8th World Conference on Experimental Heat
Transfer, Fluid Mechanics, and Thermodynamics
June 16-20, 2013, Lisbon, Portugal
MAKING IT CLEAR: FLEXIBLE, TRANSPARENT LABORATORY FLOW
MODELS FOR SOFT AND HARD PROBLEMS
Mark C. Jermy
Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
E-mail : [email protected]
ABSTRACT
For internal flows, optical measurements (e.g. flow visualization, LDA, and PIV) work well if a flat window can
be let into the walls of the system. Curved walls, however, introduce refractive distortions. Correcting for these
becomes increasingly difficult as the geometry of the surface becomes more complex, (for example, biological
structures).
If the working fluid and transparent model have the same refractive index, there is no distortion. For example, the
model can be made from fused silica, and the working fluid mixed from silicone oils. Another popular combination is
silicone resin and water-glycerol mixture. Silicones allow the casting of thin-walled, flexible models, which can be
used to study the interaction of a fluid flow with a deforming structure. Other soft materials are possible.
This paper reviews the essential considerations for refractive index matching and dynamic similarity. Known
combinations of solids and working fluids are listed. Some results, and practical tips, from the author’s group will be
presented.
Finally, an example of a soft (though at best translucent) material which mimics the behaviour of human brain
tissue under high strain rates, and which is used in studies of wounding, will be presented.
Keywords : refractive index matching, fluid-structure interaction, PIV, flow visualization
NOMENCLATURE
A cross sectional area
D diameter
d distensibility
E Young' s modulus
h wall thickness
p pressure
Re Reynolds number
St Strouhal number
U m mean velocity
α Womersley number
∆x change in parameter x
ν kinematic viscosity
ω angular frequency
1.
INTRODUCTION
Optical methods of measuring flow velocity (e.g. LDA, PIV) and
streamline configuration (flow visualization) have the advantage
that they can be set up so that they do not disturb the flow being
studied. These methods have been widely applied to external and
internal flows. Internal flows present a particular challenge, in
that many systems of interest have walls or boundaries of
complex shape. If the laser beam (or other probe light) and
scattered signal light passes through a curved wall, it will be
distorted. The consequences may range from minor distortion of
an image (e.g. imaging through a mildly curved wall) to
complete loss of signal (e.g. an LDA system unable to form
interference fringes). For walls of simple configuration, for
example cylindrical surfaces with a single radius of curvature
which is similar in magnitude to the distances between the
components, the distortion may be corrected during
post-processing (1). In other simple systems, it may be possible
to orient the probe light and detector so that what little distortion
occurs can be ignored. An example is a imaging in an i.c. engine
cylinder, replacing some section of the cylindrical bore with a
transparent element, illuminating with a light sheet with a plane
perpendicular to the cylinder axis (introducing minimal
distortion into the light sheet), and viewing through a flat
window in the piston. Where the system under study does not
have a simple geometry which can be exploited in this way,
refractive index matching is an attractive option.
The principle of refractive index matching is to choose a flowing
fluid (hereafter called the working fluid) and a wall material
which have near-identical refractive indices (a mismatch of a
few percent is permissible unless the very best image quality is
required). Several factors must be considered:
a. Material and fluid selection
b. Construction of the model
c. Dynamic similarity
d. Temperature control
e. Mixture control
Figure 1 shows the clarity which can be achieved by adjusting
the refractive index of the working fluid.
Table 2: A selection of candidate working fluids
Water
Aqueous solutions
Glycerine
Zinc iodide
Sodium iodide
Figure 1: A checkerboard pattern viewed through a silicone
model when filled with (left) air, (centre) 70% glycerol 30%
water, and (right) 61% glycerol 39% water
2. MATERIAL AND FLUID SELECTION
Several published studies have reviewed the literature on
selection of refractive matching materials, and this paper does
not set out to produce an exhaustive review. Of note is reference
(2) which is the basis of Table 1 and Table 2, with some
information on additional materials from (3) and (4). The table is
not exhaustive, but covers the most popular materials. (5) and (6)
offer some other combinations, and a discussion of issues
relevant to index matching in concentrated suspensions of
granular materials.
Table 1: A selection of candidate transparent solids.
Glass
Borosilicate or
aluminosilicate
(Pyrex and other
low
thermal
expansion
glasses)
Fused quartz
Optical glasses
Polymers
FEP (fluorinated
ethylene
propylene)
Acrylic (PMMA)
Polycarbonate
Casting resins
Epoxy based
Urethane based
Acrylic based
PMMA
Silicone
elastomer
1.47-1.49
1.4584
1.45-1.96
1.33
Low stiffness
1.47-1.49
1.58
1.56
1.49
1.49-1.53
1.49
1.415-1.47
Can be made by
stereolithography
Dow-Corning
Sylgard 184 notable
for its low ref. index
Potassium
thiocyanate
Ammonium
thiocyanate
Sodium thiocyanate
CaCl2
Sucrose
ρ/ρ0
1
µ/µ0
1
1.33-1.47
1.33-1.62
1.33-1.5
(higher values
around 60wt%
NaI)
1.33-1.49
1-1.26
1-1490
1-1.39
1-2.4
1.33-1.50
1-1.15
1-2.1
1.33-1.48
1.34-1.46
1.33-1.45 (up
to
60%
sucrose)
1-1.34
1-7.5
1.33
1-1.3
(up to 60%
sucrose)
Organic liquids
Kerosene
1.45
0.82
Silicone
oil 1.47-1.4905
1.03
190
mixtures*
Mineral
oil 1.48
0.85
(paraffin oil)
Turpentine
1.47
0.87
1.49
Solvent naptha
1.50
0.67
Soybean oil
1.47
0.93
69
Olive oil
1.47
0.92
84
Castor oil
1.48
0.96
986
Tung oil
1.52
0.93
Cassia oil
1.60
Dibutyl phtalate
1.49
1.043
20
Diethyl Phtalate
1.50
1.118
12
Mixture of oil of
~1
~1
turpentine
and
Tetraline
Ethanol
1.362
0.79
Benzyl Alcohol
1.54
P-Cymene
1.49
0.857
0.87
Tetraethylene
1.458-1.459
glycol,
tetrahydropyran-2methanol
Mixture
of 1.4585
cyclooctane
and
cyclooctene
ρ0=density and µ0=absolute viscosity of pure water at 20.0oC
* e.g. Dow-Corning 550, Union Carbide L42, and similar fluids
When choosing a combination of materials, several factors must
be borne in mind:
1)
2)
3)
Compatibility: the working fluid must not corrode or
dissolve the model material or components. This is of
particular importance when using salt solutions, which
tend to corrode metal fasteners. Pipe fittings and
pumps must also be compatible.
Safety: Some of the working fluids are toxic, and safe
handling may require time consuming precautions.
Disposal of the used fluid may be costly. Some of the
organic fluids are flammable.
Temperature and mixture sensitivity. Temperature
changes during the experiment must not change the
refractive indices or the viscosity enough to upset the
index match or dynamic similarity. Likewise with
mixture changes due to evaporation.
sacrificial negative mould is used. Sand casting is such a method
commonly used in foundries. A positive, or ‘pattern’ is formed of
some easy to work material, such as wood or polymer, and the
sand is pressed around this in two halves to form a cavity with
the same shape as the pattern (Figure 3). Molten iron or steel is
poured into this cavity and allowed to set. Another type is
lost-wax casting. A positive or ‘model’ is made of some easily
meltable or soluble material. The negative is cast around this,
and when set, the model is removed by melting or washing out,
leaving a cavity into which the final material is poured.
Any seeding particles must also be chemically compatible, but
this is rarely a problem, as microbubbles, hollow glass spheres
and refractory powders rarely present problems and usually
perform well as tracer particles in liquids. Abrasion of the model
walls by particles is rarely serious enough to change the
hydraulic roughness significantly, and scratches will be rendered
invisible by the refractive index match.
2.1 Index-matching two different fluids
Where the problem under study is the mixing of two fluids of
different density, it is advantageous to have two fluids of the
same refractive index. (7) describes a method for achieving this
with glycerol and a potassium phosphate solution, and (8)
describes a method with ethanol and a solution of sodium
chloride.
Figure 2: A bronze sword cast in a two-piece mould. Photo
courtesy Jeroen Zuiderwijk.
www.bronze-age-craft.com/Bronze-Sword-Festival.htm
3. CONSTRUCTION OF THE MODEL
The solid model may be machined or cast, depending on the type
of material. Casting has particular advantages for complex
shapes such as those found in biological flow problems, as the
mould can be prepared by rapid prototyping. A casting process
used successfully in the author’s laboratory is described in (9).
There are several methods of casting, many of which date back
to the Bronze Age. In all types a negative mould is made, and the
cast material poured into the cavities in this negative.
Casting methods can be categorised according to whether the
negative mould is permanent or temporary. A permanent mould
can be used if it can be made in two or more parts, so that it can
be opened later (e.g. pouring molten bronze into a two-piece
mould cut from stone, Figure 2, or slipcasting by pouring a clay
suspension into a hollow two-piece mould). Two-piece moulds
often leave a mould line at the join which needs to be tidied up
later (in the case of a bronze sword, by sharpening).
Alternatively a permanent one-piece mould can be used if the
mould is of a flexible material, which can be pulled off the
finished piece once set (e.g. latex rubber moulds used to cast
solid clay ornaments).
Where the mould cannot be made in two pieces, a temporary or
Figure 3: A sandcasting mould and pattern. Wikimedia
commons, photo courtesy of Glenn McKechnie
For optical studies, optically flat outer surfaces are needed. The
author’s group has produced a number of models of biological
structures in silicone resin (Dow Corning Sylgard-184). The
internal hollow is a complex shape, and a combination of
methods were required to accurately form both inner and outer
surfaces. The outer negative mould, which formed the flat
viewing surfaces, was cuboid, and made of plates of PMMA
fastened with machine screws, and which could be
b disassembled
and peeled off when the model was set (Figure
Figure 4).
when we came to study patient-specific
specific problems, as the model
could be printed directly from segmented CT or MR scans of the
body part under investigation.
Onee problem remained to be solved: grains of plaster became
embedded in the silicone resin, making the inner surface
partially opaque. This was solved by coating the 3D printed
model with PVA glue before pouring the resin. The PVA glues
sold for school use are easily dissolved in warm water
(woodworking glues usually contain
conta
waterproofing agents,
which are undesirable for this application). Examples of such
negative moulds can be seen in Figure 4 and Figure 5.
Figure 4:: Mould for a silicone model of the human oral
cavity and upper airway (trachea to teeth). PMMA outer
mould and 3D printed plaster inner mould shown.
The negative of the internal hollow was formed by an adaptation
of the lost-wax method. Several materialss for this inner negative
were trialled. It had to be a material which could be removed
remo
after the silicone resin had set. Initially we tried several low
melting point materials. Wax is routinely used in the jewellery
industry, but shrinks by up to 5%
% on cooling, which introduces
errors in the finished product. Also, the wax diffused into the
resin, leaving a semi opaque
que layer at the inner surface.
su
Woods’
metal (Lipowitz’s alloy) is an alloy of bismuth, lead, tin and
cadmium which melts at 70oC, so, like wax, can be melted out
with hot water. It is toxic, but safer alternatives such as Cerrolow
can be used. Trialling these, wee had some difficulty with
shrinkage, although with careful temperature control and settling
such alloys can be used to make dimensionally-accurate
dimensionally
castings,
and are regularly used by gunsmiths to measure the internal
dimensions of chambers, so the problems we encountered can
probably be overcome.
Still seeking an alternative material, my graduate students had
noticed that chocolate can be cast with precise, sharply incised
detail, seen for example on Easter eggs. Being true empiricists,
they checked this observation
bservation by carefully testing many different
types of chocolate. Alas, the chocolate was found to shrink by a
similar amount to wax:: although the experimenter’s
experimenter waistline is
liable to expand. The solution we settledd on was to 3D print the
inner negative using a ZCorp ZPrinter 310 Plus machine. This
prints the model in a plaster powder reinforced with an organic
binder. By using a low concentration of binder,
binder the model could
be washed out with a jet of water and careful abrasion with a soft
tool. This method had
ad several advantages: the model is
dimensionally stable (no shrinkage) and can be transported and
stored for some time before use; accidental breakages can
c be
repaired with cyanoacrylate glue; and the model can
c be prepared
directly from a CAD model. This
his was particularly important
Figure 5: 3D printed plaster negative in two parts (left:
negative or human nasal cavity and upper airway; right:
negative of face
Figure 6:: Finished silicone model (of the human upper
airway) with moulds removed.
An example of a finished silicone model is shown in Figure 6. A
CT scan of a finished model showed that it reproduced the
geometry of the original CAD models used to print the negative
to a mean error of 280µm, some of which is systematic error (as
the PVA coating makes the model larger everywhere) which can
be corrected for.
hydrogel used by (10) which are refractive-index matched to
water, allowing high Reynolds numbers to be reached.
3.1 Flexible, deformable models
Some interesting fluid mechanic problems feature the
deformation of a soft or flexible solid in response to fluid
dynamic forces. Deformable, refractive index-matched models
can be constructed. Reference (9) describes the casting of
models with a wall thickness of order 1 mm. The wall thickness
can be controlled and used to determine the stiffness of the
model.
Particular care is required when casting thin-walled models.
Bubbles can easily become trapped on the walls of the mould.
Bubbles cannot be tolerated in a thin walled model, as they
drastically reduce the stiffness. A method was developed to fill
the mould slowly from the bottom (Figure 7). This produced
good models.
Figure 8: Finished thin-walled model of a stenosed artery.
4. DYNAMIC SIMILARITY,
MIXTURE CONTROL
Figure 8 is an image of a model of a stenosed (narrowed) human
artery produced in this way. The wall thickness is 1.5mm and the
material is Dow-Corning Sylgard 184. The striations running
along the length of the model are a result of the casting process.
The striations are small (the surface feels smooth to the
fingertip) and cannot be seen when the model is immersed and
filled with a refractive index matching fluid.
A promising material for soft models is the polyacrylamide
AND
For a successful experiment, several conditions must be matched.
The refractive index must be matched, of course. Where the fluid
is a mixture, this depends on the mixture fractions (e.g. salt or
glycerol concentration) which must be maintained against any
evaporation which may occur over the course of several days
work. Frequent checking of the refractive index match with a
checkerboard pattern such as that shown in Figure 1 is wise. The
refractive index also depends on the temperature, and this must
be controlled. It may be convenient to operate the working fluid
at a temperature slightly above or slightly below room
temperature, so it can be thermostatically controlled with a
heater or chiller loop.
Another reason to carefully control temperature is that it affects
the viscosity of the working fluid, and hence the Reynolds
number. As most index-matching experiments replace the
working fluid natural to the problem (e.g. air, blood, water,
fuel-air mixtures) it is important to retain dynamic similarity of
the flow. Liquids being virtually incompressible, the method is
not appropriate for compressible flow problems, so the Mach
number is low and need not be considered further. The Reynolds
number, Eq. (1), must be matched
Re =
Figure 7: Casting a thin walled model: (on right) plunger to
drive the liquid resin upwards through the mould (on left)
machined aluminium outer mould, 3D printer plaster inner
mould.
TEMPERATURE
UmD
v
(1)
To achieve this may require the model to be larger, or smaller,
than life size. For biological flow problems using water/glycerol
and silicone resin, it has proved convenient to make models two
to three times larger than life size. Besides achieving a Reynolds
number match at reasonable flow rates, the larger models are
easier to make accurately.
Where the flow is time, varying, there is an additional parameter
to be matched, which may be either the Strouhal number, Eq. (2)
St =
ωD
Um
Or the Womersley number, Eq. (3):
(2)
α=D
ω
(3)
v
The Womersley number is commonly used for biological flows,
and is related to both the Reynolds and Strouhal number by Eq.
(4):
α = Re⋅ St
(4)
With flexible models, the degree of stiffness or flexibility is an
additional parameter which must be matched. One approach is to
define the distensibility d , Eq. (5):
d=
1 ∆A
A ∆p
(5)
Distensibility relates the change in cross-sectional area ∆A to
the original (neutral or unstressed) area A and the change in
pressure ∆p . For a vessel of circular cross section, Eq. (5) can
be shown to be equivalent to Eq. (6):
d=
1
E (h D )
(6)
Note that there are two parameters which are under the
experimenter’s control: the Young’s modulus E , and the
thickness of the model wall h .
4. BIOLOGICAL MATERIALS
Biological materials have special properties, due to their
microstructure, and to fully mimic their properties in refractive
index-matched materials is ambitious. Some progress has been
made, and some examples (by no means an exhaustive list) are
discussed below.
4.1 Skin
Optical clearing agents have been used to alter the refractive
index of the intercellular fluid in human skin, to match its
refractive index to the cells. This reduces the scattering of light
and increases the depth to which non-invasive optical methods
can measure chemical or structural properties, such as oxygen
concentration or skin and muscle layer thicknesses. Optical
clearing is reviewed in (11).
4.2 Blood
Blood is a suspension of colloidal particles (principally red blood
cells, but also platelets and white cells) in an aqueous solution of
proteins and inorganic salts. It has some fascinating properties. It
clots when stagnant, as part of the healing process. It is a
non-Newtonian shear-thinning fluid, i.e. its viscosity reduces as
the shear rate increases.
Refractive index matching is often used to study the fluid
dynamics of arterial diseases. The viscosity of blood approaches
a constant value when a critical shear rate is reached, and several
authors have explorited this property, with some experimental
justification, to allow the use of a simple Newtonian blood
mimicking fluid: for example, (12) used a water-glycerol-sodium
iodide mixture to match a Sylgard 184 model. The paper gives
valuable data on the dependence of refractive index and viscosity
on temperature and concentration. Reference (9) gives
corresponding data for a mixture containing water and glycerol
only, with no salt (although about 1 mg of sodium chloride was
added per litre of mixture to improve the conductivity, so as to
obtain a reliable signal from the electromagnetic flowmeter,
though this does not change the viscosity or refractive index
significantly). Reference (13) gives further useful data on a
wider range of candidate materials, and a mathematical method
for determining the optimal match.
The non-Newtonian properties of blood cannot always be
ignored, particularly in problems where low shear stresses (and
correspondingly high local viscosities) are encountered. (14) and
(15) made PIV measurements in transparent fluids with
non-Newtonian viscosity behaviour very close to those of blood,
by mixing water, glycerol and xanthan gum.
An interesting possibility is the use of suspended particles to
achieve non-Newtonian properties, as used in test fluids for
ultrasound (16). For ultrasound, it is not necessary to match
refractive indices, but such fluids might be rendered valuable for
optical experiments by index matching using the techniques
described in (5) and (6).
4.3 Brain tissue
Bloodstain patterns are an important type of evidence at crime
scenes, and can yield important information on the position of
the victim and assailant, the weapons used and the number of
blows struck. It is not uncommon for forensic analysts to be
called to the scene of a death by gunshot wound to the head, and
to be asked to determine whether the cause is suicide or murder.
The bloodstain pattern is one useful piece of evidence. Cranial
gunshot wounds form blood stains by at least three distinct
mechanisms: an interaction of the muzzle gases with the skin
layers, tail splash as the bullet penetrates, and collapse of the
temporary cavity formed by the bullet passing through the brain
tissue. These mechanisms are not well understood, and better
understanding may lead to more, or more reliable, information
being extracted from them. The mechanics of the high
deformation, high strain rate interaction of a bullet with tissue
are complex. Experiments on animal tissue are illustrative, but
rarely repeatable, as the tissue properties vary from sample to
sample. Recent work in the author’s group has focussed on
developing a safe, repeatable simulant material for brain tissue,
and studying the interaction of this simulant with various
projectiles, using high-speed imaging. Brain tissue has complex
visco-elastic properties, but promising early results have been
obtained with mixtures of water, glycerol, and polymer fibres
(Figure 9 and Figure 10). By varying the fibre content, the
property of the simulant can be tuned.
literature,
e, which goes beyond the sources cited here, contains
many more examples, and much useful data on physical
properties of materials. There is scope for innovation in flexible
models, and liquids and solids which replicate the complex
mechanical response of biological materials.
ACKNOWLEDGEMENTS
None of the results produced by my group would have be
possible without the talent and hard work of the excellent
graduate students I have been fortunate to work with: on models
for PIV, Dr Callum Spence, Dr Patrick Geoghegan, and Dr
Nicolas Buchmann made enormous contributions. On blood and
biological materials, I am indebted to Milad Soltanipour
Lazarjan, Natalia Kabaliuk and Theresa Stotesbury, and to the
guidance of forensic scientist Dr Michael Taylor of the Institute
of Environmental and Scientific Research, NZ.
NZ
Figure 9:: A simulant with a fibrous web in a viscoelastic
matrix (bottom) fragments in a similar manner to sheep
brain tissue (top) when penetrated with a 1.9g projectile at
275ms-1. The simulant also absorbs the same
s
quantity of
kinetic energy.
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This paper has reviewed some of the essential considerations in
refractive index matching, and given some examples
example and
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