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Source-like Solution for Radial Imbibition into a Homogeneous Semi-infinite Porous Medium
  • Junfeng Xiao, Columbia University
  • Howard A. Stone, Princeton University
  • Daniel Attinger, Iowa State University
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We describe the imbibition process from a point source into a homogeneous semi-infinite porous material. When body forces are negligible, the advance of the wetting front is driven by capillary pressure and resisted by viscous forces. With the assumption that the wetting front assumes a hemispherical shape, our analytical results show that the absorbed volume flow rate is approximately constant with respect to time, and that the radius of the wetting evolves in time as r ≈ t1/3. This cube-root law for the long-time dynamics is confirmed by experiments using a packed cell of glass microspheres with average diameter of 42 μm. This result complements the classical one-dimensional imbibition result where the imbibition length ≈ t1/2, and studies in axisymmetric porous cones with small opening angles where ≈t1/4 at long times.

Reprinted with permission from Langmuir 28 (2012): 4208–4212, doi:10.1021/la204474f. Copyright 2012 American Chemical Society.

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American Chemical Society
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Junfeng Xiao, Howard A. Stone and Daniel Attinger. "Source-like Solution for Radial Imbibition into a Homogeneous Semi-infinite Porous Medium" Langmuir Vol. 28 Iss. 9 (2012) p. 4208 - 4212
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