Abstract
Today's practice of interpreting Hg capillary pressure curves — a widespread method in porosimetry — is generally unsatisfactory. This has already been demonstrated by Fatt. First, the saturation branch of such a curve is interpreted using the concept of a pore space model in which essential features of a network structure are disregarded. Second, the data provided by the desaturation branch are not used. Distributions of radii of capillaries within porous materials derived by this technique are usually incorrect in that the frequencies of occurrence of the greater radii turn out too small, those of the smaller radii too large.
We present a more reliable approach which constrains radii frequency ranges for the Hg saturated pore space and for both the part of the pore space that desaturates and the part that traps mercury when Hg pressure is released. The pore space may be of an arbitrary geometrical structure, the radii distribution may be continuous. Also, the Hg desaturation may enable one to distinguish experimentally between structural and contact angle hysteresis.
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Abbreviations
- a :
-
actual cross-section of a capillary
- a″:
-
hydrostatic equivalent circular crosssection of a capillary
- c :
-
circumference ofa
- des:
-
desaturation process, index
- i :
-
index denoting radii, radii numbers, and radii frequencies
- j :
-
number of saturated capillaries
- k :
-
upper boundary fori
- k″, k 0 ″ :
-
(mean) hydrostatic shape factor of the capillary cross-section
- T, δl :
-
mean capillary lengths
- n i :
-
number of radii of sizer i
- p c s :
-
capillary pressure of capillaries with radiusr s
- (-) δp c s :
-
difference in capillary pressure between capillaries with radiusr s ,r s-1
- \(p_j^{n_i } \) :
-
(Hg/vacuum) path probability
- r i :
-
capillary radius
- r″:
-
radius ofa″
- s :
-
index denoting the state of the capillary pressure experiment
- sat:
-
satuation process, index
- BCT:
-
bundle of capillary tubes model
- CTM:
-
chain-type model
- D:
-
dimensional
- Hg:
-
mercury
- M :
-
number of meshes within a network
- M s :
-
measured value
- N :
-
number of capillaries (radii) in a network
- N b :
-
number of border capillaries of a network in direct contact with the external Hg reservoir
- N i :
-
number of capillaries inside a network without direct contact with the external Hg reservoir
- NS:
-
network structure
- P:
-
point of intersection (indicated by ‘sat’ or ‘des’)
- ℝk :
-
k-D space of representation
- RD:
-
radii distribution
- RP:
-
radii placement
- S :
-
number of nodes (sites) within a network
- SHN:
-
single hexagonal network model
- SMN:
-
square mesh network model
- V,\(\bar V\) :
-
measured (expected) network volume during saturation or desaturation, respectively (indicated by ‘Hg’, ‘sat’, ‘2’, or ‘des’)
- V por :
-
pore volume of a network or a porous material
- Β :
-
network constant
- ε :
-
network constant (mesh density)
- η :
-
network constant (node density)
- σ :
-
surface tension of mercury
- θ:
-
contact angle of mercury
- σ,\(\bar \Sigma \) :
-
(expected) saturation/desaturation belonging toV (\(\bar V\))
- 2:
-
index denoting vacuum
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Jonas, M., Schopper, J.R. The radii inversion problem associated with the Hg capillary pressure experiment. Transp Porous Med 14, 33–72 (1994). https://doi.org/10.1007/BF00617027
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DOI: https://doi.org/10.1007/BF00617027