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Dynamic Surface Tension on the Microsecond Timescale: Thermal Inkjet Printing Applications
by
Madeline Wilson
A THESIS
submitted to
Oregon State University
University Honors College
in partial fulfillment of
the requirements for the
degree of
Honors Baccalaureate of Science in Chemical Engineering
(Honors Scholar)
Presented December 3, 2015
Commencement June 2016
2
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AN ABSTRACT OF THE THESIS OF
Madeline Wilson for the degree of Honors Baccalaureate of Science in Chemical Engineering
presented on December 3, 2015. Title: Dynamic Surface Tension on the Microsecond Timescale:
Thermal Inkjet Printing Applications .
Abstract approved: ______________________________________________________
Willie Rochefort
This project explores the relationship between microsecond-timescale dynamic surface
tension (DST) and measurable thermal inkjet printing parameters. Dynamic surface tension
affects many aspects of printing, including printing speed and ink drop shape. In addition to this,
DST is a physical input parameter for HP’s in-house computational fluid dynamics program. HP
does not currently have a way to measure DST on the 10-microsecond timescale. The
relationship between DST and measurable firing parameters has not been previously investigated
within HP. The knowledge gained from this project could lead to a new, innovative way to
predict microsecond-timescale DST.
This project had two objectives. The first was to establish the relationship between dynamic
surface tension and measurable pen fluid refill parameters. The second was to test the hypothesis
that microsecond timescale DST is correlated to measurable firing frequency parameters of a
fluid and can be used to predict dynamic surface tension on the 10-microsecond timescale.
A series of calibration fluids with known surface tensions and viscosities was created. Turn-
on energy and frequency response were tested using HP Inc. (Corvallis) baseline data tools.
Experimental results suggest that F1ss was logarithmically correlated to dynamic surface tension.
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Key Words: dynamic surface tension, DST, surface tension, thermal inkjet, printing
performance, surface tension measurement, microsecond surface tension
Corresponding e-mail address: [email protected], [email protected],
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©Copyright by Madeline Wilson
December 3, 2015
All Rights Reserved
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Dynamic Surface Tension on the Microsecond Timescale: Thermal Inkjet Printing Applications
by
Madeline Wilson
A THESIS
submitted to
Oregon State University
University Honors College
in partial fulfillment of
the requirements for the
degree of
Honors Baccalaureate of Science in Chemical Engineering
(Honors Scholar)
Presented December 3, 2015
Commencement June 2016
7
Honors Baccalaureate of Science in Chemical Engineering project of Madeline Wilson presented
on December 3, 2015.
APPROVED:
Willie Rochefort, Mentor, representing Chemical Engineering
Liney Arnadottir, Committee Member, representing Chemical Engineering
Dan Gardner, Committee Member, representing HP Inc.
Rob Pugliese, Committee Member, representing HP Inc.
Toni Doolen, Dean, University Honors College
I understand that my project will become part of the permanent collection of Oregon State
University, University Honors College. My signature below authorizes release of my project to
any reader upon request.
Madeline Wilson, Author
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ACKNOWLEDGMENTS
I would like to thank Dan Gardner, my manager at HP, for giving me the opportunity to work
on challenging and meaningful problems and for making this University Honors College
Thesis/HP collaboration possible. In addition to this, I am very appreciative of Dan’s advice on
technical communication and presentation skills.
A huge thank-you to Rob Pugliese, my HP mentor, for his incredible amount of patience and
technical knowledge. I am extremely grateful for Rob’s support throughout this project,
beginning with my initial idea and extending throughout experimentation and results. I certainly
would not have accomplished nearly as much without Rob’s help and advice. I’d also like to
thank Rob for taking the time to provide feedback, suggest improvements, and answer my
endless questions. I am very fortunate to have Rob as a co-worker and mentor.
Thanks to Dr. Skip Rochefort for serving as my OSU thesis mentor. Dr. Skip has been an
integral part of my engineering education (from high school outreach to college graduation!). Dr.
Skip has also provided me with a foundation in the fundamental engineering concepts used
throughout this project, especially heat transfer and fluid flow.
Thanks to Dr. Liney Arnadottir for serving as a thesis committee member, introducing me to
surface chemistry during my first-year summer internship, and teaching mass transport. I am
very thankful for the time Dr. Arnadottir has spent helping me to further my engineering
knowledge.
Thanks to my coworkers at HP, especially Erik Torniainen and Larry White for knowledge
and guidance, and Andrew Arndt and Brenda Dickey for instrumentation assistance. I’d also like
to thank my fellow HP summer 2015 interns William Livernois and Tiago dos Reis for their
collaboration.
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And, of course, so much thanks to my family and friends. In particular, I’d like to thank my
parents Tom and Kathleen. Without their support, none of this would have been possible.
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TABLE OF CONTENTS
ABSTRACT ....................................................................................................................................3
BACKGROUND ..........................................................................................................................11
Overview ....................................................................................................................................11
Thermal Inkjet Printing (TIJ) Functionality and Testing ...........................................................12
Static and Dynamic Surface Tension .........................................................................................15
Surfactants and Diffusion Limited Solutions .............................................................................16
Experiment Design .....................................................................................................................17
Calibration Fluid Development ..................................................................................................18
MATERIALS AND METHODS ................................................................................................20
RESULTS AND DISCUSSION ..................................................................................................22
Experimental Surface Tensions ..................................................................................................22
Measured Viscosities ..................................................................................................................24
Calibration Fluid Turn-On Energies ..........................................................................................25
Logarithmic Fitted Model ..........................................................................................................26
Predictive Model ........................................................................................................................27
CONCLUSIONS AND FUTURE WORK .................................................................................28
APPENDIX A ...............................................................................................................................29
Data Summary Tables ...............................................................................................................29
F1ss Data Tables .......................................................................................................................30
Dynamic Surface Tension Summary Tables .............................................................................32
APPENDIX B ...............................................................................................................................37
Frequency Response Graphs .....................................................................................................37
APPENDIX C ...............................................................................................................................46
MATLAB Data Importing and Predictive Model Scripts.........................................................46
MATLAB Figure Formatting Function ....................................................................................47
MATLAB Curve Fitting Toolbox .............................................................................................48
WORKS CITED...........................................................................................................................49
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BACKGROUND
Overview
Dynamic surface tension (DST) is an important physical property of inks used in thermal
inkjet (TIJ) printing because it affects printing speed. Firing frequency (defined as the number of
ink drops jetted onto the page per nozzle per second) is dependent on the physical properties of
the printed fluid, including DST. Refill behavior (characterized by how fast ink in a printhead
refills after printing) is related to the firing frequency and is also dependent on physical fluid
properties.
Dynamic surface tension is an input parameter for Hewlett-Packard’s internal computational
fluid dynamics program (CFD3), which is used to simulate ink flow through printheads. CFD3
has been in development since the 1980s and is a powerful computational tool with the capability
to model three-dimensional fluid flow for thermal inkjet printing applications. However, CFD3’s
limitations include differences between simulated and experimental data and required physical
input parameters that are difficult or impossible to measure. Improved DST knowledge would
increase CFD3’s accuracy earlier in R&D cycles and potentially reduce costs associated with the
physical design process.
This project had two objectives. The first was to establish the relationship between dynamic
surface tension and measurable pen fluid refill parameters. The second was to test the hypothesis
that microsecond timescale DST is correlated to measurable firing frequency parameters of a
fluid and can be used to predict dynamic surface tension on the 10-microsecond timescale.
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Thermal Inkjet Printing (TIJ) Functionality and Testing
Thermal inkjet (TIJ) printheads are microfluidics MEMS devices composed of firing,
control, and data circuitry, fluidic firing chambers, and fluidic channel routing. Figure 1 shows a
scanning electron microscope (SEM) printhead cross-section for a single HP TIJ firing chamber.
Under steady-state conditions, the nozzles and firing chambers are filled with ink. During firing,
an electrical current passes through a resistor at the firing chamber base and is dissipated as heat.
Heat causes the ink inside the firing chamber to vaporize and expand through the nozzle. During
refill, ink flows though the routing channels into the firing chamber for the next firing event.
This project involves two relevant printing tests: turn-on energy (TOE) and frequency
response. The TOE is the minimum energy supplied to the firing resistor required to eject a drop
Figure 1. Printhead cross-setion. Ink flows through silicon channels. An electrical
current is passed through the thin-film resistor to vaporize the ink. The ink bubble
expands and is ejected through the nozzle onto the page.
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of ink from the firing chamber. The TOE test is performed by supplying a range of energy values
to the firing resistor, firing ink drops onto a scale, and recording the drop weight. Once the
energy decreases past a certain value, the drop weight steeply decreases (Figure 2). This lowest
energy value is called the “turn-on energy” since it is the minimum energy required to print.
The second test measures the firing frequency response of the pen. “Firing the pen” is
equivalent to “printing an ink drop,” but instead of printing the drop onto paper, the ink is ejected
onto a carefully calibrated scale. Drop weight vs. firing frequency (measured in kHz, or
thousands of drops per second) is recorded. The frequency response provides information on
Figure 2. An example turn-on energy curve. A range of energy values is supplied to the printhead
and the resulting drop weights are recorded. The value at which the drop weight sharply decreases
is the minimum turn-on energy (about 0.88 μJ for this pen).
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refill behavior, characterized by how fast the ink can flow through printhead channels and how
much time is required before the next drop can be printed. An example frequency response curve
is shown in Figure 3. F1ss, a directly measurable quantity, can be obtained from the frequency
response. F1ss is related to the meniscus of the ink droplet before it is ejected from the printhead.
It occurs when the drop meniscus starts to bulge between firing events. F1ss can be determined
graphically from test data and is indicated on Figure 3.
Figure 3. An example frequency response curve produced by firing the printhead at a
range of frequencies and recording drop weight. F1ss occurs when is marked with a red
dashed line. F1ss provides information on refill and firing behavior.
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Static and Dynamic Surface Tension
All intermolecular interactions are identical for atoms or molecules in a pure bulk fluid.
Cohesive (like) forces are distributed equally among molecule. Surface molecules have fewer
identical neighbors on which to distribute their intermolecular forces, resulting in increased force
on remaining neighbors. This causes an interfacial pressure difference between the fluid and its
surroundings and results in a meniscus (Jovanovic). This molecular configuration contributes to
the phenomena known as surface tension. Surface tension is defined as the force required to tear
along a row of surface molecules, as shown in Figure 4.
Surface tension is a measure of the relative strength between like intermolecular forces within
the fluid and unlike intermolecular forces at the fluid/surroundings interface. Surface tension is
essentially a measure of how tightly molecules stick together.
Static surface tension occurs when a fluid is at equilibrium with its surroundings, such as
when it is at rest. This is different from dynamic surface tension, which is a function of time and
Force/Length
Figure 4. Surface molecules exhibit different intermolecular behavior
than bulk molecules because they have fewer identical neighbors.
Surface tension can be visualized as the force needed to tear a row of
molecules across a given length.
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occurs when fluid is not at equilibrium. Composite inks experience dynamic surface tension
during printing.
Surfactants and Diffusion Limited Solutions
Surfactant molecules are used to reduce static surface tension and are composed of two parts:
a nonpolar hydrocarbon tail and a polar head. Figure 5 shows the structure of sodium stearate, a
generic surfactant molecule.
Most HP inks are water-based. Water has high surface tension due to hydrogen bonding,
which occurs when a hydrogen atom is attracted to a highly electronegative atom. Since the
hydrocarbon tail of the surfactant is nonpolar, it does not want to interact with polar water
molecules. The surfactant molecules combat this by diffusing to the fluid surface and adsorbing
at the air/fluid interface. This creates a thin layer of surfactant molecules on the surface of the
fluid. The surfactant molecules physically orient themselves in between the water molecules and
O O-
Na+
Nonpolar Tail Polar Head
Figure 5. Sodium stearate (soap) – an example surfactant molecule. Sodium
stearate is not a surfactant used in HP inks, but is shown here to demonstrate
the general molecular structure.
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decrease the strong intermolecular forces on the fluid surface. Surfactant molecules disrupt
intermolecular forces on the surface of the fluid, not within the fluid itself.
However, surfactant molecules take time to reach the surface of the fluid (Liao). A
conservative diffusion time estimate for a surfactant molecule is 0.1 seconds (Pietryzk). Since
the thermal inkjet printing timescale is approximately 10 microseconds, surfactant molecules do
not have time to reach the ink drop’s surface between firing events. Because of this, surface
tension measurements are diffusion limited. This means that the static and dynamic surface
tensions of most inks are different (Figure 6).
Experimental Design
The long-term goal is to develop a model that predicts dynamic surface tension as a function
of F1ss. This project takes the first step towards that goal by investigating the relationship
between F1ss and dynamic surface tension using simple, controlled fluids with known physical
properties. It is important to understand the behavior of simplified fluids (as demonstrated in this
project) before continuing to more complex fluids.
Figure 6. Surfactant molecules are mixed within the surrounding fluid for dynamic surface
tension (left) . This is what occurs to the surfactant molecules in an ink drop during printing.
For static surface tension (right), the surfactant molecules have positioned themselves on the
surface of the fluid, reducing surface tension.
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These simple calibration fluids differ from complex fluids (such as composite inks) because it
is possible to determine both their static and dynamic surface tension. Since surface tension is a
controlled variable, it is possible to analyze unambiguously how surface tension affects F1ss.
The fluid surface tensions (equal static and dynamic) ranged from 28 to 54 dynes/cm, which is
representative of real ink surface tensions.
For this project, fluid viscosity variations were minimized to isolate surface tension effects on
F1ss. However, fluid composition differences resulted in a viscosity range of approximately
12%, which indicates the fitted curve is valid within this viscosity range. F1ss values for each
fluid were determined from frequency response data obtained using Corvallis HP baseline data
tools. Experimental details are described in the Materials and Methods section of this report.
Calibration Fluid Development
It was required that the calibration fluids had approximately equal static and dynamic surface
tensions and constant viscosities. Surfactants could not be used to adjust surface tension because
their diffusion timescale is greater than the 10-microsecond TIJ printing timescale. The fluid
mixtures were composed of deionized water and 1-propanol (Vazquez, Alvarez, and Navaza).
1-propanol (Figure 7) was chosen because of its structure, polarity, and miscibility with water.
1-propanol is the longest single hydroxyl, hydrocarbon-chained alcohol that is completely
miscible with water. Its nonpolar structure is long enough to disrupt the strong intermolecular
forces between water molecules but, in combination with the polar hydroxyl functional group on
the end of the molecule, it is small enough to miscible with water at all concentrations.
19
Adding surfactant to fluid changes surface molecular interactions. Adding alcohol changes
molecular interactions within the fluid. It was expected that adding 1-propanol to water would
result in approximately equal static and dynamic surface tensions since the mixture would not be
diffusion limited. Verification was done with a Kruss BP2 bubble pressure tensiometer (Kruss).
The BP2 tensiometer has the capability to measure surface tension on a minimum timescale
of 10 milliseconds using the Young-Laplace Equation (equation 1). This equation relates the
internal gas bubble pressure (p) to the bubble’s radius of curvature (r) and surface tension (σ):
𝑝 =2𝜎
𝑟
The solutions were tested on the range of 10-1000 milliseconds. Although this is greater than
the timescale of interest for this project, the BP2 was used to help determine whether or not the
surface tension of the calibration fluids was time-dependent. If the surface tension did not change
over the 10-1000 millisecond timescale, change on shorter timescales was unlikely. This
assumption could have been a source of error if 1-propanol behaved like a surfactant instead of a
fluid mixture, but this is unlikely based on the structure of 1-propanol.
Figure 7. 1-propanol molecule. Used to decrease surface tension of water/alcohol
mixtures. The polar hydroxyl group enabled complete solubility with water. The
hydrocarbon portion disrupted hydrogen bonding within fluid mixtures, lowering the
surface tension.
(1)
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MATERIALS AND METHODS
Materials
Deionized water
1-propanol (Sigma Aldrich)
Scales, hot plates, glassware, stir bars, pipettes, and fumehoods from HP research and
development chemistry laboratory (Corvallis Building 3, Lower)
Kruss BP2 Bubble Pressure Tensiometer
Anton-Paar 500 Density and Sound Measurement Device
Double-Wall Brookfield DV-I+ Viscometer
HP Printheads (9 nanogram target drop weight, noncircular bore)
Pen filling instrument in HP’s Quest Laboratory (Corvallis Building 3, Upper)
Baseline data collection tools in HP’s pen testing area (Corvallis Building 8, Lower)
Methods
Calibration fluids were prepared by mixing deionized water with 1-propanol. 1-propanol
concentrations ranged from 2.5 to 20 weight percent (Table A1, Appendix A). Equal dynamic
and static surface tensions were verified with the Kruss BP2 bubble pressure tensiometer (Figure
9, Results and Discussion). Surface tensions were measured multiple times at surface ages
between 10 and 1000 milliseconds and were averaged for each fluid (Tables A1 and A3,
Appendix A). Fluid viscosities (55°C) were tested with a Brookfield DV-I+ viscometer (Figure
10, Results and Discussion).
Pens were filled with calibration fluids using the vacuum tool in Building 3 Quest Lab. Turn-
on energy and frequency response (NDrop) tests were performed using Building 8 drop weight
characterization tools. Two pulses were applied. Precursor pulse width (length of first voltage
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application time) was 0.3 microseconds. The second pulse width was 0.9 microseconds. Dead
time between pulses was 0.07 microseconds. A curve was fitted to the data using Microsoft
Excel.
22
RESULTS AND DISCUSSION
Surface tension decreased with added 1-propanol. Experimental surface tension was similar to
previously published data (Vazquez, Alvarez, and Navaza). Figure 8 shows surface tension vs.
weight percent 1-propanol. See Tables A1 and A2, Appendix A, for recorded data.
Static and dynamic surface tensions were approximately equal. Figure 9 shows surface
tension vs. time for the water/1-propanol mixtures. For comparison, a real ink (Nemesis K) is
included on the graph. The real ink exhibits changes in surface tension over time, but the
calibration fluids had constant surface tension. All calibration fluid surface tension variations
were well within the tensiometer’s range of error (+/- 2 dyne/cm). See Tables A1 and A3,
Figure 8. Surface tension vs. weight % 1-propanol. Surface tension decreased as 1-
propanol percentage increased. This was expected based on previously published data by
Vazquez et al.
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Appendix A, for data. Tensiometer readings on the 10-15 microsecond timescale were at the
Kruss instrument’s lower limit, which could have been a source of error. Slight decreases in
surface tension over time could have been another source of error but were likely not large
enough to significantly affect F1ss results.
Replicates for the 7.5% 1-propanol solution were collected to ensure tensiometer
repeatability. Each trial was very similar to the others. The average surface tension difference
between the three replicate trials was 0.1 dyne/cm (much less than the tensiometer’s range of
error, 2 dyne/cm). Figure 10 shows surface tension vs. time for these replicates. Tables A1.3 and
Figure 9. Surface tension vs. time for water/1-propanol mixtures. Surface tensions were
essentially constant over time, unlike the surface tension of a real ink (shown on graph above).
real ink (dynamic surfactant behavior)
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A4 (Appendix A) shows tabulated results.
Figure 10. Tensiometer repeatability data. Experimental surface tension vs. time for 7.5% 1-
propanol/water solutions. The average surface tension difference was less 0.1 dyne/cm (much
less than the tensiometer’s range of error, 2 dyne/cm). For all replicates, the start-time to end-
time surface tension change was less than 1 dyne/cm.
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Experimental viscosity variations (measured with a double-wall Brookfield DV-I+
Viscometer) were within 12%. The range of calibration fluid viscosities was much smaller than
the viscosity range of typical inks to minimize viscosity effects on F1ss. Experimental viscosities
are recorded in Table A1, Appendix A. Figure 11 shows calibration fluid viscosity vs. surface
tension. Viscosity variations were likely due to instrumental noise and did not appear to show a
clear trend in relation to surface tension.
Turn-on energies (TOE) were within the range of normal aqueous inks. Figure 12 shows TOE
vs. surface tension. All TOE values were calculated using Drop Weight 2008 software installed
on baseline data tool computers (Table A1, Appendix A). The slight variation in TOE values
could have been a source of error since lower TOE values indicate lower ink vaporization
Figure 11. Experimental viscosity (measured at 55° C) vs. surface tension for
calibration fluids (circular markers). Viscosity was essentially constant among fluids
for the purpose of this project (within 12%). Solid line references average viscosity.
Square markers indicate pure fluid viscosities (deionized water and 1-propanol).
26
temperatures. However, TOE differences were small in comparison to surface tension
differences and likely had only minor effects on F1ss.
Figure 13 shows F1ss as a function of surface tension. Vertical error bars are two-sided 90%
confidence intervals on F1ss. Horizontal error bars are two-sided 90% confidence intervals for
surface tension. Surface tension variation was minimal, so horizontal error bars are negligibly
small for most of the fluids. It appeared that F1ss and surface tension were logarithmically
correlated. The fitted curve had the form shown in equation 2. The R2 value was 0.95, indicating
a strong correlation between F1ss and dynamic surface tension for the calibration fluids. Figure
13 shows that F1ss and surface tension are correlated for the calibration fluids.
𝐹1𝑆𝑆 = 24 ∙ 𝑙𝑛(𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛) − 66
Figure 12. Turn-on energy vs. surface tension. Calculated by Drop
Weight 2008 software installed on baseline data tool computers. All
TOE values were within the normal range of aqueous inks.
(2)
27
The largest source of error was likely due to graphically estimating F1ss from experimental
drop weight data. Missing or plugged printhead nozzles may have contributed to experimental
noise. Graphical F1ss estimations are shown in Appendix C.
To predict surface tension from F1ss, water is included as a data point to reflect the behavior
of very high surface tension fluids. Surface tension is graphed on the y-axis and F1ss plotted on
the x-axis. Figure 14 shows the predictive experimental model. Two different fluids are included
to assess the accuracy of the model: Puffer ink and Nemesis ink (Table A1.2, Appendix A). At
55˚C, Puffer’s viscosity is approximately 1 cp and Nemesis ink’s viscosity is approximately 1.4
cp. The exact dynamic surface tension of both inks are unknown. Puffer’s static surface tension
is 29 dyne/cm and Nemesis’s static surface tension is 45 dyne/cm. Dynamic surface tension
Figure 13. Surface tension vs. F1ss. Solid line indicates fitted logarithmic curve.
Vertical error bars show 90% confidence intervals on F1ss. Horizontal error bars show
90% confidence intervals for surface tension. The R2 value of 0.95 indicated a strong
correlation between F1ss and surface tension.
28
should be higher than static surface tension for both inks, but static surface tension is included on
the graph as a relative reference point. The model does not appear to accurately predict the
dynamic surface tension of Nemesis ink, but may be somewhat closer for Puffer ink. This is
likely explained by viscosity differences between calibration fluids and inks since the viscosity
of Puffer ink is closer to the viscosity range of the calibration fluid. A solution to these
differences might include creating a series of surface tension vs. F1ss curves by preparing more
controlled calibration fluids with varied viscosity ranges.
Figure 13. Surface tension vs. F1ss for dynamic surface tension prediction. Water is included to
reflect refill behavior of high-surface tension fluids. Static surface tensions for Puffer and Nemesis ink
are included as reference points. True dynamic surface tension for both inks is unknown, but is higher
than listed static values. The model does not appear to accurately predict dynamic surface tension for
Nemesis ink, but may be closer for Puffer. This is likely due to viscosity differences since Puffer’s
viscosity is closer to that of the calibration fluids. Calibration fluid viscosities ranged from 0.83 to
0.93 at 55˚C. At this temperature, Nemesis’s viscosity is approximately 1.4 cp and Puffer’s is 1.0 cp.
surface tension=a∙eb∙F1ss+c
a=0.0006467, b=0.3607, c=31.73
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CONCLUSIONS AND FUTURE WORK
Surface tension and F1ss appeared to be logarithmically correlated for the experimental
calibration fluids. However, the fitted model did not accurately predict dynamic surface tension
for fluids outside of the calibration fluid viscosity range. The next steps in this project will be to
create more controlled calibration fluids with different viscosity ranges, measure F1ss in the
same manner described previously, and test whether the more complex model is able to
accurately predict dynamic surface tension for fluids with varied viscosities.
30
APPENDIX A
Experimental Data
1-Propanol Surface Tension F1SS F1SS 90% CI Surface Tension 90% CI Turn-On Energy Viscosity
Approx. Weight % dyne/cm kHz kHz dyne/cm µJ cp
2.5 53.5 29.1 0.73 0.04 0.898 0.89
5 45.7 28.2 1.15 0.09 0.887 0.88
7.5 40.5 24.9 0.73 0.05 0.872 0.84
10 38.2 24.1 0.78 0.06 0.877 0.84
12.5 34.1 20 0.34 0.08 0.852 0.83
15 31.4 18.5 0.4 0.06 0.841 0.87
17.5 31.2 16 1.96 0.37 0.837 0.91
20 28.8 15.4 0.73 0.16 0.827 0.93
Summary Table
Fluid Viscosity (55˚C) Surface Tension (approx.)
cp dyne/cm
Water 0.5 72
Nemesis Ink 1.4 45+
Puffer Ink 1.0 29+
Replicate # Avg. Surface Tension Standard Deviation Range
dyne/cm dyne/cm dyne/cm
2 40.0 0.29 0.91
3 40.0 0.28 0.92
4 39.9 0.26 0.85
Overall Standard Deviation Overall Range of Avgd. Surface Tensions
dyne/cm dyne/cm
0.06 0.10
Table A1.1. Experimental data summary table. Surface tensions obtained from Kruss BP2 Bubble Pressure Tensiometer and are averaged over 10-1000 millisecond time range (see Table A3 for raw data). F1ss values are averages of multiple trials (see Table A2 for details). Confidence intervals (90%) are two-sided. Viscosity obtained from Brookfield DV-I+ Viscometer (55 °C).
Table A1.2. Fluids used to assess model accuracy – physical property data.
Table A1.3. Replicate Summary for 7.5% 1-Propanol
31
Trial F1ss (kHz)
1 28.5
2 28.5
3 30
4 29.5
St Dev 0.75
Average 29.1
90% CI 0.73
2.5% 1-Propanol
Trial F1ss
1 29.5
2 30
3 27.5
4 26
5 28
6 28
St Dev 1.44
Average 28.2
90% CI 1.15
5% 1-Propanol
Trial F1ss
1 25.5
2 24
3 25.5
4 24.5
St Dev 0.75
Average 24.9
90% CI 0.73
7.5% 1-Propanol
Table A2. F1ss data. All F1ss values in kHz. All confidence intervals are two sided. See Appendix C for graphical F1ss estimations.
32
Trial F1ss
1 23.5
2 25
3 24
4 23
5 25
St Dev 0.89
Average 24.1
90% CI 0.78
10% 1-Propanol
Trial F1ss
1 20
2 18.5
3 19
St Dev 0.76
Average 19.2
90% CI 0.34
12.5% 1-Propanol
Trial F1ss
1 19
2 18.5
3 18.5
4 18
St Dev 0.41
Average 18.5
90% CI 0.40
15% 1-Propanol
Trial F1ss
1 15
2 15.5
3 16
4 16
5 16.5
6 13.5
7 15
St Dev 0.99
Average 15.4
90% CI 0.73
20% 1-Propanol
33
Time (ms) ST (dyne/cm)
10.03 71.7
12.63 72.4
15.63 72.3
17.45 72.0
24.84 71.9
31.19 71.9
39.36 71.8
49.54 71.8
62.26 71.8
78.4 71.8
98.6 72.0
120.07 71.9
150.93 72.0
190.11 72.1
239.21 72.2
301.19 72.2
378.36 72.2
476.76 72.2
599.9 72.2
755.76 72.2
953.28 72.3
1007.96 72.3
Avg 72.1
Range 0.67
St Dev 0.21
90% CI 0.09
Water (Calibration)
Table A3. Dynamic surface tension data collected from Kruss BP2 Bubble Pressure Tensiometer. All surface tension values in dyne/cm and times in milliseconds.
34
Time (ms) ST (dyne/cm)
9.93 53.8
9.98 53.7
10.39 53.8
15.78 53.7
19.8 53.5
25.41 53.6
31.16 53.5
39.55 53.6
49.39 53.5
58.62 53.5
78.84 53.5
108.12 53.5
123.53 53.4
153.46 53.5
190.31 53.5
239.16 53.5
300.46 53.6
378.36 53.5
476.89 53.5
599.7 53.5
754.91 53.5
956.35 53.5
Avg 53.5
Range 0.37
St Dev 0.10
90% CI 0.04
2.5% 1-Propanol
Time (ms) ST (dyne/cm)
9.99 46.19
10.06 46.16
12.45 46.16
15.69 45.92
19.8 45.79
24.79 45.75
26.14 45.75
39.26 45.65
49.58 45.72
62.23 45.59
69.73 45.62
98.62 45.55
119.87 45.55
150.81 45.52
189.76 45.49
272.65 45.49
327.69 45.52
380.06 45.52
476.57 45.55
599.57 45.55
755.99 45.52
956.31 45.55
Avg 45.7
Range 0.70
St Dev 0.22
90% CI 0.09
5% 1-Propanol
35
Time (ms) ST (dyne/cm)
9.92 40.6
10.05 40.5
12.47 40.7
13.41 40.7
19.75 40.7
24.87 40.6
30.42 40.5
39.54 40.5
49.49 40.5
62.61 40.5
78.34 40.4
99.46 40.4
114.61 40.4
151.08 40.4
190.59 40.4
244.57 40.4
300.89 40.4
380.3 40.3
476.59 40.3
603.57 40.4
756.64 40.3
954.04 40.3
Avg 40.5
Range 0.44
St Dev 0.12
90% CI 0.05
7.5% 1-Propanol
Time ST
10.09 38.59
12.5 38.53
15.66 38.50
19.69 38.46
22.72 38.36
31.26 38.33
39.23 38.29
50.2 38.29
57.93 38.23
71.89 38.20
98.57 38.16
120.15 38.20
146.32 38.16
190.35 38.13
241.36 38.16
301.6 38.10
380.42 38.13
478.31 38.16
603.57 38.10
757.87 38.13
951.09 38.13
1000.79 38.13
Avg 38.2
Range 0.50
St Dev 0.15
90% CI 0.06
10% 1-Propanol
36
Time (ms) ST (dyne/cm)
9.91 34.5
9.92 34.5
12.43 34.5
15.66 34.3
19.68 34.3
24.75 34.2
31.34 34.2
39.33 34.1
49.42 34.2
62.35 34.1
63.06 34.1
109.73 34.1
119.88 34.0
151.06 34.0
218.05 34.0
240.93 34.1
304.31 34.0
380.74 34.0
478.02 33.9
605.93 33.9
758.99 33.9
968.34 33.9
Avg 34.1
Range 0.67
St Dev 0.20
90% CI 0.08
12.5% 1-Propanol
Time (ms) ST (dyne/cm)
9.97 31.8
10.07 31.7
12.42 31.7
15.66 31.7
19.66 31.6
24.82 31.6
31.23 31.6
39.53 31.6
50.2 31.5
62.48 31.5
78.56 31.4
98.64 31.5
119.76 31.3
153.63 31.4
190.25 31.4
270.09 31.3
301.13 31.3
379.52 31.3
477.28 31.4
605.13 31.3
759.07 31.4
952.1 31.3
Avg 31.5
Range 0.44
St Dev 0.15
90% CI 0.06
15% 1-Propanol
37
Time (ms) ST (dyne/cm)
9.94 32.6
10.01 32.5
11.59 32.4
13.52 32.2
19.83 32.0
24.96 31.9
29.42 31.8
39.43 31.7
49.54 31.5
62.3 31.3
78.4 31.1
99.49 30.9
121.77 30.8
155.04 30.7
207.46 30.6
239.7 30.4
343.61 30.3
379.74 30.2
478.35 30.2
604.53 30.1
754.84 30.0
957.04 30.1
Avg 31.2
Range 2.54
St Dev 0.88
90% CI 0.37
17.5% 1-Propanol
Time (ms) ST (dyne/cm)
9.93 29.4
9.98 29.3
11.41 29.2
14.29 29.2
17.77 29.1
24.75 28.9
27.39 29.0
39.56 29.0
49.43 28.9
62.56 28.9
79.22 28.8
99.72 28.8
120.43 28.8
151.45 28.7
190 28.6
238.75 28.5
300.94 28.4
379.02 28.4
515.75 28.2
603.09 28.3
758.41 28.2
960.05 28.2
Avg 28.8
Range 1.19
St Dev 0.37
90% CI 0.15
20% 1-Propanol
38
Time (ms) ST (dyne/cm)
9.92 40.6
10.05 40.5
12.47 40.7
13.41 40.7
19.75 40.7
24.87 40.6
30.42 40.5
39.54 40.5
49.49 40.5
62.61 40.5
78.34 40.4
99.46 40.4
114.61 40.4
151.08 40.4
190.59 40.4
244.57 40.4
300.89 40.4
380.3 40.3
476.59 40.3
603.57 40.4
756.64 40.3
954.04 40.3
Time (ms) ST (dyne/cm)
10.6 40.6
11.6 40.6
15.1 40.4
19.3 40.3
23.9 40.2
29.5 40.1
37.5 40.0
47.7 40.0
59.8 39.9
74.3 39.9
95.5 39.8
119.2 39.8
149.5 39.8
190.9 39.7
239.6 39.8
304.8 39.8
385.9 39.7
489.5 39.7
622.3 39.7
800.8 39.7
1003.8 39.7
Table A4. Dynamic surface tension data collected from Kruss BP2 Bubble Pressure Tensiometer for 7.5% 1-propanol replicates. All surface tension values in dyne/cm and times in milliseconds.
39
Time (ms) ST (dyne/cm)
10.4 40.6
11.7 40.4
15.1 40.4
18.9 40.3
23.5 40.2
29.6 40.1
38 40.1
47.7 40.1
59.3 39.9
74.7 39.9
93.4 39.8
120.4 39.8
149.2 39.8
193.1 39.8
240.1 39.8
303.4 39.7
384 39.7
492.7 39.7
624.9 39.7
796.6 39.7
1005.1 39.7
Time (ms) ST (dyne/cm)
10.1 40.5
12.1 40.4
14.8 40.5
18.9 40.2
24.6 40.1
30.5 40.0
37.4 40.0
47.3 40.0
58.9 39.9
74.7 39.9
95.7 39.9
119 39.8
150.6 39.9
191.8 39.8
238.9 39.8
303 39.8
383.3 39.7
489.9 39.7
621 39.7
797 39.7
1007.4 39.7
40
APPENDIX B
Frequency Response Graphs (generated with Drop Weight 2008 software on drop weight tools
in Corvallis)
Estimated F1ss values are shown by orange lines on the graph. F1ss was generally chosen as the
“valley” of the concave region on the graphs. For all graphs, the y-axis is drop weight in
nanograms and the x-axis is firing frequency in kilohertz. F1ss estimation was likely the largest
source of error for this project. Graphically estimating F1ss values can be subjective. Care was
taken to consistently estimate F1ss for each fluid. Note that all graphs are rotated 90° to better fit
on the page.
41
Dro
p w
eig
ht
(ng)
vs.
fir
ing
freq
uen
cy (
kHz)
fo
r 2
.5%
1-p
rop
ano
l/w
ater
mix
ture
42
Dro
p w
eig
ht
(ng)
vs.
fir
ing
freq
uen
cy (
kHz)
fo
r 5
% 1
-pro
pan
ol/
wat
erm
ixtu
re
43
Dro
p w
eig
ht
(ng)
vs.
fir
ing
freq
uen
cy (
kHz)
fo
r 7
.5%
1-p
rop
ano
l/w
ater
mix
ture
44
Dro
p w
eig
ht
(ng)
vs.
fir
ing
freq
uen
cy (
kHz)
fo
r 1
0%
1-p
rop
ano
l/w
ate
rmix
ture
45
Dro
p w
eigh
t (n
g) v
s. f
irin
g fr
equ
ency
(kH
z) f
or
12
.5%
1-p
rop
ano
l/w
ater
mix
ture
46
Dro
p w
eigh
t (n
g) v
s. f
irin
g fr
equ
ency
(kH
z) f
or
15
% 1
-pro
pan
ol/
wat
erm
ixtu
re
47
Dro
p w
eigh
t (n
g) v
s. f
irin
g fr
equ
ency
(kH
z) f
or
17
.5%
1-p
rop
ano
l/w
ater
mix
ture
48
Dro
p w
eig
ht
(ng)
vs.
fir
ing
freq
uen
cy (
kHz)
fo
r 2
0%
1-p
rop
ano
l/w
ate
rmix
ture
49
APPENDIX C
MATLAB script used to import surface tension data
% Madeline Wilson % Summer/Fall 2015 % Data import for Curve Fitting Toolbox
% import surface tension and F1ss from Tables 1 and 2 data=xlsread('forplot'); surface_tension=data(:,1); F1ss=data(:,2); % CI=data(:,3); % two-sided 90% confidence interval % open MATLAB's Curve Fitting Toolbox cftool
MATLAB script used to create predictive surface tension model
% import data from previously run script thesis.m surface_tension=data(:,1); F1ss=data(:,2); % plot the data figure plot_experimental=plot(F1ss,surface_tension,'bo');, grid set(plot_experimental(1),'MarkerEdgeColor','k','MarkerFaceColor','r'); xlabel('F1ss (kHz)') ylabel('Surface Tension (dyne/cm)') % custom equation (exponential) from Curve Fitting Tool a=0.0006467; b=0.3607; c=31.73; x=[5:0.001:35]; y=a.*exp(b.*x)+c; hold on plot_trendline=plot(x,y,'LineWidth',2.3); ylim([20 90]); xlim([10 35]); legend('Experimental','Fitted Curve','Location','northwest') fnicefig fnicefig
50
MATLAB function used in above script to format figure
function fnicefig % Dr. K. Levien, CHE 461 S2015, Oregon State University % A function to make a Simulink or MATLAB Figure "nice" for copying. % Set size of axis tic labels and axes thickness and plot lines.
set(0,'ShowHiddenHandles','on')
set(gca,'LineWidth',2,'FontName','Times New Roman','FontSize',14, ... 'GridLineStyle','-'), grid
% Set all line thicknesses to 2. h1 = findobj(gca,'Type','line'); set(h1,'LineWidth',2)
% Set xlabel, ylabel and title font name and size. h2 = get(gca,'Xlabel'); set(h2,'FontName','Calibri (Body)','FontSize',14) % h3 = get(gca,'Ylabel'); set(h3,'FontName','Calibri (Body)','FontSize',14) % h4 = get(gca,'Title'); set(h4,'FontName','Calibri (Body)','FontSize',14)
set(0,'ShowHiddenHandles','off')
51
MATLAB curve fitting toolbox screenshot
52
Works Cited
Jovanovic, Goran. "Surface Tension Forces I." Transport Phenomena I. Oregon State University,
Corvallis. Oct. 2014. Lecture.
"Bubble Pressure Tensiometer." Web. 20 Nov. 2015.
http://www.kruss.de/services/education-theory/glossary/bubble-pressure-tensiometer/>.
Levien, Keith. “fnicefig.m.” Process Control. Oregon State University, Corvallis. Spring 2015.
MATLAB code.
Liao, Ying-Chih. “Estimating Effects of Surfactant Redistribution on Drop Formation in Thermal
Inkjet Process.” Hewlett-Packard. Unpublished internal document. Web. 30 July 3015.
Pietrzyk, Joe. “Designing to F1ss: Part 1.” Hewlett-Packard. Unpublished internal document. Web. 30
July 2015.
Vazquez, Gonzalo, Estrella Alvarez, and Jose M. Navaza. "Surface Tension of Alcohol + Water from
20 to 50 Degrees C." Journal of Chemical & Engineering Data 40.3 (1995): 611-14. Web. 30
July 2015.
