impact dynamics of newtonian and non-newtonian fluid ...cj82pq13f/... · and volume2 (2.78±0.2mm...
TRANSCRIPT
IMPACT DYNAMICS OF NEWTONIAN AND NON-NEWTONIAN
FLUID DROPLETS ON SUPER HYDROPHOBIC SUBSTRATE
A Thesis Presented
By
Yingjie Li
to
The Department of Mechanical and Industrial Engineering
in partial fulfillment of the requirements
for the degree of
Master of Science
in the field of
Mechanical Engineering
Northeastern University Boston, Massachusetts
December 2016
Copyright (©) 2016 by Yingjie Li All rights reserved. Reproduction in whole or in part in any form requires the prior written permission of Yingjie Li or designated representatives.
ACKNOWLEDGEMENTS
I hereby would like to appreciate my advisors Professors Kai-tak Wan and
Mohammad E. Taslim for their support, guidance and encouragement throughout the
process of the research. In addition, I want to thank Mr. Xiao Huang for his generous help
and continued advices for my thesis and experiments. Thanks also go to Mr. Scott Julien
and Mr, Kaizhen Zhang for their invaluable discussions and suggestions for this work.
Last but not least, I want to thank my parents for supporting my life from China. Without
their love, I am not able to complete my thesis.
TABLE OF CONTENTS
DROPLETS OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IMPACTING
SUPER HYDROPHBIC SURFACE .......................................................................... i
ACKNOWLEDGEMENTS ...................................................................................... iii
1. INTRODUCTION .................................................................................................. 9 1.1 Motivation ......................................................................................................... 10 1.2 Characteristic outcomes from a droplet impact on solid surface ............. 11 1.3 Super hydrophobic surface ............................................................................ 12 1.4 Related theories ............................................................................................... 14
2. Experiments ...................................................................................................... 19 2.1 Experimental apparatus ........................................................................................ 19 2.2 Preparation of super hydrophobic surface ........................................................ 27 2.3 Droplet generation ................................................................................................. 29 2.4 Experimental procedures ..................................................................................... 31 2.5 Surface tension measurement ............................................................................. 37
3. Results and discussion ................................................................................... 38 3.1 Definition ................................................................................................................ 38 3.2 Droplet impact behaviors ..................................................................................... 45 3.3 Weber number and impact behavior ................................................................... 61 3.4 Viscosity and Spreading ....................................................................................... 67
4. Conclusion ........................................................................................................ 73
5. Suggestions and Future work ........................................................................ 73
REFERENCES ....................................................................................................... 74
Appendix ............................................................................................................... 78
LIST OF FIGURES Figure 1 : Examples of characteristic outcomes from a water droplet impact on solid
surface . .................................................................................................................12 Figure 2: Sketch of a hydrophobic surface and hydrophilic surface ...............................13 Figure 3: Water droplet with 150° contact angle ............................................................13 Figure 4: Viscosity of Newtonian, Shear Thinning and Shear Thickening fluids as a
function of shear rate .............................................................................................14 Figure 5: Experimental apparatus schematic illustration ...............................................21 Figure 5a: High speed camera ......................................................................................22 Figure 5b: Light source, RPS CoolLED 100 Studio Light RS-5610 ...............................23 Figure 5c: Rainin pipette ...............................................................................................24 Figure 5d: Conduct chamber. .......................................................................................25 Figure 5e: Tokina optical lens. ......................................................................................26 Figure 6: : Self assembled monolayer made of HDFT molecules ..................................27 Figure 7: Illustration of droplet generation .....................................................................30 Figure 8: Illustration of a micropipette positioning .........................................................33 Figure 9: Camera setting at pre-focusing stage ............................................................34 Figure 10: Camera setting at experiment stage ...........................................................35 Figure 11: Illustration of record button ..........................................................................36 Figure 12: Sketch of experiment camera locations ......................................................36 Figure 13: Pendant drop schematic ..............................................................................37 Figure 14: Illustration of pendant droplet method measurement ...................................38 Figure 15: Spreading stage of a water droplet impact on a solid surface ......................39 Figure 16: Recoiling stage of a water droplet impact on a solid surface ........................40 Figure 17: Rebound stage of a water droplet impact on a solid surface ........................40 Figure 18: Illustration of contact diameter .....................................................................41 Figure 19: Illustration of rim, spire, film and capillary waves .........................................42 Figure 20: Illustration of jet ...........................................................................................43 Figure 21: Illustration of smooth rim ..............................................................................43 Figure 22: Illustration of fragmentation ..........................................................................44 Figure 23: A water droplet with D =2.6mm and v =1.45 m/s impacted on a super
hydrophobic surface ..............................................................................................46 Figure 24: A milk droplet with D =2.75mm and v =1.91 m/s impacted on a super
hydrophobic surface ..............................................................................................49 Figure 25: A 5% corn starch droplet with D =3.41mm and v =1.72 m/s impacted on a
super hydrophobic surface .....................................................................................52 Figure 26: A 5% corn starch droplet with D =3.40mm and v =1.71 m/s impacted on a
super hydrophobic surface .....................................................................................55 Figure 27: A blood droplet with D =2.93mm and v =1.81m/s impacted on a super
hydrophobic surface ..............................................................................................57
Figure 28: A blood droplet with D =3.28m and v =1.72m/s impacted on a super hydrophobic surface ..............................................................................................59
Figure 29: Spires number K vs impact velocity v of water droplet with volume 1(3.6mm±0.1mm) and volume 2(2.6mm±0.2mm) ..................................................62
Figure 30: Spires number K vs impact velocity of milk droplet with volume 1(3.4±0.16mm) and volume 2(2.5±0.15mm) ..........................................................62
Figure 31: Spires number K vs impact velocity of 5% corn starch solution droplet with volume 1(3.4±0.13mm) and volume 2(2.5±0.22mm) ..............................................63
Figure 32: Spire number K vs velocity of 15% corn starch solution with volume 1(3.3±0.18mm) and volume 2(2.4±0.18mm) ..........................................................63
Figure 33: Spire number K vs velocity of rabbit blood with volume 1(3.3±0.2mm) and volume 2(2.97±0.13mm) .......................................................................................64
Figure 34: Spire number K vs velocity of 1:1 diluted blood with volume 1(3.25±0.1mm) and volume2 (2.78±0.2mm) ...................................................................................64
Figure 35: K vs Weber number of all experimental fluids ..............................................66 Figure 36: Illustration of pinched section and bulging section .......................................67 Figure 37: Schematic of hypothetical droplet evolution with time variation ....................69 Figure 38: Time variation of spread factor .....................................................................69 Figure 39: Impact of water droplet, milk droplet and blood droplet from t0 to t8 ..............71
ABSTRACT
Conventional rheological methods such as viscometry to characterize linear
and nonlinear viscosity behavior requires an excessive amount of sample liquid,
which is practically impractical due to the time and cost constraints, for instances,
in blood, and other scarce and expensive bio-fluids. There is an urge for a handy
tool to quickly evaluate the intrinsic properties of a liquid.
In this thesis, droplet of Newtonian (e.g. water) and non-Newtonian liquids
(e.g. shear thinning blood, shear thickening starch solution) with a desired
dimension is released by a pipette from a vertical distance. Gravitational attraction
gives rise to an impact velocity, and the droplet hits a rigid hydrophobic surface
with a liquid-substrate contact angle of 150o. An experimental set up equipped
with a manual pipette, high speed camera, and substrate holder etc. is constructed
to capture the geometrical change over the sequential the impact-spread-recoil-
rebound process. Upon impact, the droplet turns into an expanding pancake
geometry with coronal spires developing over time. In extreme conditions of high
impact velocity, splashing or fragmentation is observed. The video records are
analyzed in terms of the classical dimensionless Weber number (We) which
comprises impact velocity and surface tension. Other measurements are made:
(i) duration of droplet on the substrate, and the change in contact area at droplet-
substrate interface, prior to rebounce, (ii) critical droplet dimension and impact
velocity leading to fragmentation, (iii) jet formation at rebounce, (iv) maximum
number of spires, and (v) wavelength of radial Rayleigh wave. Comparison
between Newtonian and non-Newtonian liquids are made, and non-linear
behaviors are observed. Weber number is shown to be insufficient in describing
spire formations. Non-linear viscosity, playing an indispensable role in droplet
geometric deformation, must be incorporated in droplet dynamics.
Keywords: Droplet, Spires, Non-Newtonian fluids, Shear thinning, Shear
thickening, Blood, Viscosity, Surface tension
1. INTRODUCTION
The phenomenon of liquid droplets impacting and spreading on a solid surface —
such as rain drops falling on a windshield — is ubiquitous in daily life. The
underlying mechanics has been historically appealing to many great scientists,
including the Nobel laureate Pierre-Gilles de Gennes [1]. Many excellent works
[2-7] of water droplet impacting solid surface have been documented in the
literature. Recently, how the wettability of the solid and the viscosity [8-13] of the
fluid affecting the instability [14-16] of droplet impact and heat transfer [17-21] have
drawn extensive attention from around the globe. Numerous industrial applications
have been established, based on the fundamental understanding of the physical
processes of droplet impact. Examples include cooling of hot surfaces [18, 22, 23],
injection printing [24, 25], microfabrication [26] and laser induced transfer (LIT) [27-
29]. So far most studies have focused on Newtonian, rather than non-Newtonian,
liquids. However, a wide variety of fluids encountered in science and technology—
such as biological fluids (e.g. blood, synovial fluid, saliva), adhesives, dairy
products and polymeric fluids — do not exercise classical Newtonian fluid
behavior. A Newtonian liquid is one in which the viscosity is independent of shear
strain rate at constant pressure and temperature [30]. Non-Newtonian fluids, on
the contrary, are characterized by their non-linear and time-dependent viscosity,
which is a function of [31]
1.1 Motivation
Recently, non-Newtonian bio-fluids have attracted much interest in the
scientific community, due to their wide applications in life sciences [32, 33]. For
instance, a comprehensive understanding of the rheology of non-Newtonian fluids
will facilitate the study of pathophysiology. It is logical to presume that the viscosity
of blood, for example, changes with pathologic conditions because the apparent
viscosity is determined by hematocrit, red blood cell (RBC) aggregation and
plasma viscosity, which are influenced by such factors as infections, hypertension
and diabetes [34-36]. The pathologic conditions of blood samples from virus- or
bacteria-infected patients change rapidly with time. For example, in malaria-
infected patients, the multiplication of the plasmodium parasite and its life cycle
causes a large quantity of red blood cells (RBC) burst quickly and periodically [37].
Conventionally, in order to monitor a patient’s pathologic conditions, blood samples
are taken and prepared for cytometry and observation under optical microscope,
which are time-consuming and incapable to track the transient behavior of RBC,
that is known to change rapidly within 1-2 minutes [35, 36, 38-40]. It is highly
desirable if the transient changes in blood viscosity can be empirically quantified
to identify infection and associated pathologic conditions.
In classical fluid mechanics and droplet dynamics, Weber number and
Reynolds number play an essential role in geometric changes of droplet impact on
a surface. The sequential droplet deformation during impact, spreading, recoil and
rebound can serve as indicators of surface tension, viscosity, advancing and
receding contact angles, and, albeit, the rheological properties of fluid.
Conventional methods such as viscometry require an excessive amount of sample
liquid [34, 41], which is impractical for blood and other scarce and expensive bio-
fluids. A rigorous but quick quantification of hematology and pathophysiology is
most welcome for research in biology and medical science in general.
1.2 Droplet impact on solid surface
Six characteristic morphological stages are involved when Newtonian droplets
impact a solid surface, and are discussed by R. Rioboo [42], as shown in Fig. 1.
“Deposition” on hydrophilic surfaces and “receding break-up” are related to
wettability and lie beyond the scope of this thesis. “Prompt splash”, “corona
splash”, and “partial / complete rebounce” are expected in non-Newtonian fluid
impacting on a super hydrophobic substrate with an advancing contact angle of
150o. During “corona splash”, an impacting droplet turns into a “pancake” with
uniform thickness, followed by “spires” developing at the rim, and might ultimately
fragment or splash under special circumstances. This thesis focuses on the
experimental investigation. A high-speed camera is used to perform in-situ
observation over a range of droplet dimension and impact velocity.
Figure 1: Water droplet impacts a solid surface according to Rioboo.
1.3 Super hydrophobic surface
The natural self-cleaning ability of lotus leaves is appealing to the scientific
community. The fascinating phenomenon is strongly related to micro-/nano-scale
surface roughness and hydrophobicity, and has wide industrial applications.
Related papers are voluminous in the literature. Smooth and super-hydrophobic
surfaces are used in the present study. Contact angle is determined by the
wettability of the solid surface. A hydrophobic surface has a contact angle
exceeding 90o is hydrophobic, and becomes super-hydrophobic > 130o. In
contrary, a surface with < 90o is hydrophilic as illustrated in Figure 2. . Figure 3
shows a water droplet standing on a super hydrophobic surface with ≈150o.
Figure 2: Sketch of a hydrophobic surface and hydrophilic surface[43]
Figure 3: Water droplet with with ≈150o
1.4 Existing models 1.4.1 Newtonian and non-Newtonian behavior
In fluid mechanics, the viscosity of a Newtonian liquid is a constant
independent of the rate of change of shearing strain over time, , but depends
only on temperature and pressure [44]. Conversely, a non-Newtonian fluid
exercises nonlinear viscous behavior, as its viscosity changes as a function of ,
𝜇 = 𝑓(�̇�) (1)
as illustrated in Figure 4.
Figure 4: Viscosity of Newtonian, Shear Thinning and Shear Thickening
fluids as a function of shear rate[45].
Non-Newtonian Fluids are in general categorized into four types based on
the change of viscosity: thixotropic, rheopectic, shear thinning and shear
thickening. Shear thickening liquid has its 𝜇 increasing with �̇�, while shear thinning
fluids has a monotonic decreasing 𝜇(�̇�). Should 𝜇 changes with time, the fluid is
either thixotropic or rheopectic. Table 1 summarizes the four non-Newtonian types.
Type of
behavior Description Example
Thixotropic Viscosity decreases
with stress over time
Honey – keep stirring, and
solid honey becomes liquid
Rheopectic Viscosity increases with
stress over time
Cream – the longer you whip it
the thicker it gets
Shear thinning
or pseudoplastic
Viscosity decreases
with increased stress Blood, tomato sauce
Shear thickening
or dilatant
Viscosity increases with
increased stress Corn starch solutions
Table 1: Summary of four types of non-Newtonian liquids
This study investigates a range of Newtonian and non-Newtonian fluids.
Water is the classic representative of Newtonian liquid. Milk only simulates
Newtonian, as its viscosity is fairly constant over strain rate at room temperature.
Corn starch solution is non-Newtonian shearing thickening. Here, it comprises
100% pure corn starch from local supermarket with a concentrations of 5% and
15% by mass. Rabbit blood purchased from Innovative Research serves as shear
thinning liquid. In our droplet experiments, blood samples are either as-received
or diluted with distilled water at 1:1 volume ratio. Table 2 summarizes properties
of the liquid in this study.
Table 2: Weber number and droplet initial diameter are measured from
experiments. Surface tension is measured by Fordham’s pendant drop
method [46].
1.4.2 Non-dimensional parameters
The dimensionless Weber and Reynolds number play important roles in
droplet dynamics. Weber number is a dimensionless number useful in analyzing
fluid flows where there is an interface between two different fluids, or, in the present
context, the droplet-substrate interface. They are defined by
𝑊𝑒 =𝜌𝑣2𝐷
𝜎 (2)
𝑅𝑒 =𝜌𝑣𝐷
µ (3)
Liquid Weber number
We
Droplet diameter D(mm)
Liquid density ρ(kg/m3)
Surface tension
σ(mN/m)
Distilled water 30.82~235.38 2.4~3.7 1000 72
Whole Milk 34.83~218.95 2.35~3.56 1035 60.05
5%Corn starch solution
33.46~215.23 2.28~3.53 1052.63 67.65
15% Corn starch solution
49.75~253.27 2.22~3.48 1176.47 62.34
Blood 120.48~242.01 2.84~3.50 1082.15 56.30
Diluted blood at 1:1 volume ratio
58.54~211.68 2.58~3.35 1042.7 68.05
where ρ, σ, µ are denoted as the density, surface tension, and viscosity of the
liquid, respectively, and D and the v are denoted as droplet diameter before impact,
and impact velocity, respectively. We is a measure of the relative importance of
the fluid's inertia compared to its surface tension [49], and indicates whether the
kinetics or the surface tension energy is dominant. According to the literature,
water droplet impacting on a super hydrophobic surface with We << 1, surface
tension dominates and droplet remains roughly spherical. This study considers
only We > 1. Re is the ratio of inertial forces to viscous forces within a fluid. Bhola
and Chand [47] investigated spire formation at the rim of a molten wax droplet and
asserted that the number of coronal spires given by
𝑘 =𝑊𝑒0.5𝑅𝑒0.25
4√3 (4)
Marmanis and Thoroddsen [48] investigated a variety of liquid droplets impacting
a paper surface and found k to be a function of (We0.25Re 0.5)0.7. Such model is not
not applicable to non-Newtonian fluids as expected.
1.4.3 Related models of characteristic behaviors
The dynamic behaviors of droplet impact can be described as three stages:
spreading, recoiling and rebound, which are characterized by capillary waves, rim
instability and jetting governed by different mechanisms. There are qualitative
model discussing shock wave, moving contact line, capillary wave, Rayleigh-
Plateau instability, Rayleigh-Taylor instability, air cavity, and pinch-off dynamics.
The capillary waves observed at the early spreading stage is thought to be
depending on generation of shock wave. The wavelength is a function of surface
tension and viscosity as well as droplet kinematic input such as impact velocity.
The Rayleigh-Plateau instability is related to “break-up” of a liquid jet, while
Rayleigh-Taylor instability underlies the break up of an interface between two
dissimilar fluids of different densities. The combined model is expected to be valid
in the perturbation and fragmentation of the rim of a droplet upon impact. Jet was
first observed by Worthington when he investigated a milk droplet impact in liquid
pool, and was coined “Worthington Jet”. Similar jets are found in droplet impacting
a solid surface. Air cavity dynamics and pinch-off dynamics closely related
subjects.
In this thesis, the dynamics of droplet impact, specifically rim instability, is
investigated experimentally. The results are compared with theoretical analysis
based on Rayleigh-Plateau instability. Another graduate student in our research
group, Xiao Huang, is currently building a theoretical model in this context. From
Huang’s unpublished work, the number of the spires during a water droplet impact
is given by
𝑘 = 0.9421 ∗ [log(𝑊𝑒)]4 − 0.4122 (5)
Detailed comparison between this model and the experimental results will be
discussed in Chapter 3
2. Experiments
The experimental setup and its components for this study are outlined
below, and so are the step-by-step procedures.
2.1 Experimental apparatus
Figure 5 shows the assembled homemade apparatus and the components.
Specifications are given below:
High speed camera, Edgertronic Monochrome: The high speed camera,
Edgertronic, whose exposures are able to be down to 1/200,000 seconds,
resolution settable from 192x96 to 1280x1024, ISO 400-6400 and frame
rates up to 17,791 fps (resolution dependent)
Light source, RPS CoolLED 100 Studio Light RS-5610: The RPS Studio
LED Studio Light uses a single 100 watts (energy usage) LED that produces
light equal to 1000 watts when the 8” reflector is attached to it. The light
output is adjustable yet the color temperature of the light stays a constant
daylight (5200°K). Mounts to any standard 5/8” light stand spigot. The on/off
switch is in the 3-meter power cord. Complete with 8” Bowen’s mount style
reflector that will accept a standard umbrella, shower cap style diffuser, and
protective cap.
Pipette, Rainin Classic PR-200: The volume range of PR-200 is from 20 µL
– 200 µL, and the manual increment is 0.2 µL. Accuracy of the pipette is ±
2.5 % per 0.5 µL and precision is ± 1 % per 0.2 µL.
Aluminum experimental conduct chamber: The apparatus is designed and
assembled by an undergraduate capstone group, which is made of
assembled aluminum rack and provides adjustable impact angle and impact
velocity.
Optical lens, Tokina 100mm f/2.8: This lens is a macro lens for digital
camera, capable of life-sized (1:1) reproduction at 11.8 in. (30 cm). The
lens' multi-coating matches the highly reflective silicon based CCD and
CMOS sensors in digital SLR cameras, while the optics give full coverage
and excellent sharpness on 35mm film. The focal length is 28-70mm, close
focus up to 0.7 meter, working distance is 115mm.
Figure 5: Experimental setup comprising a frame (d) with the two
platforms (A and B) and mounting fixtures for the micropipette (c), a light
source (b), and the camera-lens assembly (a and e, respectively). The
the camera-lens assembly is mounted on Platform A, and it is height and
angle adjustable. The super hydrophobic surface is placed on Platform
B. The vertical micropipette is mounted directly above the super
hydrophobic surface and is used to dispense the sample droplet.
Figure 5a: High-speed camera. The camera has a computer
interface to record the experiments at 6000 frame per second (fps).
Recording is automatically triggered.
Figure 5b: RPS CoolLED 100 Studio Light RS-5610. The LED light is
mounted on the conduct chamber (d) and provides light in case of
recording video with high fps.
Figure 5c: Rainin pipette. Micropipette is used to dispense the sample
droplets. During an experiment, the pipette tip was filled prior to
adjust the volume adjustment knob (VAK). When it was time to
dispense the droplet, the VAK was turned in the clockwise to
decreasing volume. This gradually dispenses the fluid from the pipette
tip, forming a gradually-growing droplet pendant at the end. When
then pendant reached a critical volume, it broke free from the tip, and
fell downward.
Figure 5d: Metal frame for assembly.
Figure 5e: Tokina optical lens
2.2 Preparation of super-hydrophobic surface
There are many standard ways to create super-hydrophobic surfaces made
from polymers, metals or carbon nanotubes for different purposes. In the present
work, a copper sheet is used as the substrate. All chemicals are purchased from
Sigma-Aldrich. The surface is prepared by two consecutive steps. Two main
processes are composed to make the surfaces. First, we follow the instructions
outlined in UVA super hydrophobicity manual [49] created by Backer et al. By
silver coating with nano-scale surface roughness is produced by reacting the
copper surface with silver nitrate. The silver cations (Ag+) are reduced by copper
to metal silver. The coated copper sheet is then immersed in heptadecafluoro-1-
decanethiol (HDFT) solution, resulting in a self-assembled monolayer with non-
polar molecular segments as shown in Figure 6.
Figure 6: Self assembled monolayer made of HDFT molecules[50]
Step 1: Substrate preparation
Copper sheet (2cm x 5cm) is polished using a 500-grit pad under fingertip
pressure. The residual copper and abrasive particles are wiped off using a tissue.
The plate is examined for surface roughness using an optical microscope.
Step 2: Fine polish
Polishing is repeated using grit pads of 800, 1200, 1500 and 2000 till a mirror
surface is obtained. For the purpose of easily recognizing the polished side and
facilitating capture by tweezers, pliers are used to bend up one corner of the copper
toward polished face.
Step 3: Chemical solution preparation
Four beakers are prepared and labelled. Beaker 1 is filled with 40mL of silver
nitrate (AgNO3), Beaker 2 with 40mL of De-ionized (DI) water, Beaker 3 with 40mL
of dichloromethane (CH2CL2) and 11.5mL Heptadecafluoro-1-decanethiol
(HDFT), and Beaker 4 with 40mL of dichloromethane (CH2CL2). Gentle stirring is
applied at each stage.
Step 4: Super hydrophobic surface creation
The polished Cu sheet is placed by using the tweezers in AgNO3 (Beaker 1) with
the polished side facing up for 2 minutes. The Cu sheet is then transferred to DI
water (Beaker 2) for 20 seconds and blown dry with a nitrogen gun. The Cu sheet
is then placed in Beaker 3 for 5 minutes. The sheet is finally dropped in in
dichloromethane (Beaker 4) for 20 seconds and blown dry.
2.3 Droplet generation
A micropipette is used to generate and dispense liquid droplets. The volume
adjustment knob (VAK) is set to 20 µL before filling the disposable plastic tip with
sample liquid. Two distinct methods are used to dispense a droplet. In method
(i), the plunger is depressed to eject the droplet. There is limited control over the
velocity of the droplet. In method (ii), the pipette tip is filled prior to adjusting the
VAK. When it is time to dispense the droplet, the VAK is turned in the clockwise
direction to decrease volume. This gradually dispenses the fluid from the pipette
tip, forming a gradually-growing pendant drop at the tip. When the drop reaches
a critical size, it breaks free from the tip, and falls downward. This method,
illustrated in Fig. 7, is used to ensure a zero initial velocity.
Figure 7. Droplet generation
2.4 Experimental procedures
Step 1: Experimental apparatus assembly
The pipette (Fig. 5c) is held by a fixture vertically above the super-hydrophobic
surface on platform B. The high speed camera-lens assembly is mounted on
platform A to videotape the experiments. The light source (b) is mounted next to
platform B in a direction pointing to the target plate.
Step 2: Camera and Micropipette
The height h between the micropipette tip and the super hydrophobic surface as
shown in Fig. 8. Initially h is set to be 12.7 mm (0.5 inches) from platform B. Height
of Platform B is adjustable to vary the flight distance. Height of Platform A is also
adjustable to fine tune the camera position. Both platform A and B are kept
horizontal. The working distance L between the camera and target substrate is
set to be 600 mm.
Step 3: Camera setting
Camera is computer controlled and its setting includes two stages: pre-focusing
and experiment. At pre-focusing setting stage, camera is set as shown in Fig. 9
and lens (e) is rotate to focus. The position of the camera is adjusted to make sure
the surface is placed in the center on the screen. The setting is then switched to
experiment stage as shown in Fig. 10 and lens (e) is rotate to focus again. The
ISO, light intensity and aperture ae modulated correspondingly to make sure the
brightness is proper to see the details on the substrate.
Step 4: Experimental operations of taking horizontal view videos
Method (ii) mentioned in Chapter 2.3 is used to generation droplets. The record
button as shown in Fig. 11, is trigger at the instant of droplet impact evolution
completed. The height of h is increased by adjusting platform A with an increment
of 6.35mm (0.25 in) and limited at the elevation of 140 mm (5.5 in). Experiments
of each elevation repeat 5 times.
Step 5: Experimental operations of taking 45o view videos
The camera is regulated to the positon as shown in Fig. 12 by adjusting the height
and angle of platform A. Then septs 3 and 4 are repeated.
Figure 8: Illustration of a micropipette positioning
Figure 9: Camera setting at pre-focusing stage
Figure 10: Camera setting at experiment stage
Figure 11: Illustration of record button
Fig. 12 Sketch of experiment camera locations
2.5 Surface tension measurement
Surface tension is measured by pendant drop method [46]. The shape of
the drop a result of the relationship between the surface tension and gravity. The
pendant drop geometry is presumably universal and is independent of liquid
intrinsic properties such as surface tension. A snapshot is taken at the pipette tip
and is analyzed according to the classical theory to deduce surface tension.
Fig 13: Pendant drop schematic [51]
𝑆 =𝑑𝑠
𝑑𝑒 (6)
where 𝑑𝑒 is the droplet diameter at its maximum width and 𝑑𝑠 is the width at the
distance of 𝑑𝑒 from the bottom, and 𝑆 is the ratio of 𝑑𝑠 and 𝑑𝑒 ,as illustrated in
Fig.13. Then surface tension can be found by putting
𝜎 =∆𝜌𝑔𝑑𝑒
2
𝐻 (7)
where ∆𝜌 is the density difference between the interface, 1/H is a value dependent
on S and the calculation tables from are given in Appendix.
Figure 14: Illustration of pendant droplet method measurement
3. Results and discussion
In this section, necessary terminological names are defined. Droplet impact
behaviors of Newtonian and non-Newtonian fluids are discussed. The influence of
impact velocity, droplet diameter and Weber number on the formation of spires on
the rim are investigated. Experimental results are compared to Huang’s theoretical
model. The effects of viscosity exerted on spreading are studied.
3.1 Definition To better understand the droplet impact behaviors, necessary terminological terms
are defined in this area section prior to discussion.
3.1.1 Stage, contact diameter and impact velocity
In droplet dynamics, three stages are observed during droplet impact
evolution: spreading, recoiling and rebounce. The spreading stage, as shown in
Figure 15, begins at the instance of the droplet impacting on the target surface,
and ends when the droplet reaches its maximum lateral spreading. At this stage
the droplet spreads radially, and the contact diameter increases. The recoiling
stage, as shown in Fig. 16, begins when the droplet contracts from its extent of
maximum spread. When the contact diameter is equal to 0, the droplet lifts off the
surface. This final stage of rebounce is shown in Fig. 17. The contact diameter (Dc)
is illustrated in Fig. 18. Impact velocity is given as
𝑣 = √2𝑔ℎ (8)
where ℎ is the released height denoted at Chapter 2.4.
Figure 15: Spreading stage of a water droplet impact on a solid surface.
The spreading stage begins at the instance of the droplet impacting on
the super hydrophobic surface and ends when droplet reaches its
maximum spreading.
Figure 16: Recoiling stage of a water droplet impact on a solid
surface. The recoiling stage begins when the droplet reaches its
maximum spreading, and ends at the instance when the contact
diameter is equal to 0.
Figure 17: Rebounce of a water droplet after impact. The contact
diameter equals to 0.
Figure 18: illustration of contact diameter
3.1.2 Spires, film and jet
Corona splashing is one of the six types of droplet outcomes mentioned at
Chapter 1.2. During corona splashing, the spires are found and developed from
the perturbations around the rim. The number of the spires at its maximum
spreading is counted and denoted as k. The relation between the number of the
spires k and the liquid properties is studied and discussed in subsequent sections.
The central area of the droplet where the capillary waves are found and observed
is termed the “central film”. Illustration is shown in Fig. 19. At the recoiling stage,
the droplet shoots back in the opposite direction of the droplet impact as a pillar
and this behavior is defined as the “jet”, which is shown in Fig. 20.
Figure 19: Rim, spire, film and capillary waves
Figure 20: Jet
Figure 21: Smooth rim without spires
Figure22: Fragmentation
3.1.3 Smooth rim and fragmentation
Figure 21 shows a typical droplet with small We, the rim is smoother and no
spire is observed. with smooth rim. Figure 22 shows another droplet with high We,
fragmentation with splashing is observed.
3.2 Droplet impact behaviors
3.2.1 Droplet impact behaviors of Newtonian fluids
Most research works in the literature are based upon Newtonian water. The
present study exploits water droplet impact on super hydrophobic surface. Fig. 7
consists of an image sequence of water droplet with D = 2.6mm and 𝑣 =1.45m/s
impacting on a super hydrophobic surface. It showed the successive stages of
droplet impact evolution, with time from initial impact indicated. The water droplet
was recorded from t=0 at which right before the droplet landing on the super
hydrophobic surface. The rim of the droplet was unstable, since spires were
generated around the edge. As time went on, it continued to spread and reached
its maximum spread at t =2.33ms. At the same time, the number of spires also
reached its maximum. As the water of droplet continued flowing outward from the
center film to the rim, the thickness of the central film and contact area decrease,
while the size of the spires increased. At t=3.33ms and t=4.5ms, growth of spires
resulted in spire merging and spire number decreased. During the entire process,
surface tension acted against the increase in surface area. The spires were pulled
back together by surface tension, and eventually the droplet lifted off the surface
at t =12ms.
Figure 23: A water droplet with D =2.6mm and 𝑣 =1.45 m/s impacted
on a super hydrophobic surface. Scale bar was shown at t=0. At
t=1ms, the droplet was impacting on the substrate. At t=2.33ms, the
droplet reached its maximum spreading and 16 spires were counted.
From t=2ms to t=4.5ms, corona rim was presented. At t=12ms, the
droplet was pulled together by surface tension.
Whole milk is usually taken to be a Newtonian fluid, even though it is not a
pure substance like water. This is because it does not differ appreciably from
Newtonian behavior at room temperature during shelf life. Figure 8 shows a series
of photos of a milk droplet with v =1.91 m/s and D =2.75mm impacting on a super
hydrophobic surface. Spiky and sharp spires show up around the rim when the
droplet hit the solid surface at t = 0.67ms. The number of spires is counted as 14
when the milk droplet reached its maximum spreading at t =2.5ms. It is evident
that central fluid flows radially towards the rim, reducing the thickness and contact
area. Spires merge at t = 4ms. When t = 5ms, the spires number reduces to 8. At
t =7ms, the spires retreats towards the center, as surface tension tends to minimize
the droplet surface area. At t = 9.83ms, fragmentation occurs. Milk droplet are
observed to be more stable than water, as the rim is smoother and coronal spires
are fewer.
Figure 24: A milk droplet with D =2.75mm and 𝑣 =1.91 m/s impacted
on a super hydrophobic surface. Scale bar was shown at t=0. At
t=0.67ms, the droplet was impacting on the substrate. At t=2.5ms,
the droplet reached its maximum spreading and 14 spires were
counted. From t=2ms to t=5ms, corona rim was presented. At t=7ms,
the droplet was pulled back to the center by surface tension. At
t=9.83ms, fragmentation was observed.
3.2.2 Shear thickening and shear thinning fluids
In shear thickening fluids, viscosity increases with strain rate. When shear
is applied, the fluid thickens and its behavior becomes solid-like. Two different
concentrations of corn starch solutions — sometimes called oobleck — are
investigated in this research: 5% and 15% by mass.
Fig. 25 shows a droplet of 5% corn starch solution with v =1.72 m/s and D
= 3.41mm impacting on a super-hydrophobic surface. Spires begin to appear at t
= 0.83ms. Fluid then flows radially to the rim turning into flat pancake at t = 1.67ms.
Spires are were obtuse at the tip. At t = 3.83ms, the droplet spreads to its
maximum diameter, and 16 spires are observed around the rim. Additional minor
spires protrudes from the rim and merge with the adjacent spire from t = 5.7ms to
7.3ms. At t=15ms, the droplet pulls back together by surface tension, followed by
jetting.
Figure 25: A 5% corn starch droplet with D =3.41mm and 𝑣 =1.72 m/s
impacted on a super hydrophobic surface. Scale bar was shown at
t=0. At t=0.83ms, the droplet was impacting on the substrate. At
t=3.83ms, the droplet reached its maximum spreading and 16 spires
were counted around the rim. From t=0.83ms to t=7.33ms, corona
splash was presented. At t=9.5ms, the droplet was pulled back to the
center by surface tension. At t=15ms, the droplet jetted.
Figure 26 shows the impact of a 15% corn starch droplet with 𝑣 =1.71 m/s
and D =3.40mm. Unlike water, milk and the 5% corn starch solution, the highly
concentrated corn starch droplet spreads on the solid substrate with a smooth
round rim like a bowler hat at t = 0.33ms. Perturbation on the rim emerges as
protrusions. The protrusions grow into spires since more and more fluid flows
towards the rim. Spreading of the droplet on the solid surface is out of sync with
the spire growth. When the droplet reaches its maximum spreading at t = 4ms, no
new spire is generated, but the existing spires do not develop fully until t = 5.17ms.
The spires are obtuse and rounded. The droplet remains symmetric and is
apparently more stable. After reaching the maximum contact area, the pancake
recoils and the adjacent spires coalesce. The spires do not have sufficient inertia
to detach or the ability to detach from the mother drop to form secondary droplets.
The droplet retreats due to surface tension, followed by jetting at t =13.5ms.
Figure 26: A 5% corn starch droplet with D =3.40mm and 𝑣 =1.71 m/s
impacted on a super hydrophobic surface. Scale bar was shown at
t=0. At t=0.33ms, the droplet was impacting on the substrate. At
t=4ms, the droplet reached its maximum spreading and 14 spires
were counted around the rim. At t=5.17ms, the spires were
developed completely. From t=4ms to t=7.83ms, corona splash was
presented. At t=9.67ms, the droplet was pulled back to the center by
surface tension. At t=13.5ms, the droplet jetted.
3.2.3 Droplet impact behavior of shear thinning fluids
In shear thinning fluids (e.g. blood), viscosity decreases with strain rate. In
this work, rabbit blood as received and diluted blood are investigated. Figure 27
shows impact of a blood droplet with v =1.81m/s and D =2.93mm. The droplet
spreads with a rounded and smooth rim without perturbations at t = 1ms. At t =
2.67ms, the droplet reaches its maximum spreading, and 9 spires develop at the
rim. Upon recoil at t=5.67ms and t=6.67ms, the droplet retracts radially and
capillary waves are observed on the central film. At t=14.5ms, jetting occurs.
Figure 27: A blood droplet with D =2.93mm and v =1.81m/s impacted
on a super hydrophobic surface. Scale bar was shown at t=0. At
t=1ms, the droplet was impacting on the substrate and there was no
perturbation observed on the rim. At t=2.67ms, the droplet reached
its maximum spreading and 9 spires were counted around the rim.
At t=4ms, the spires were developed completely. From t=2.67ms to
t=4.67ms, corona splash was presented. The droplet was pulled
back to the center by surface tension at t=9.67ms and jetted at
t=14.5ms.
Figure 28 shows diluted blood droplet with D =3.28mm and v =1.72 m/s. At t = 1ms,
perturbation around the rim is seen. The spires are obtuse and regular, which are
quite different from the sharp and spiky spires in milk. These spires distribute at
approximate equidistance on the rim with similar size and shape. Symmetry
persists throughout the impact-recoil process, contrasting the irregular and
asymmetric spires in water droplet. At t = 3.17ms, the droplet reaches its maximum
contact diameter with 12. At t = 6.5ms, capillary waves are observed on the central
film. At t = 19.67ms, jetting occurs. The jet is large in cross section and comprises
most of the overall mass.
Figure 28: A blood droplet with D =3.28m and v =1.72m/s impacted
on a super hydrophobic surface. Scale bar was shown at t=0. At
t=1ms, the droplet was impacting on the substrate and there were
perturbations observed on the rim. At t=3.17ms, the droplet reached
its maximum spreading and 12 spires were counted around the rim.
At t=4.17ms, the spires were developed completely. From t=1ms to
t=6.5ms, corona splash was presented. The droplet was pulled back
to the center by surface tension at t=10.67ms and jetted at
t=19.67ms.
3.3 Weber number and impact behavior
3.3.1 Velocity and spire formation
Velocity and droplet diameter are two variables that can be varied as
desired. Two different sizes of water droplets are created and released by different
pipette tips with varying heights. Figs.29-34 show the relation of number of spires
as a function of impact velocity for droplets of two different sizes. V1 and V2
represented the volume of larger and small droplets respectively. Regardless of
the fluid nature, increase in impact velocity leads to more spires. With the same
velocity, large droplets generate more spires. From Equation (2), the square of
velocity and the diameter are directly proportional to We. Higher impact velocity
and a large droplet volume trigger more perturbation and provide more kinetic
energy to the liquid to generate more spires. The number of spires is directly
proportional to We no matter the fluid involved is Newtonian or non-Newtonian.
Fig. 29: Spires number K vs impact velocity v of water droplet with
volume 1(3.6mm±0.1𝑚𝑚) and volume 2(2.6mm±0.2𝑚𝑚)
Figure 30: Spires number K vs impact velocity of milk droplet with
volume 1(3.4±0.16𝑚𝑚) and volume 2(2.5±0.15𝑚𝑚)
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5
The
nu
mb
er o
f sp
ires
k
Impact velocity v m/s
V1 Water
V2 Water
V1
V2
0
2
4
6
8
10
12
14
16
0 0.5 1 1.5 2 2.5
The
nu
mb
er o
f sp
ires
K
Impact velocity v m/s
V1 Milk
V2 Milk
V1
V2
Figure 31: Spires number K vs impact velocity of 5% corn starch
solution droplet with volume 1(3.4 ±0.13𝑚𝑚 ) and volume
2(2.5±0.22𝑚𝑚)
Figure 32: Spire number K vs velocity of 15% corn starch solution
with volume 1(3.3±0.18𝑚𝑚) and volume 2(2.4±0.18𝑚𝑚)
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5
The
nu
mb
er o
f si
pre
s K
Impact velocity v m/s
V1 5% CS
V2 5% CS
V1
V2
0
2
4
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5
The
nu
mb
er o
f si
pre
s K
Impact velocity v m/s
V1 15% CS
V2 15% CS
V1
V2
Figure 33: Spire number K vs velocity of rabbit blood with volume
1(3.3±0.2𝑚𝑚) and volume 2(2.97±0.13𝑚𝑚)
Figure 34: Spire number K vs velocity of 1:1 diluted blood with volume
1(3.25±0.1𝑚𝑚) and volume2 (2.78±0.2𝑚𝑚)
0
2
4
6
8
10
12
14
16
0 0.5 1 1.5 2 2.5
The
nu
mb
er o
f si
pre
s K
Impact velocity v m/s
V1 Blood
V2 Blood
V1
V2
0
2
4
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5
The
nu
mb
er o
f si
pre
s K
Impact velocity v m/s
V1 1:1 DilutedBlood
V2 1:1 DilutedBlood
V1
V2
3.3.2 Weber number and spire formation
A positive correlation of k(We) is expected in both Newtonian and non-
Newtonian fluids. Figure 35 shows k(We) for water, milk, blood, 1:1 diluted blood,
5% corn starch, and 15% corn starch, along with Huang’s theoretical perdition.
Curve fitting in Figure 35 shows monotonic increasing k(We) for all liquids. From
his work, k is predictable and is a function of We. Huang’s model is capable of
predicting the number of spires in water but not the non-Newtonian fluids. The
phenomenological equations of each fluid are shown below. For
Water, 𝑘 = 6 × 10−6𝑊𝑒3 − 0.0029𝑊𝑒2 + 0.547𝑊𝑒 − 18.769
Milk, 𝑘 = −2 × 10−6𝑊𝑒3 + 0.0005𝑊𝑒2 + 0.0543𝑊𝑒 − 0.5028
5% corn starch, 𝑘 = 14.011 × 𝑙𝑛(𝑊𝑒) − 56.697
15% corn starch, 𝑘 = −3 × 10−6𝑊𝑒3 − 0.0013𝑊𝑒2 + 0.0549𝑊𝑒 − 0.5028
Blood, 𝑘 = 20.453 × 𝑙𝑛(𝑊𝑒) − 99.417
Diluted blood, 𝑘 = 6 × 10−7𝑊𝑒3 − 0.0008𝑊𝑒2 + 0.279𝑊𝑒 − 12.129
It is apparently that We alone is not sufficient to predict the impact behavior,
especially the number of spires.
Figure 35: K vs Weber number of all experimental fluids
Figure 35 shows the best fits of the liquid investigated. The higher the
surface tension the more spires are generated at the same We (c.f. Table 2). It is
worthwhile to remark that the dilute corn starch solution has roughly the same
as dilute blood, and their k(We) overlap. This is also true for the concentrated corn
starch solution and milk. Such correlation is quite consistent with the Rayleigh-
Plateau instability. The surface tension–driven instability describes a stream of
fluid that breaks into smaller droplets. When a drop impacts on a solid surface,
perturbation around the rim appears as crest and valley of waves with positive and
negative curvatures in regular intervals or wavelength [52]. Liquid with higher
tends to create more spires with the same We.
0
5
10
15
20
25
0 50 100 150 200 250 300
K
We
We Water
Weber Milk
Weber Corn starch 5%
Weber Corn starch 15%
Weber Blood
Weber 1:1 Diluted Blood
Xiao' theoretical predition
Water(72,1000)
Milk(60.05 1035)
Corn starch 5%(67.6,1052.63)
Corn starch 15%(62.34 1176.47)
Blood(56.30 1082.15)
Figure 36: Illustration of pinched section and bulging section
3.4 Viscosity and Spreading
Toivakka [53] demonstrated that both and have negative influence on
initial spreading. But how they affect the impact behavior remains unclear. The
contact diameter Dc immediately after impact should be a function of time as shown
schematically in Figure 37. If two different droplets (e.g. blood and water) with the
same We impact a super-hydrophobic surface, pushes Dc(t) to the right. Higher
prolongs the contact interval. Increase in shifts the curves up as surface
tension constrains the spreading and minimizes the surface area. Figure 38 shows
lateral spreading of water, milk and blood droplets. Since it is difficult to generate
the droplets with identical initial diameter D by the pipette, instantaneous diameter
Dc is normalized with respect to D. Here D is defined to be the diameter just before
impact at to = 0. Water, milk and blood spread from to to their maximum extent at
t2 = 3.33ms, t4 = 4.17ms and t3=3.83ms. Recoil follows immediately. At t5=7.33ms,
water droplet begins to jet and is lifted off the substrate at t8=12.5 ms. Surface
flaws on the substrate cause some droplet to stick. Blood and milk droplets jetted
at t6=9 ms and t7=10.17 ms respectively, but no complete lift-off is observed. Liquid
Table 3 summarizes the liquid properties and behavior. The measurements are
qualitatively consistently with the hypothesis: (i) maximizes spreading, and (ii)
delays spreading and prolongs contact. It is remarkable that water droplets lead
to numerous coronal spires contrasting the fairly smooth rims in blood. Viscosity
does not seem to control the spire formation directly, but apparently prolongs the
contact time and the impact-spread-recoil process. Viscosity slows down the
advancing and retreating fronts. Figure 39 shows the droplet geometry as function
of time.
Figure 37: Schematic of hypothetical droplet evolution with time variation
Figure 38: Time variation of spread factor
Liquid Water Whole Milk Blood
Weber number 122.01 122.60 120.48
Reynolds number 4224.43 1691.44 1832.72
Spire number 14 10 0
Surface tension (mN/m)
72 60.05 56.30
Viscosity (cp) 1 3[54] 2.6[55]
Initial diameter (mm) 2.75 3.38 2.67
Time of maximum spreading (ms)
3.33 4.17 3.83
Time of jetting (ms) 7.33 10.17 9
Maximum dc/Do 6.79 7.29 7.62
Table 3: Droplets properties and behavior
Figure 39: Impact of water, milk and blood droplets from t0 to t8. At
t=t1, three droplets was impacting on the super hydrophobic surface.
At t=t2, water droplet reached its maximum spreading. At t=t3, blood
droplet reached its maximum spreading. At t=t4, milk droplet
reached its maximum spreading. At t=t5, water droplet started to jet.
At t=t6, blood started to jet. At t=t7, milk started to jet. At t=t8, water
droplet lifted off the surface.
4. Conclusion
Spire generation by liquid droplet impact is investigated based on the
classical model of Weber number. Our experimental data supports a positive
correlation between Weber number and the number of spires, k, in both Newtonian
and non-Newtonian fluids. A droplet impact with higher Weber number leads to
more spires at the rim. It is also found that number of spires increases with surface
tension. Comparison between theory and experiment shows that classical model
for Newtonian liquids is inadequate to predict spire formation in non-Newtonian
fluids. Viscosity affects the droplet geometric deformations during impact
evolution, and must be incorporated into the model involving Weber number.
Nonlinear viscosity prolongs the contact time with the substrate and therefore
modifies the impact-recoil process. Droplet impact provides a tool to gauge
surface tension and nonlinear viscosity in short time.
5. Suggestions and Future work
To explore the relation between liquid intrinsic properties of the fluids and
droplet deformation upon impact, it is recommended to repeat the experiments
with corn starch and blood of a wide range of concentration. New experimental
set-up with automatic volume and impact velocity control is necessary in the long
run. Surface preparation and characterization of the super-hydrophobic substrate
are necessary to minimize the statistical variation.
REFERENCES
1. De Gennes, P.-G., F. Brochard-Wyart, and D. Quéré, Capillarity and
wetting phenomena: drops, bubbles, pearls, waves. 2013: Springer
Science & Business Media.
2. Šikalo, Š., et al., Analysis of impact of droplets on horizontal surfaces.
Experimental Thermal and Fluid Science, 2002. 25(7): p. 503-510.
3. Yarin, A., Drop impact dynamics: splashing, spreading, receding,
bouncing…. Annu. Rev. Fluid Mech., 2006. 38: p. 159-192.
4. Merlen, A. and P. Brunet, Impact of drops on non-wetting biomimetic
surfaces. Journal of Bionic Engineering, 2009. 6(4): p. 330-334.
5. Lubarda, V.A., Mechanics of a liquid drop deposited on a solid substrate.
Soft Matter, 2012. 8(40): p. 10288-10297.
6. Rein, M., Phenomena of liquid drop impact on solid and liquid surfaces.
Fluid Dynamics Research, 1993. 12(2): p. 61.
7. Rioboo, R., M. Marengo, and C. Tropea, Time evolution of liquid drop
impact onto solid, dry surfaces. Experiments in Fluids, 2002. 33(1): p. 112-
124.
8. BAYER, I.S. and C.M. MEGARIDIS, Contact angle dynamics in droplets
impacting on flat surfaces with different wetting characteristics. Journal of
Fluid Mechanics, 2006. 558: p. 415-449.
9. Xu, L., et al., Contact line mobility in liquid droplet spreading on rough
surface. Journal of Colloid and Interface Science, 2008. 323(1): p. 126-
132.
10. Zapałowicz, Z., Critical contact Weber number for toluene droplets
dropping onto the heated wall surface. Experimental thermal and fluid
science, 2002. 25(7): p. 523-528.
11. Bolleddula, D.A., Droplet impact and spreading of viscous dispersions and
volatile solutions. 2011, University of Washington.
12. Raman, K.A., et al., Lattice Boltzmann simulations of droplet impact onto
surfaces with varying wettabilities. International Journal of Heat and Mass
Transfer, 2016. 95: p. 336-354.
13. Sprittles, J. and Y. Shikhmurzaev, The dynamics of liquid drops and their
interaction with solids of varying wettabilities. Physics of Fluids (1994-
present), 2012. 24(8): p. 082001.
14. Roisman, I.V., On the instability of a free viscous rim. Journal of Fluid
Mechanics, 2010. 661: p. 206-228.
15. Krechetnikov, R. and G.M. Homsy, Crown-forming instability phenomena
in the drop splash problem. Journal of colloid and interface science, 2009.
331(2): p. 555-559.
16. Roisman, I.V., K. Horvat, and C. Tropea, Spray impact: rim transverse
instability initiating fingering and splash, and description of a secondary
spray. Physics of Fluids (1994-present), 2006. 18(10): p. 102104.
17. Zimparov, V., Enhancement of heat transfer by a combination of three-
start spirally corrugated tubes with a twisted tape. International Journal of
Heat and Mass Transfer, 2001. 44(3): p. 551-574.
18. Griffith, T.S., L. Al-Hadhrami, and J.-C. Han, Heat transfer in rotating
rectangular cooling channels (AR= 4) with angled ribs. Journal of heat
transfer, 2002. 124(4): p. 617-625.
19. Zamfirescu, C. and F. Chiriac, Heat transfer measurements on ammonia
forced convection boiling in vertical tubes. Experimental thermal and fluid
science, 2002. 25(7): p. 529-534.
20. Šikalo, Š., N. Delalić, and E. Ganić, Hydrodynamics and heat transfer
investigation of air–water dispersed flow. Experimental thermal and fluid
science, 2002. 25(7): p. 511-521.
21. Xu, J., Y. Li, and T. Wong, High speed flow visualization of a closed loop
pulsating heat pipe. International Journal of Heat and Mass Transfer,
2005. 48(16): p. 3338-3351.
22. Grissom, W.M. and F. Wierum, Liquid spray cooling of a heated surface.
International Journal of Heat and Mass Transfer, 1981. 24(2): p. 261-271.
23. Pasandideh-Fard, M., et al., Cooling effectiveness of a water drop
impinging on a hot surface. International journal of heat and fluid flow,
2001. 22(2): p. 201-210.
24. Seerden, K.A., et al., Ink‐jet printing of wax‐based alumina suspensions.
Journal of the American Ceramic Society, 2001. 84(11): p. 2514-2520.
25. Derby, B., Inkjet printing ceramics: From drops to solid. Journal of the
European Ceramic Society, 2011. 31(14): p. 2543-2550.
26. Vaezi, M., H. Seitz, and S. Yang, A review on 3D micro-additive
manufacturing technologies. The International Journal of Advanced
Manufacturing Technology, 2013. 67(5-8): p. 1721-1754.
27. Willis, D.A. and V. Grosu, Microdroplet deposition by laser-induced
forward transfer. Applied Physics Letters, 2005. 86(24): p. 244103.
28. Kuznetsov, A.I., et al., Laser fabrication of large-scale nanoparticle arrays
for sensing applications. Acs Nano, 2011. 5(6): p. 4843-4849.
29. Zywietz, U., et al., Laser printing of silicon nanoparticles with resonant
optical electric and magnetic responses. Nature communications, 2014. 5.
30. Merrill, E.W., Rheology of blood. Physiol. Rev, 1969. 49(4): p. 863-888.
31. Chhabra, R.P. and J.F. Richardson, Non-Newtonian Flow and Applied
Rheology - Engineering Applications (2nd Edition). Elsevier.
32. Hassager, O., Negative wake behind bubbles in non-Newtonian liquids.
1979.
33. Debrégeas, G., P.-G. De Gennes, and F. Brochard-Wyart, The life and
death of" bare" viscous bubbles. Science, 1998. 279(5357): p. 1704-1707.
34. Akers, W.J. and M.A. Haidekker, Precision assessment of biofluid
viscosity measurements using molecular rotors. Journal of biomechanical
engineering, 2005. 127(3): p. 450-454.
35. Sochi, T., Non-Newtonian rheology in blood circulation. arXiv preprint
arXiv:1306.2067, 2013.
36. Baskurt, O.K. and H.J. Meiselman. Blood rheology and hemodynamics. in
Seminars in thrombosis and hemostasis. 2003. New York: Stratton
Intercontinental Medical Book Corporation, c1974-.
37. Schlagenhauf-Lawlor, P. and M. Funk-Baumann, PDQ Travelers' malaria.
2005: PMPH-USA.
38. Xie, S., E. Iglesia, and A.T. Bell, Effects of hydration and dehydration on
the structure of silica-supported vanadia species. Langmuir, 2000. 16(18):
p. 7162-7167.
39. McKay, M.D., R.J. Beckman, and W.J. Conover, A comparison of three
methods for selecting values of input variables in the analysis of output
from a computer code. Technometrics, 2000. 42(1): p. 55-61.
40. Vlastos, G.A., C.C. Tangney, and R.S. Rosenson, Effects of hydration on
blood rheology. Clinical hemorheology and microcirculation, 2003. 28(1):
p. 41-49.
41. Chhabra, R.P. and J.F. Richardson, Non-Newtonian flow and applied
rheology: engineering applications. 2011: Butterworth-Heinemann.
42. Rioboo, R., C. Tropea, and M. Marengo, Outcomes from a drop impact on
solid surfaces. Atomization and Sprays, 2001. 11(2).
43. Gaellen Aziz, N.D.G.a.R.M., Incorporation of Primary Amines vis Plasma
Technology.
44. Panton, R.L., Incompressible Flow. 2013: Wiley.
45. http://www.rheosense.com/applications/viscosity/newtonian-non-
newtonian, Shear stress as a function of shear rate for several kinds of
fluids.
46. Fordham, S., On the Calculation of Surface Tension from Measurements
of Pendant Drops. Proceedings of the Royal Society of London. Series A.
Mathematical and Physical Sciences, 1948. 194(1036): p. 1-16.
47. Bhola, R. and S. Chandra, Parameters controlling solidification of molten
wax droplets falling on a solid surface. Journal of materials science, 1999.
34(19): p. 4883-4894.
48. Marmanis, H. and S. Thoroddsen, Scaling of the fingering pattern of an
impacting drop. Physics of Fluids (1994-present), 1996. 8(6): p. 1344-
1346.
49. UVA_super_hydrophobicity_lab_manual.
50. Backer, K.K.D., Simple Fabrication of a Superhydrophobic Surface.
51. http://www.thermopedia.com/content/30/, Pendant drops schematic.
52. Breslouer, O., Rayleigh-Plateau Instability: Falling Jet. Project Report,
Princeton University, 2010.
53. Toivakka, M. Numerical investigation of droplet impact spreading in spray
coating of paper. in Spring advanced coating fundamentals symposium.
2003.
54. http://www.vp-scientific.com/Viscosity_Tables.htm, Viscosity tables of V&P
SCIENTIFIC, INC.
55. Viscosity Measurement of Whole Blood. Anton Paar.
Appendix