Physical Theory for Capillary Flow Phenomena

@article{Miller1956PhysicalTF,
  title={Physical Theory for Capillary Flow Phenomena},
  author={Edward E. Miller and R. D. Miller},
  journal={Journal of Applied Physics},
  year={1956},
  volume={27},
  pages={324-332}
}
From the assumption that the microscopic behavior of the liquid in an unsaturated porous medium is controlled by the physical laws of surface tension and viscous flow, differential equations governing the macroscopic flow in such a medium are deduced. No special pore‐shape assumptions are required, but one topological approximation is needed; i.e., that neither isolated drops nor isolated bubbles occur. Several nonessential simplifying assumptions are used; i.e., that the macroscopic properties… 

Figures from this paper

Macroscopic equations for flow in unsaturated porous media
This dissertation describes averaging of microscale flow equations to obtain a consistent description of liquid flow in unsaturated porous media on the macroscale. It introduces a new method of
Steady State Flow in an Unsaturated, Two-Dimensional, Macroscopically Homogeneous, Miller-Similar Medium
The influence of microscopic heterogeneity on flow through a macroscopically homogeneous, variably saturated medium is studied by numerical simulations in a two-dimensional, Miller-similar medium. As
Transport of conservative chemical through an unsaturated two‐dimensional Miller‐similar medium with steady state flow
Numerical simulation of water flow in a two-dimensional, macroscopically homogeneous, Miller-similar medium showed the existence of a network of flow channels with two complementary states separated
Pore-scale considerations of the air-water interface or rough surface on flow in porous media
Understanding flow in porous media is a challenging problem in many fields of fundamental science and engineering. This dissertation focuses on flow behavior at the pore scale, including observation
Penetration and Displacement in Capillary Systems
Spontaneous capillary penetration of a liquid into pore spaces filled with a fluid is a flow driven by interfacial pressure differences. The magnitude of the pressure difference across each
Similarity Hypothesis for Capillary Hysteresis in Porous Materials
A quantitative description of the capillary hysteresis properties of a porous material is developed through bivariate distribution density function ƒ(α, β), where α and β are wetting and drying
Relative permeabilities from two- and three-dimensional pore-scale network modelling
We present a computer study of two-phase flow in a porous medium. The porous medium is represented by an isotropic network of up to 80 000 randomly placed nodes connected by thin tubes. We then
The difference between semi-continuum model and Richards’ equation for unsaturated porous media flow
Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach
Investigation of representing hysteresis in macroscopic models of two‐phase flow in porous media using intermediate scale experimental data
Incorporating hysteresis into models is important to accurately capture the two phase flow behavior when porous media systems undergo cycles of drainage and imbibition such as in the cases of
...
...

References

SHOWING 1-4 OF 4 REFERENCES
Capillary conduction of liquids through porous mediums
The flow of liquids in unsaturated porous mediums follows the ordinary laws of hydrodynamics, the motion being produced by gravity and the pressure gradient force acting in the liquid. By making use
Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith
  • W. Haines
  • Geology
    The Journal of Agricultural Science
  • 1930
A recapitulation of the main features of the moisture distribution in an ideal soil is given in order to emphasise a point previously neglected, namely, that the changes are not in the main strictly