Diffusion processes in unsaturated porous media studied with nuclear magnetic resonance techniques [Elektronische Ressource] / vorgelegt von Germán David Farrher

Farrher

Sujets

• Physik

Informations

• Publié par: universitat_ulm
• Publié le: 01 janvier 2006
• Nombre de lectures: 6
• Langue: English
• Poids de l'ouvrage: 7 Mo

Extrait

Universität Ulm
Sektion Kernresonanzspektroskopie
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Diffusion processes in unsaturated porous media studied with
Nuclear Magnetic Resonance techniques




DISSERTATION
zur Erlangung des Doktorgrades Dr. rer. nat.
Der Fakultät Naturwissenschaften
Der Universität Ulm



vorgelegt von
Germán David Farrher
aus Maggiolo, Argentinien




Ulm, 2006










































Amtierender Dekan: Prof. Dr. Klaus-Dieter Spindler

Erstgutachter: Prof. Dr. Rainer Kimmich
Zweitgutachter: Prof. Dr. Hartmut Jex

Tag der Promotion: 31.01.2007






Dedicated to my parents,
my grandparents,
my brothers,
and to the loves of life, Tali, Damian and Noa.

Diffusion processes in unsaturated porous media studied with Nuclear
Magnetic Resonance techniques

Abstract
Unsaturated porous media form two-phase systems consisting of the liquid and its
vapor. Molecular exchange between the two phases defines an effective diffusion
coefficient which substantially deviates from the bulk value of the liquid. The objective
of the present thesis is to study self-diffusion under such conditions by varying both
the filling degree of the porous medium and the diffusion time. The main experimental
tool was a combination of two different NMR field gradient diffusometry techniques.
For comparison, diffusion in a porous medium was modeled with the aid of Monte
Carlo simulations.
The NMR diffusometry techniques under consideration were the pulsed gradient
stimulated echo (PGStE) method, the fringe field stimulated echo (FFStE) method, and
the magnetization grid rotating frame imaging (MAGROFI) method. As liquids, water
and cyclohexane were chosen as representatives of polar and nonpolar species. The
porous glasses examined were Vycor with a mean pore size of 4 nm and VitraPor#5,
with a pore size ranging from 1 to 1,6 µm.
It is shown that water or cyclohexane in Vycor, show opposite tendencies as a
function of the filling degree. Upon reduction of the filling degree of cyclohexane in
VitraPor#5, the effective diffusion coefficient increases by a factor of up to ten times
the value in the bulk liquid due to the vapor phase contribution. On the other hand,
the effective diffusion coefficient of water first decreases and then increases when the
filling degree is reduced. The different dependences on the filling factor for polar and
non-polar adsorbate species are attributed to different effective tortuosities
represented by different exponents in Archie’s law anticipated in the two-phase
exchange theory presented.
Using a combination of the FFStE and the MAGROFI technique permits one to
cover four decades of the diffusion time from 100 µs to 1 s. The time dependences
acquired in this way were compared with Monte Carlo simulations of a model
structure in a time window of eight decades, from 125 ps up to 12.5 ms. As far as the
accessible time ranges overlap, the diffusion behavior was found to be qualitatively
equivalent. The contribution of the vapor phase to the effective diffusivity is shown to
be particularly efficient on a diffusion time scale corresponding to root mean squared
displacements of the order of the pore dimension.
NMR microscopy of VitraPor#5 partially filled with water or cyclohexane reveals
heterogeneous distributions of the liquid on a length scale much longer than the pore
dimension. This is attributed to the spatial variation of the granular microstructure
visible in electron micrographs. As a consequence of the inhomogeneous filling degree,
the effective transverse relaxation time varies, which in turn leads to NMR imaging
contrasts. The NMR methods employed, that is, a combination of FFStE and
MAGROFI diffusometry, provide effective diffusion coefficients not affected by spatial
variations of the transverse relaxation time, in contrast to the PGStE method: The
FFStE and MAGROFI techniques render the effective diffusion coefficient averaged
over the whole sample irrespective of the local relaxation time.


Contents




1 Cumulative thesis ………............................................................................................................... 1
1 Introduction ............................................................................................................................... 2
2 Theoretical background .......................................................................................................... 3
2.1 Diffusion ........................................................................................................................... 3
2.2 The two-phase exchange model in NMR diffusometry ......................................... 4
a) The general liquid/vapor exchange limit …..................................................... 8
b) The slow liquid/vapor exchange limit ............................................................. 9
c) The fast liquid/vapor exchange limit .............................................................. 9
3 Experimental techniques, methods and samples ........................................................... 10
3.1 The pulsed gradient stimulated echo (PGStE) technique …............................... 10
3.2 The fringe-field stimulated echo (FFStE) technique ............................................ 11
3.3 The magnetization grid rotating frame imaging (MAGROFI) technique ......... 12
3.4 NMR microscopy techniques ...................................................................................... 13
3.5 Numerical simulation methods ................................................................................. 13
3.6 Instruments and sample preparation ...................................................................... 14
4 Experimental and theoretical results ................................................................................. 16
4.1 Effective diffusion coefficient as a function of the filling factor and the
vapor phase contribution in unsaturated porous media ................................... 16
4.2 NMR imaging experiments .......................................................................................... 18
4.3 Time-dependent diffusion coefficient ....................................................................... 19
5 Discussion and conclusions ................................................................................................. 21

Bibliography ........................................................................................................................................... 23

2 Zusammenfassung ........................................................................................................................ 27

3 Curriculum Vitae .......................................................................................................................... 29

4 List of Scientific Publications ................................................................................................. 33

5 Original papers .............................................................................................................................. 35