Thickening Suspensions e ARCH

86 Pages·2012·6.03 MB·English

Capillary Breakup of Discontinuously Rate
I
MASSACHUSETTS INSTffTE
Thickening Suspensions OF TECHNOLOGY
JUN 2 8 2012
by
Pawel J. Zimoch UBRARIES
e ARCH
B.S., Mechanical and Materials Science and Engi
2010, Harvard University (Cambridge, MA)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2012
@ Massachusetts Institute of Technology 2012. All rights reserved.
A uthor ................. .......
Department of Mechanical Engineering
May 24, 2011
Certified by.....................
Anette Hosoi
Professor, Mechanical Engineering
Thesis Supervisor
Accepted by ...................
David E. Hardt
Graduate Officer, Department Committee on Graduate Students

Capillary Breakup of Discontinuously Rate Thickening
Suspensions
by
Pawel J. Zimoch
Submitted to the Department of Mechanical Engineering
on May 24, 2011, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
In this study, we investigated the behavior of Discontinuously Rate Thickening Sus-
pensions (DRTS) in capillary breakup, where a thin suspension filament breaks up
under the action of surface tension forces.
We performed experiments with 55% by weight suspension of cornstarch in glyc-
erol. To minimize the effect of gravity on the experiments, we developed a new
experimental method, where the filament is supported in a horizontal position at the
surface of an immiscible oil bath by the interfacial tension of the oil-air interface. It
was found that after a brief transition period, the radius of the filament decreases
at an exponentially decaying rate, which is half the deformation rate at which the
apparent viscosity of DRTS appreciably increases beyond it's low-deformation rate
value. Late in the filament's evolution, a bead forms in its center, leading to forma-
tion of morphologically complex, high aspect ratio structures. It was found that the
formation of these structures is caused by the viscous drag exerted on the filament
by the oil bath.
The behavior of DRTS filaments in capillary breakup was modeled with 1- dimen-
sional approximations to momentum and mass balance equations, which are valid in
the limit of slender geometry of the filament. The rheology of the suspension was mod-
eled with a simple function diverging at the deformation rate at which the increase in
viscosity becomes appreciable. The governing nonlinear coupled partial differential
equations were solved numerically with a finite volume scheme using the Newton's
method. It was found that this simple model reproduces the observed behavior well.
It was found that in contrast to Newtonian filaments, the viscous stress in the
DRTS filaments reaches a plateau and does not increase indefinitely. This is a result
of a coupling between the nonlinear rheology of the suspension and the nonlinearity
associated with evolving shape of the filament. It was found that the evolution
of DRTS filaments with no external viscous drag depends on the value of a single
parameter, i/Wi, which is a function of the Weissenberg number Wi associated with
the flow, and the aspect ratio of the filament . When i/Wi < 1/3, the viscous stress
at the center of the filament scales as (- , and when i/Wi > 1/3, the viscous stress
scales as Wi-1. These findings are supported by analytical arguments based on the
governing equations in the regime where i/Wi < 1/3.
The formation of the beaded structures was investigated, focusing on the appear-
ance of the first bead at the center of the filament. It was found that the viscous
drag from the environment plays a central role in formation of the beads. Numerical
solutions, theoretical arguments and experiments were found to be in agreement.
Thesis Supervisor: Anette Hosoi
Title: Professor, Mechanical Engineering
Acknowledgments
First and foremost, I would like to express my gratitude to my family and my girlfriend
Jacqueline Nkuebe, who supported me every day during my work on this project, and
whose presence in my life made this work enjoyable.
I would like to thank my advisor, Professor Anette (Peko) Hosoi, for her insightful
and constructive critique of my work, and for her unwavering support and trust in
me. I would also like to thank Professor Gareth H. McKinley for his willingness to
share with me his knowledge and experience.
Finally, I would like to thank all members of the Hatsopoulos Microfluids Labora-
tory for creating a fantastic work environment, and for sharing their experience with
me.
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Contents
1 Introduction 9
2 Experiments 13
3 Mathematical Model 17
4 Results and Discussion 21
5 Conclusion 27
A Experimental methods 29
B Mathematical Model 33
B.1 The governing equations ........................ . 35
B.2 Viscosity function and its impact on filament evolution . . . . . . . . 42
B.3 Derivation of governing equation by Control Volume analysis . . . . . 44
B.4 Nondimensionalization of the governing equations . . . . . . . . . . . 47
B.5 Parameter range covered by this study and range of valdity of equations 51
C Numerical simulation 53
C.1 Equations solved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
C .2 Source Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
D Model equations solutions and Analysis 71
D.1 Effect of thickening on evolution of the filament . . . . . . . . . . . . 72
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D.2 No drag behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
D.3 Analytical arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
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Chapter 1
Introduction
Complex, high aspect ratio structures, such as strings with embedded functionalized
elements ("beads") (Figure 1.1), can find applications in optics [16], self-assembly,
bioengineering, and custom material design [7]. It was recently shown that such struc-
tures can be created by polymerizing a liquid filament undergoing capillary breakup
[16]. Exploiting surface tension driven instabilities in liquids enables generation of
such complex geometries at small scales [24] and allows use of efficient microfluidic
techniques for processing [22].
Currently, formation of Beads-on-a-String (BOAS) structures is achieved by ex-
ploiting either electrohydrodynamic (EHD) pressure [16] or complex properties of
polymers [3, 8, 21]. In both cases, the factors affecting the properties of the formed
structure, such as size and relative placement of beads, are not well understood
[3, 16, 24].
We show that BOAS structures can be formed in a controlled way by utilizing
the known effect of viscous drag on capillary breakup [26, 27, 28]. Placing a filament
undergoing breakup in a bath of immiscible viscous fluid results in creation of a rich
variety of structures, depending on the properties of both fluids [27, 26]. Here, we
couple this effect with Non-Newtonian rheology of Discontinuously Rate Thickening
Suspensions (DRTS)1 to extend the lifetime of the filament and enable formation of
'The more commonly used name, Discontinuously Shear-Thickening Suspensions, is made more
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Figure 1.1: Typical Beads-on-a-String (BOAS) structures. (a) Solution of PolyEthyle-
neOxide solution (PEO) in water, surrounded by air. (b) Solution of PEO
solution in water, in corn oil bath. (c) Solution of polystyrene in styrene oil,
in glycerol bath. (d) Suspensions of cornstarch in glycerol, in corn oil bath.
(e) Suspension of silica in water, in corn oil bath. Scale bars: 1mm.
high-aspect ratio structures and subsequent polymerization.
The defining feature of DRTS is a sharp increase in viscosity at a critical deforma-
tion rate crit (Figure 1.2) [1]. The behavior of these materials in a given flow can be
pt( ) [Pa -s]
200 -
100 -
50 -
20
0.01 0.1 0.5 5.0
Figure 1.2: Shear rheology of 55% wt. suspension of cornstarch in glycerol, measured in
a parallel plate geometry.
characterized by a Weissenberg number Wi = if1/it, where Af9 is the characteristic
deformation rate of the flow. The suspensions are nearly Newtonian for Wi < 1, and
thickening significantly affects the flow when Wi ~ 1.
general here to account for the fact that the main deformation mode in capillary breakup is extension.
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