity of nonspherical particles in viscous media in cylindrical tubes,”
Powder Technol. 85, 83 (1995) . - J. Ou, B. Perot, and J. P. Rothstein, “Laminar drag reduction in microchannels using ultrahydrophobic surfaces,” Phys. Fluids 16, 4635 (2004).
- J. Hyväluoma and J. Harting, “Slip flow over structured surfaces with entrapped microbubbles,” Phys. Rev. Lett. 100, 246001 (2008).
- S. A. Koehler, S. Hilgenfeldt, E. R. Weeks, and H. A. Stone, “Drainage of single Plateau borders: Direct observation of rigid and mobile interfaces,” Phys. Rev. E 66, 040601 (2002).
- O. Pitois, C. Fritz, and M. Vignes-Adler, “Liquid drainage through aqueous foam: Study of the flow on the bubble scale,”
J. Colloid Interface Sci. 282, 458 (2005) . - J. Sur and H. K. Pak, “Capillary force on colloidal particles in a freely suspended liquid thin film,” Phys. Rev. Lett. 86, 4326 (2001).
- H. A. Stone, A. D. Stroock, and A. Ajdari, “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip,”
Annu. Rev. Fluid Mech. 36, 381 (2004) . - S. J. Neethling and J. J. Cilliers, “Modeling flotation froths,”
Int. J. Min. Process. 72, 267 (2003) . - F. Rouyer, private communication (2009).
- S. H. Lee and L. G. Leal, “Motion of a sphere in the presence of a plane interface. Part II. An exact solution in bipolar coordinates,”
J. Fluid Mech. 98, 193 (1980) . - K. D. Danov, R. Aust, F. Durst, and U. Lange, “Slow motions of a solid spherical particle close to a viscous interface,”
Int. J. Multiphase Flow 21, 1169 (1995) . - A. V. Nguyen and G. M. Evans, “Movement of fine particles on an air bubble surface studied using high-speed video microscopy,”
J. Colloid Interface Sci. 273, 262 (2004) . - K. D. Danov, R. Aust, F. Durst, and U. Lange, “Influence of the surface viscosity on the drag and torque coefficients of a solid particle in a thin liquid layer,”
Chem. Eng. Sci. 50, 263 (1995) .
