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Gravity Effects in Diffusive Coarsening of Bubble Lattices: von Neumann's Lawvon Neumann modelled the evolution of two-dimensional soap froths as a purely diffusive phenomenon; the area growth of a given cell was found to depend only on the geometry of the bubble lattice. In the model, hexagons are stable, pentagons shrink and heptagons grow. The simplest equivalent to the area growth law is / approximately t(sub beta). The result depends on assuming (1) an incompressible gas; (2) bubble walls which meet at 120 deg and (3) constant wall thickness and curvature. Each assumption is borne out in experiments except the last one: bubble wall thickness between connecting cells varies in unit gravity because of gravity drainage. The bottom part of the soap membrane is thickened, the top part is thinned, such that gas diffusion across the membrane shows a complex dependence on gravity. As a result, experimental tests of von Neumann's law have been influenced by effects of gravity; fluid behavior along cell borders can give non-uniform wall thicknesses and thus alter the effective area and gas diffusion rates between adjacent bubbles. For area plotted as a function of time, Glazier (J.A. Glazier, S.P. Gross, and I. Stavans, Phys. Rev. A. 36, 306 (1987); J. Stavans, J.A, Glazier, Phys. Rev. Lett. 62, 1318 (1989).) suggest that in some cases their failure to observe von Neumann's predicted growth exponent ((sup beta)theor(sup =1; beta)exp(sup =0.70 + 0.10)) may have been the result of such "fluid drainage onto the lower glass plate". Additional experiments which varied plate spacing gave different beta exponents in a fashion consistent with this suggestion. During preliminary long duration experiments (approximately 100 h) aboard Spacelab-J, a low-gravity test of froth coarsening has examined (1) power law scaling of von Neumann's law (beta values) in the appropriate diffusive limits; (2) new bubble lattice dynamics such as greater fluid wetting behavior on froth membranes in low gravity; and (3) explicit relations for the gravity dependence of the second moment (or disorder parameter) governing the geometric spread in cell-sidedness around the mean of perfect hexagonal filling. By reducing the gravity-induced distortion in lattice wall thickness, the diffusion-limited regime of bubble coarsening becomes available for performing critical tests of network dynamics.
Document ID
19990079361
Acquisition Source
Marshall Space Flight Center
Document Type
Reprint (Version printed in journal)
Authors
Noever, David A.
(NASA Marshall Space Flight Center Huntsville, AL United States)
Date Acquired
August 19, 2013
Publication Date
January 1, 2000
Subject Category
Fluid Mechanics And Heat Transfer
Meeting Information
Meeting: Aerospace Sciences
Location: Reno, NV
Country: United States
Start Date: January 11, 2000
End Date: January 14, 2000
Sponsors: American Inst. of Aeronautics and Astronautics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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