On Modeling Mercury Intrusion
Effects in Pores of Axial Symmetry and
Attenuated Cross-Section
Isaac Kornhauser, Carlos Felipe, Marcos Esparza,
Armando Domínguez, Fernando Rojas
Departamento de Química
Universidad Autónoma MetropolitanaIztapalapa, México
Centro Interdisciplinario Sobre
Medio Ambiente y Desarrollo,
Instituto Politécnico Nacional, México
ÁREA DE FISICOQUÍMICA DE
SUPERFICIES
The Original Ideas of this Work are those of the Late Professor Vicente Mayagoitia: Physical Chemistry
of Surfaces Area, Department of Chemistry, Universidad Autónoma Metropolitana,-Iztapalapa, Mexico
Main goals of this study are:
1) The influence of the pore wall angle of
inclination on the intrusion pressure and
radius of curvature of the liquid-vapor
interface
2) The occurrence of jump-like Hg Penetration
in circular pores of attenuated cross-section
(3) The existence of a snap-off mechanism
during Hg intrusion depending on the kind of
structure
Mayan Observatory
Chichen Itzá, Yucatán, México
Área de Fisicoquímica de
Superficies
Simulation of Hg intrusion. Canthotaxis effect
Washburn equation:
Snap-off is assumed to happen in the smallest
bonds if the two extremes of these throats are
connected through continuous liquid paths to
the external Hg supply
Fisicoquímica de Superficies
Cebeci equation:
The pore wall angle of inclination, , is given in terms of
the slope of the line tangent to the pore wall (i.e. ∂R/ ∂ X) at p
X as:
  2  tan (dR / dX )
1
  tan1 (dR / dX )
 dR / dX  0
 dR / dX  0
The Washburn equation taking into account the
inclination of the pore wall can be written as:
P  2 cos / R
lv
V  V1  V2
X
2
R
0
V1    R 2 dX  

2
(1  A)
0
Circular Pore Shapes with Attenuated Cross-Section
R / nm
R / nm
100
Structure 1
100
0
-100
Structure 2
0
-100
0
100
200
300
400
0
500
100
Structure 3
100
R / nm
R /nm
300
400
500
X/ nm
X / nm
100
200
0
Structure 4
0
-100
-100
0
100
200
300
X / nm
Axial Pore Modeling
400
500
0
100
200
300
400
500
X / nm
R=R0 exp(BX)[1+cos2(NX)]/(1+A)

The Laplace stability condition can be written as:
 (P / V )T  (P / Vp )T  0
Parameters of Circular Functions with Attenuated
Cross-section for the Simulation of Axially Symmetric
Pore Entities
Structure
R0 × 10-2/nm
A
B ×103/nm- N ×102/nm-1
1
1
1.0
0.2
-1.0
1.0
2
1.0
0.2
-1.0
2.5
3
1.0
2.0
-1.0
1.0
4
1.0
2.0
-1.0
2.5
Fisicoquímica de Superficies
dR / dX  0
d 2 R / dX 2  0
Simulation of Hg intrusion in Structure 1
Advancing meniscus labeled after the abcissa value
100
Structure 1
0,008
Hg Penetration Curve
Structure 1
Jump 2
3
R  R0
Vp / m
400
300
180
0
90
X=0
R / nm
0,006
0,004
0,002
Jump 1
-100
0
100
200
300
X / nm
Atlanteans of Tula
México
400
500
0,000
60
70
80
90
100
110
120
P/bar
Área de Fisicoquímica de Superficies
130
Mercury intrusion in Structure 2
0,010
100
Structure 2
Hg Penetration Curve
Structure 2
3
Vp / m
460
340
210
0
85
X=0
R / nm
0,008
0,006
0,004
0,002
-100

0,000
0
100
200
300
400
X/ nm
The Castle, Chichén Itza,Yucatan
500
40
60
80
100
120
140
P/bar
ÁREA DE FISICOQUÍMICA DE
SUPERFICIES
160
Mercury intrusion in Structure 3
0,006
100
Hg Penetration Curve
Structure 3
Structure 3
3
Vp / m
400
250
200
140
180
0
70
X=0
R /nm
0,004
-100
0,002
0,000
0
100
200
300
X / nm
400
500
50
100
150
200
250
300
P/bar
Fisicoquímica de Superficies
350
400
Hg intrusion in Structure 4
Snap-off
0,006
100
Hg Penetration Curve
Structure 4
Structure 4
Vp / m
3
370
440
330
220
200
150
110
0
65
0
R / nm
0,004
0,002
-100
0,000
0
100
200
300
X / nm
400
500
50
100
150
200
250
P/bar
300
350
400
Conclusions
Hg is introduced into a sequence of bulges and
necks in a jump-wise fashion, similar to that that has
been observed during imbibition experiments..
The threshold intrusion pressure in this kind of
structures is seldom defined by the narrowest radius
of a given pore throat; something similar is expected
to be obtained for retraction curves (i.e. the widest
section of a bulge cavity will not be defining the
extrusion pressure)
Meniscus snap-off leading to Hg retention can arise
during intrusion.
Fisicoquímica de Superficies
Some more information about Hg porosimetry
Adsorption Science & Technology
2006 Volume 24 Number 8, 623-643
Mechanistic and Experimental Aspects of the
Structural Characterization of Some Model and
Real Systems by Nitrogen Sorption and
Mercury Porosimetry
Carlos Felipe, Fernando Rojas, Isaac Kornhauser,
Matthias Thommes and Giorgio Zgrablich
Particle &Particle Systems. Charact. 23 (2006) 48–60
Domain Complexion DiagramsRelated to Mercury
Intrusion-Extrusion inMonte Carlo-Simulated
PorousNetworks
Carlos Felipe*, SalomónCordero*, IsaacKornhauser*,
GiorgioZgrablich**, Raul López**,
FernandoRojas*
Thank you for your kind attention
Glimpses of 4 great scientists
and better persons!
Prof. Douglas H.
Everett
Dr. Mike
Haynes
Profs. Vicente Mayagoitia & Giorgio Zgrablich