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On Modeling Mercury Intrusion On Modeling Mercury Intrusion Effects inEffects in Pores of Axial Symmetry Pores of Axial Symmetry

and Attenuated Cross-Sectionand Attenuated Cross-Section

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

Isaac Kornhauser, Carlos Felipe, Marcos Esparza, Armando Domínguez, Fernando Rojas

Departamento de QuímicaUniversidad Autónoma Metropolitana-Iztapalapa, MéxicoCentro Interdisciplinario SobreMedio Ambiente y Desarrollo,Instituto Politécnico Nacional, México

Área de Fisicoquímica deÁrea de Fisicoquímica de SuperficiesSuperficies

Main goals of this study are:Main goals of this study are:

1)1) The influence of the pore wall angle of The influence of the pore wall angle of inclination on the intrusion pressure inclination on the intrusion pressure and radius of curvature of the liquid-and radius of curvature of the liquid-

vapor interfacevapor interface 2) The occurrence of jump-like Hg 2) The occurrence of jump-like Hg

Penetration in circular pores of Penetration in circular pores of attenuated cross-sectionattenuated cross-section

(3) The existence of a snap-off (3) The existence of a snap-off mechanism during Hg intrusion mechanism during Hg intrusion

depending on the kind of structuredepending on the kind of structure

Mayan ObservatoryChichen Itzá, Yucatán, México

Simulation of Hg intrusion. Canthotaxis effect

Washburn equation:Cebeci equation:

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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

0/)/(tan2 1 dXdRdXdR

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 point X as:

0/)/(tan 1 dXdRdXdR

RP lv /cos2

The Washburn equation taking into account the inclination of the pore wall can be written as:

21 VVV

X

A

RdXRV

02

202

1 )1(

0 100 200 300 400 500

-100

0

100

R /

nm

X/ nm

Structure 2

Circular Pore Shapes with Attenuated Cross-Section

0 100 200 300 400 500

-100

0

100

R

/ n

m

X / nm

Structure 1

0 100 200 300 400 500

-100

0

100

R /

nm

X / nm

Structure 3

0 100 200 300 400 500

-100

0

100

R /

nm

X / nm

Structure 4

R=R0 exp(BX)[1+cos2(NX)]/(1+A)Axial Pore Modeling Axial Pore Modeling

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0)/()/( TpT VPVP

The Laplace stability condition can be written as:

Structure R0 × 10-2/nm A B ×103/nm-1 N ×102/nm-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

Parameters of Circular Functions with Attenuated Cross-section for the Simulation of Axially Symmetric

Pore Entities

Área de Fisicoquímica de SuperficiesAtlanteans of TulaMéxico

Simulation of Hg intrusion in Structure Simulation of Hg intrusion in Structure 11

Advancing meniscus labeled afterAdvancing meniscus labeled after the abcissathe abcissa valuevalue

0/ dXdR0/ 22 dXRd

0RR

60 70 80 90 100 110 120 1300,000

0,002

0,004

0,006

0,008

Vp

/ m

3

P/bar

Hg Penetration Curve Structure 1

Jump 1

Jump 2

0 100 200 300 400 500

-100

0

100

40

0

30

0

18

0

90

X=

0

R /

nm

X / nm

Structure 1

Mercury intrusion in Structure 2

The Castle, Chichén Itza,YucatanÁREA DE FISICOQUÍMICA DEÁREA DE FISICOQUÍMICA DE

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0 100 200 300 400 500

-100

0

100

46

0

34

0

21

0

85

X=

0

R /

nm

X/ nm

Structure 2

40 60 80 100 120 140 1600,000

0,002

0,004

0,006

0,008

0,010

Vp

/ m

3

P/bar

Hg Penetration Curve Structure 2

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0 100 200 300 400 500

-100

0

100

X=

0

70

20

0

14

0

18

0

25

0

40

0

R /

nm

X / nm

Structure 3

50 100 150 200 250 300 350 4000,000

0,002

0,004

0,006

Vp

/

m3

P/bar

Hg Penetration Curve Structure 3

Mercury intrusion in Structure 3

0 100 200 300 400 500

-100

0

100

37

04

40

33

0

22

0

20

0

65

11

0

0 150

R /

nm

X / nm

Structure 4

50 100 150 200 250 300 350 4000,000

0,002

0,004

0,006

Vp

/ m

3

P/bar

Hg Penetration Curve Structure 4

Hg intrusion in Structure 4Snap-off

ConclusionsHg 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.

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Adsorption Science & Technology2006 Volume 24 Number 8, 623-643Mechanistic and Experimental Aspects of theStructural Characterization of Some Model andReal Systems by Nitrogen Sorption andMercury PorosimetryCarlos Felipe, Fernando Rojas, Isaac Kornhauser,Matthias Thommes and Giorgio Zgrablich

Some more information about Hg porosimetry

Particle &Particle Systems. Charact. 23 (2006) 48–60Domain Complexion DiagramsRelated to MercuryIntrusion-Extrusion inMonte Carlo-Simulated PorousNetworksCarlos Felipe*, SalomónCordero*, IsaacKornhauser*, GiorgioZgrablich**, Raul López**,FernandoRojas*

Thank you for your kind attention

Glimpses of 4 great scientists and better persons!

Dr. Mike Haynes

Prof. Douglas H. Everett

Profs. Vicente Mayagoitia & Giorgio Zgrablich