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Fluid dynamics of single levitated drops by fast NMR techniques [Elektronische Ressource] / Andrea M. Amar

108 pages
Ajouté le : 01 janvier 2006
Lecture(s) : 39
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Fluid dynamics of single levitated drops by
fast NMR techniques
Von der Fakultat¨ fur¨ Mathematik, Informatik und Naturwissenschaften
der Rheinisch-Westf¨ alischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades einer Doktorin der
Naturwissenschaften genehmigte Dissertation
vorgelegt von
Licenciada en F´ısica
Andrea M. Amar
aus Buenos Aires, Argentina
Berichter: Universit¨ atsprofessor Dr. Dr. h.c. (RO) Bernhard Blumic¨ h
Hochschuldozent PD Dr. Siegfried Stapf
Tag der mundlic¨ hen Prufung:¨ 14. Juli 2006
Diese Dissertation ist auf den Internetseiten der
Hochschulbibliothek online verfugbar.¨Berichte aus der Physik
Andrea M. Amar
Fluid dynamics of single levitated drops
by fast NMR techniques
D 82 (Diss. RWTH Aachen)
Shaker Verlag
Aachen 2006In one drop of water are found all the secrets
of all the oceans.
Kahlil GibranBibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche
Nationalbibliografie; detailed bibliographic data are available in the Internet
at http://dnb.d-nb.de.
Zugl.: Aachen, Techn. Hochsch., Diss., 2006
Copyright Shaker Verlag 2006
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior permission
of the publishers.
Printed in Germany.
ISBN-10: 3-8322-5795-0
ISBN-13: 978-3-8322-5795-8
ISSN 0945-0963
Shaker Verlag GmbH • P.O. BOX 101818 • D-52018 Aachen
Phone: 0049/2407/9596-0 • Telefax: 0049/2407/9596-9
Internet: www.shaker.de • e-mail: info@shaker.deContents
1 Introduction 1
2 Fluid Dynamics of Drops 7
2.1 TheNavierStokesequation ....................... 8
2.1.1 HistoricalBackground ...................... 8
2.1.2 Someresultsandapproximations ................ 10
2.2 Bubbles and drops ............................ 11
2.3 Contaminantsandmasstransfer..................... 17
3 Nuclear Magnetic Resonance 21
3.1 NMRImaging ............................... 21
3.1.1 Scanningk-space . ........................ 22
3.1.2 Selectiveimaging ......................... 25
3.2 NMRVelocimetry............................. 26
3.2.1 Propagator formalism....................... 27
3.2.2 Combinationofvelocityandimaging .............. 27
4 Experimental 31
4.1 Theapparatus(measurementdevice) .................. 33
4.1.1 Themeasurementcell ...................... 34
4.1.2 Binarysystem........................... 36
4.1.3 Flowrate-Pumpcalibration 39
4.1.4 Dosimeter(dropgeneration) ................... 40
4.2 NMRsequences/spectrometers 41
4.2.1 SystemI .............................. 43
4.2.2 SystemII . ............................ 44
4.3 Stability checks . . 47
iii Contents
4.4 DropFormation .............................. 50
5 Results and Discussions 59
5.1 SystemI:OMCTS ............................ 60
5.2 SystemII:Toluene 66
5.2.1 5.2.1. Example 1: Ellipsoidal toluene drop with symmetrical
convection . 68
5.2.2 Example 2: Ellipsoidal toluene drop with symmetrical convec-
tionandrigidcapgrowingwithtime. .............. 72
5.2.3 Example3: Differentsizedrops ................. 77
5.2.4 Example 4: Ellipsoidal toluene drop with symmetrical convec-
tion and rolling (pattern in the XY plane) ........... 80
6 Conclusions and Outlook 85
Bibliography 89
Publications by the Author 95Chapter 1
Introduction
Liquid-liquid extraction processes are of widespread use in chemical engineering and
have their most important application in cleaning procedures where contaminants
in a bulk, valuable fluid component (donator phase) are being removed by bringing
it into contact with a second, disperse phase (acceptor phase). Ideally, donator and
acceptor phase are immiscible, while the contaminant (transfer phase) is soluble in
both fluids. In order to provide maximum transfer within a given amount of time, a
large concentration difference of the contaminant and a large interface area between
the two main phases are desired. This is often realized by dispersing the acceptor
phase into a swarm of droplets and allowing it to pass through the continuous phase
exploiting the density differences between phases.
It is a well-known fact that the efficiency of mass transfer between the two phases
is determined by convective transport made possible through circulation occurring
both inside and outside of the droplets. Mass-transfer can be, in fact, substan-
tially faster than would be expected from pure diffusive transport across the drop
interface. Mass transfer rates are underestimated by orders of magnitude by the
analytical solution of Kronig and Brink [Kro1], but also by 2D-axisymmetric CFD
simulations for non-deformable droplets with an ideally mobile interfacial region,
which do not make use of approximated solutions of the Navier Stokes equations
[Wah1, Gro1]. Modelling mass-transfer, however, depends on a precise knowledge
of the fluid dynamics inside the drop, which in turn can be understood theoretically
only by taking into account sufficiently detailed models of the boundary layer prop-
erties. The single-droplet behaviour, which needs to be understood as a basis for the
extraction-column design, is determined by mass transfer and sedimentation, which
take place simultaneously and influence each other. Although in the past, several
12 Chapter 1. Introduction
theoretical, numerical and experimental investigations on single droplets have been
carried out, sedimentation velocities and mass-transfer rates cannot be predicted a
priori; experimental data can only be matched by additional empirical parameters.
The only experimental evidence for fluid dynamics is usually delivered from integral
measurements of the mass transfer in an extraction column or in single-drop cells
[Hen1, Hen2]. Although particle tracer methods have been used to visualize the flow
pattern in drops directly [Sav1, Dav1, Cli1] (Figure 1.1), these are limited in their
applicability with respect to resolution and dimensionality, frequently monitoring
only motion in suitable sections within the drop. Furthermore, they represent an
invasive technique which can compromise the validity of the results derived about
the fluid flow field. For instance, it is known that the fluid dynamics of the drop can
be very sensitive to small concentrations of impurities in the system which tend to
accumulate at the interface.
Figure 1.1: Visualization of internal circulation in a levitated drop using tracer particles
[Dav1].
Pulsed field gradient (PFG) NMR appears to be an exceptionally suitable tech-
nique for non-invasively monitoring the drop’s internal fluid dynamics and its change
with time. In the recent literature, the versatility of velocity encoded imaging and its
applicability to model systems and problems from the field of chemical engineering
have been demonstrated. Methods based on conventional imaging are often pro-
hibitively slow to achieve sufficient spatial resolution in a reasonable experimental
time which is required to monitor processes that are potentially instationary (see the
compilation about flow NMR in [Fuk1]). Therefore, several attempts have been made
to combine multi-pulse and/or multi-acquisition imaging techniques with velocity
encoding modules. While a long lifetime of the signal and a comparatively slow

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