The friction of a mesh-like super-hydrophobic surface
When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic s...
When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic s...
A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence
Our work focuses on the sweep-stick mechanism of particle clustering in turbulent flows introduced by Chen et al. [L. Chen, S. Goto, and J. C. Vassilicos, “Turbulent clustering of stagnation poi...
Our work focuses on the sweep-stick mechanism of particle clustering in turbulent flows introduced by Chen et al. [L. Chen, S. Goto, and J. C. Vassilicos, “Turbulent clustering of stagnation poi...
Optimal shapes for best draining
Phys. Fluids 21, 113102 (2009); doi:10.1063/1.3262844
Published 4 November 2009
You are not logged in to this journal. Log in
The container shape that minimizes the volume of draining fluid remaining on the walls of the container after it has been emptied from its base is determined. The film of draining fluid is assumed to wet the walls of the container, and is sufficiently thin so that its curvature may be neglected. Surface tension is ignored. The initial value problem for the thickness of a film of Newtonian fluid is studied, and is shown to lead asymptotically to a similarity solution. From this, and from equivalent solutions for power-law fluids, the volume of the residual film is determined. The optimal container shape is not far from hemispherical, to minimize the surface area, but has a conical base to promote draining. The optimal shape for an axisymmetric mixing vessel, with a hole at the center of its base for draining, is also optimal when inverted in the manner of a washed wine glass inverted and left to drain.
©2009 American Institute of Physics
| History: | Received 4 August 2009; accepted 16 October 2009; published 4 November 2009 |
| Permalink: |
http://link.aip.org/link/?PHFLE6/21/113102/1 |
Connotea
CiteULike
del.icio.us
BibSonomy
REFERENCES (11)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- J. H. Snoeijer, J. Ziegler, B. Andreotti, M. Fermigier, and J. Eggers, “Thick films of viscous fluid coating a plate withdrawn from a liquid reservoir,” Phys. Rev. Lett. 100, 244502 (2008).
- D. Quéré, “Fluid coating on a fiber,”
Annu. Rev. Fluid Mech. 31, 347 (1999) . - B. T. Lubin and G. S. Springer, “The formation of a dip on the surface of a liquid draining from a tank,”
J. Fluid Mech. 29, 385 (1967) . - C. Y. Chow and W. M. Lai, “Unsteady axisymmetric flows of a liquid draining from a circular tank,”
AIAA J. 10, 1032 (1972) . - Q. N. Zhou and W. P. Graebel, “Axisymmetrical draining of a cylindrical tank with a free surface,”
J. Fluid Mech. 221, 511 (1990) . - B. Mohammadi and O. Pironneau, “Shape optimization in fluid mechanics,”
Annu. Rev. Fluid Mech. 36, 255 (2004) . - J. M. Bourot, “On the numerical computation of the optimum profile in Stokes flow,”
J. Fluid Mech. 65, 513 (1974) . - O. Pironneau, “Optimum design in fluid mechanics,”
J. Fluid Mech. 64, 97 (1974) . - M. Roper, T. M. Squires, and M. P. Brenner, “Symmetry unbreaking in the shapes of perfect projectiles,” Phys. Fluids 20, 093606 (2008).
- A. Saint-Jalmes, M. U. Vera, and D. J. Durian, “Free drainage of aqueous foams: Container shape effects on capillarity and vertical gradients,”
Europhys. Lett. 50, 695 (2000) . - T. B. Benjamin, “Wave formation in laminar flow down an inclined plane,”
J. Fluid Mech. 2, 554 (1957) .
