Samuel Kim

Summer URG (June 25, 2018 – August 17, 2018)

Driscoll Physics Lab, Northwestern University

Abstract

According to the principle of free fall, only gravity acts upon an object in midair. However, as with all scientific principles, free fall plays out differently in practice. In my experiment, I first explored the effect of glycerol weight-percentage on the maximum spread of drops of glycerol-water released onto smooth glass from various heights. with greater spread indicating greater kinetic energy present within the drop. I found that glycerol weight-percentage is inversely related to maximum spread. Moreover, the greater the glycerol weight-percentage is, the higher the viscosity of the drop due to higher friction between drop particles and the smaller the potential spread of the drop. Next, I performed a similar experiment on colloidal suspensions. I found that colloid weight-percentage is also inversely related to maximum spread of the drop at the heights tested. However, as colloidal suspensions are non-Newtonian fluids, they lack a linear relationship between viscosity and shear stress, which results in equal spread for a dilute colloidal suspension and water, disrupting the trend of greater spread for lower colloid weight-percentage. Also, since colloidal suspensions are composed mainly of water and water has low viscosity relative to glycerol-water, colloidal suspensions show greater maximum spread than does glycerol-water at each height dropped. As a result of completing this project, I gained a first-hand understanding of how the principle of free fall plays out in real life using different concentrations of glycerol and colloids in water.

Introduction

Splashing is a meaningful area of study due to its presence in art, technology and nature. First, splash drop patterns in watercolor painting contribute to the final appearance of a painting as well as to the physical properties of the paint itself.2 In addition, changing the size and velocity of a drop of ink in inkjet printing affects the outcome of a print.1 Finally, splashing plays a central role in soil erosion by influencing the rate of erosion, thereby affecting the constitution of the ground.7

English physicist Arthur Worthington laid the groundwork for the study of splashing in the late 18th and early 19th centuries by taking photographs of drop impacts using early high speed cameras.7 In addition, the outset of Charge-Coupled Devices (CCDs) in 1969 marked the inception of electronics-based photography.6 Photographs produced through this method result from photons that convert to charge. In the current century, high speed videos of drop impacts can be analyzed frame by frame.3 These innovations in videography have led to the modern-day high speed camera, which I have been using to observe the time evolution of either a liquid or a colloidal drop impact on a glass plate.

Although there have been numerous studies of the drop impacts of pure substances, there have only been preliminary studies exploring whether a particle dissolved in a drop can alter the drop’s splash.5 Hence, I explored the question, “How does the splash of a mixture vary based on the concentration of a particle?” by comparing the spread of drops of glycerol-water Newtonian fluids and of colloidal silica suspensions. The Newtonian fluids have a linear relationship between viscosity and shear stress4, and the colloidal suspensions have silica particles distributed throughout water.

Impact velocity (Vf)

For my theoretical impact velocities, I plugged in values of h = 0.2 m, 0.3 m, 0.4 m, 0.5 m, 0.6 m and 0.65 m into the equation Vf = 2*g*h derived from the kinematic equation Vf2 = Vi2 + 2ah, where Vf is final velocity (m/s), Vi is initial velocity (m/s), a is acceleration (m/s2), and h is height (m); I plugged in Vi = 0 m/s and a = g = 9.81 m/s2. Theoretically, only height, rather than the weight of a drop, has an effect on velocity.

To obtain my measured impact velocities, I used the Main Setup (Appendix A) with the camera positioned parallel to the table surface. Using PCC, I took sideview videos of water droplets impacting the glass plate, and I released these water droplets at the heights listed above. I then converted these PCC files to Tagged Image File Format (TIFF) and opened them in ImageJ. Using the Thresholding feature, I tracked the vertical displacement of the drop by recording the y-coordinate for every frame in which the whole drop was visible and intact; the overall change in displacement over time at a particular height equaled the measured Vf at that height.

Analysis

As evidenced by the blue line of slope 1 on the Vf (measured) vs. Vf (theoretical) graph, the measured impact velocities are systematically lower than the corresponding theoretical velocities. This is due to the air resistance that causes an opposing force to the force of gravity that pulls the drop downward, lowering the overall measured impact velocities. The fact that air resistance is not factored into the kinematic equation Vf = 2*g*h leads to the higher values of theoretical impact velocities.

dmax experiment – Newtonian fluids

For this part of my experiment, I prepared pure water and glycerol-water mixtures of 60 wt% and 80 wt% glycerol in water. I took a “top view” photo of the drop and captured its maximum spread using the software application Phantom Camera Control (PCC). The drop became distorted vertically in the PCC matrix, but the drop virtually lacked horizontal distortion, meaning that I measured the horizontal spread with reasonable accuracy. I thus took five videos at six different heights for each of the three fluids; I also made sure to capture an image of a scale in order to set the proportion of my recordings.

Important

The water and glycerol-water must be sufficiently cleaned up with an appropriate procedure. During my experimentation, I had to redo my 60% and 80% data because my first cleaning procedure did not sufficiently remove glycerol from the glass plate. See Appendix C for specific instructions.

Analysis

Generally, the lower the concentration of glycerol in a glycerol-water mixture is, the greater the spread at a particular height (Figure 2). This is because glycerol has a high viscosity relative to water, meaning that there is greater friction between glycerol molecules. The concentration of glycerol in a particular drop is therefore inversely related to its potential spread at a particular height. In addition, the maximum spread (d_max) of both the 60 wt% and 80 wt% glycerol-water mixtures appear to have relatively more linear slopes overall than that of water, which has a large jump from 0.1 m to 0.2 m. This may be due to the higher cohesion of pure water at 0.1 m, meaning that the water molecules within the water drop were able to better stick together at a low height.

dmax experiment – colloidal suspensions

For the second part of my experiment, I used two colloidal suspensions with concentrations of 10 wt% and 50 wt%. Instead of collecting data a second time for water, I simply plotted my water data from the first part of my experiment against that of the data I obtained for the colloidal suspensions. I also changed the experimental setup by using an electronic pipette to release my drops, as the supply of colloids was not large enough to be pumped through a tube. Furthermore, I took two videos at the same six heights as in part one for the same reason of conserving the colloids. I used the same software to take videos and create a plot (Figure 3).

Before colloidal suspension data collection, I had to “clean” my colloidal suspension mixtures. See Appendix D for a description of this process.

Analysis

Similar to glycerol-water mixtures, the lower the concentration of colloid in a fluid is, the greater the spread at a particular height (Figure 3). However, there is a discrepancy at 0.1 m and 0.2 m, as the dilute (10 wt% colloid) suspension has greater than and about equal spread, respectively, to water at those heights. As described above, the cohesion of pure water likely explains the large jump in spread from 0.1 m to 0.2 m. Also, the fact that these suspensions are composed of water with suspended particles, rather than water mixed with another fluid makes it clear why the data as a whole for both colloidal suspensions is higher than that of the glycerol-water solutions and why the “dilute” and “water” lines intersect each other. Finally, as colloidal suspensions are not Newtonian fluids, both the “dilute” and “concentrated” lines lack a linear curve, as does the glycerol-water.

Discussion and Conclusion

“How does the splash of a colloidal suspension vary in form based on the concentration of colloidal particle?”

Generally, the higher the concentration of a particle in water, the smaller the magnitude of a splash of that mixture. Specifically, the type of particle involved affects the extent to which the magnitude of a splash is altered; that is, glycerol-water mixtures were shown to have smaller spreads than colloid-water suspensions. This is because the addition of glycerol to a mixture increases the internal friction within a mixture as a whole and thereby reduces the spread of a drop as the concentration of glycerol was raised. On the other hand, because colloids were suspended within the mixture rather than mixing uniformly throughout, the overall viscosity of the mixture remained close to that of water.

Additionally, the higher the starting height is and, subsequently, the higher the impact velocity of a drop is, the greater the spread of the drop impact. This is due to the greater amount of potential energy from the higher starting height, which overcomes the friction that characterizes the viscosity of the drop during impact and leads to a larger spread. Water mostly followed this pattern, as it has the lowest viscosity of the substances used, while the other substances showed less change in spread from height to height.

What Comes Next

There are several ways one can continue this project. In regards to the colloidal suspensions, one can start by preparing colloidal suspensions of more than two concentrations and collecting data based on the numerical values of those concentrations, rather than simply testing a “dilute” and a “concentrated” substance. One can also experiment with more than one type of colloid, as different colloids have different effects on splash.

In addition, one can replace water with ethanol in glycerol-water and colloid-water mixtures to make glycerol-ethanol and colloid-ethanol mixtures, respectively. Taking these steps may result in drops having a systematically larger impact diameter, as the high surface tension of a water drop allows it stay more intact. Finally, one can release drops at heights above 60 cm to determine the threshold at which a drop ceases to remain intact at impact..

Acknowledgements

I would like to thank Dr. Michelle Driscoll for her guidance and for providing her lab at Northwestern University, and all of the equipment and supplies needed for this experiment were provided through her lab. I would also like to thank Srishti Arora, Joey McCourt and Phalguni Shah for their instruction throughout this project.

APPENDICES

Appendix A: Materials and Setup

• Allen keys
• Chemicals
• DI water, epoxy adhesive, glycerol, Milli-Q water, silica colloids, tap water, base bath
• Chemistry lab equipment
• Analytical balance, centrifuge, electronic bath, epoxy, glass slides, kimwipes, nitrile gloves, oven, paper towels, pipettes, rubber air bladder, test tubes, transfer pipettes, ultrasonic bath, ultraviolet lamp, vials, viscometers, Vortex Genie, wax paper
• Computer software
• ImageJ, Jupyter Notebook (Anaconda), Olympus CellSens, Phantom Camera Control (PCC)
• Digital calipers
• Glass plate
• High speed cameras – large and small
• Magnetic torpedo level (bubble balancer)
• Modeling clay, plastic tubing, syringe, syringe needles syringe pump
• Nitrogen pump
• Olympus Microscope
• Optical supplies from Thorlabs, Inc.
• Angle clamps, bases, poles, post holder, posts, rail, rail carriers, scale, screws, table
• Portable LED light
• Syringe
• Syringe needles – yellow, brown, pink, orange, green, magenta
• O.D. (Outer Diameters) – measured with digital calipers
• Yellow 0.90 mm
• Brown 1.07 mm
• Pink 1.27 mm
• Orange 1.82 mm
• Green 2.11 mm
• Magenta 2.54 mm
• Tripod

Main Setup

Rail: Secure a base onto an optical rail, and install the optical rail into the table via the base, using Allen keys and screws. Then, twist a post holder into a mounting platform, secure the mounting platform into a mounting bracket onto the rail at a desired height, and tighten the screws from the side; insert and tighten a short to medium length post into the post holder to be used for the syringe needle and for the pipette tip during the drop experiments.

Light: Use a portable LED light in this experiment to light up the drop while in motion while taking videos. Rest the light against the rail upright during videos of the drops’ side view, and set the light flat on the table underneath the glass during top view videos.

Camera: Mount either the small or large camera onto the tripod by snapping the base into place, making sure the tripod is balanced. Adjust the height and angle of the camera as needed.

Syringe: Install syringe pump onto the elevated counter to maximize table space. Turn on the syringe pump, and make sure the volume is set at the volume of the syringe; adjust other settings as needed. Fill the syringe with the intended liquid for the Newtonian fluids experiments. Install this filled syringe, connect plastic tubing to the syringe, and attach a syringe needle to the other end of the plastic tubing. Stick the needle through the tiny hole of the post secured onto the rail; use modeling clay to minimize movement of the needle. Press ‘Run’ button when ready.

Drop Impact Site: Using optical bases, vertically secure two long optical posts into the table, slightly farther apart than the width of the plate. Using angle clamps, secure short poles such that they point toward one another, and slide the free ends of these poles through rail carriers used to hold up the glass plate. Insert the glass plate between the two rail carriers such that its faces are parallel to the surface the table; check this using the magnetic torpedo level balance.

Analytical balance: Each time I measured a substance or an object, I placed a plastic tub or some other container onto the weighing pan of the balance and tared it to reset the detected mass to zero. For mass measurements of the same kind (e.g. glycerol-water), I used the same container and tared each time I made a new measurement.

Appendix B: Defining terms

r0 – radius of a drop in midair

d0 – diameter of a drop in midair

dmax – maximum diameter of a drop impact

outer diameter (O.D.) – diameter of a syringe needle measured with calipers

h – height

Vf – impact velocity of drop as it impacts the glass

Appendix C: Preparing Milli-Q Water and Cleaning

Preparing Milli-Q Water

Each new day of experimentation, take a Milli-Q water bottle and empty it if contains leftover water from the day before; the water must be as contaminant-free as possible. Make sure that the resistance reading of the Milli-Q water dispenser shows 18.20 MΩ*cm; if not, press “Nonstop” until it does. Keeping a glass beaker under the dispenser, turn the wheel, and let the water run.

Place a capless bottle underneath the running water, fill it up part way, and pour out the contents. Then, fill up the bottle again, and remove it from the running water. Rinse the bottle cover, shake it off, and fasten it onto the bottle.

Cleaning Glass Plate (beginning of each use)

For each duration of time that you use the glass plate, clean it with the prepared base bath in the chemistry lab. Wearing nitrile gloves, pour some base bath on either face of the glass plate, and rub it over the glass plate completely.

Next, turn on the tap, and try to remove as much base bath as possible. The water should make a fan shape as it glides off the glass plate. Subsequently, wash the glass plate with DI water, then Milli-Q water until the plate is sufficiently clean. Finally, dry the plate using the electronic dryer so as to prevent traces of dried water droplets on the surface of the plate.

Cleaning Glass Plate (in between trials)

For experiments involving water, a simple wipe with kimwipes or a paper towel and an optional blast of nitrogen are sufficient.

If any amount of glycerol is involved, follow these instructions. Wet a paper towel with Milli-Q water, and press it down onto the substance to absorb as much of it as possible; repeat this as many times as necessary. Then, apply water directly onto the glass and dry using kimwipes; repeat until there is no trace of glycerol. Finally, use a lintless wipe to remove as much lint as possible, and as a finishing touch, blast nitrogen to blow away trace particles of lint.

Cleaning Viscometer

To clean a viscometer after use, run it several times with Milli-Q water. When all glycerol droplets have been removed, place the viscometer in the oven. Keep it in the oven until all the water evaporates from the inside of the viscometer, remove it, wait for it to cool down, and place it back into its box.

Appendix D: Preparing the colloids for experimentation

Sample Preparation

Take a fresh test tube (1) of colloid suspended in ammonia; the colloid will be floating freely throughout the mixture. Using an analytical balance, mass this test tube in a beaker and tare. Remove this test tube, and place an empty one (2) of the same size in the beaker with the cap on the edge of the weighing pan. Add Milli-Q water to this test tube until the mass reads near -0.05 g. Fasten the cap on this test tube, and add Parafilm until the mass reads 0.00 g. Then, remove the test tube, but keep the mass reading where it is at.

Open up the centrifuge cover, and insert the colloidal suspension test tube and the water test tube into opposite and equivalent holders inside. Close the cover, set the speed at around 3000 rpm, and set the time at around 20 minutes. After one round of centrifuging, the colloid will be condensed into a pellet at the bottom of (1). Open up (1), and use a pipette to remove as much ammonia as possible. Place the open test tube (1) into the beaker on the analytical balance, and place the cap on the edge of the weighing pan, as you did with (2). Fill (1) with Milli-Q water until the mass reads near -0.05 g. Then, as before, fasten the cap and add Parafilm until the mass reads 0.00 g.

Next, use the vortex genie to disperse the condensed colloidal pellet of (1), and centrifuge (1) again, using (2) to balance the centrifuge as before. Then, remove (1) and remove and replace the liquid above the colloid pellet with the same volume of water. Repeat this process until there is barely any trace of ammonia smell in the the fluid.

Once you have used the vortex genie on (1) for the last time, float (1) in the ultrasonicator bath. Keep it in the bath for a total of two hours, but replace the water with cold DI water every thirty minutes. Also, never leave the bath on right before you leave the lab. Once this step is finished, let (1) settle overnight.

The next day, remove 10 mL of the top part of (1) and relocate it to another test tube (3) of the same volume. Mix up (3) using the vortex genie. Take 10 μL from (3) and relocate to a microcentrifuge tube (4). Then, dilute (4) by adding 1000 μL of water. Parafilm (4) and mix using the vortex genie.

Microscope Slide Preparation

Using tweezers, take a capillary tube and lower it into the microcentrifuge tube (4) so that it absorbs diluted colloidal suspension. Then, center this capillary tube onto a glass microscope slide and use epoxy to adhere the ends of the capillary tube onto the slide, resulting in a prepared slide. Then, insert the prepared slide under the ultraviolet lamp to cure the epoxy for 90 seconds. The slide is ready for examination under the microscope.

Take the prepared slide and secure it above the objective lens of the microscope with the capillary tube on the bottom face of the slide. Turn on the microscope, the microscope control panel, and the LED light, and open up the Olympus cellSens software. Have the magnification initially set at 10X, and adjust the light to maximum brightness such that there are no red spots on the screen. Move the microscope platform in the y-direction until you find an edge of the slide. Then, starting with the coarse adjustment knob and ending with the fine adjustment knob, adjust until the edge of the slide is in focus; make sure that the coarse magnifier does not come into contact with the objective.

Once the edge of the slide is in focus, keep moving in the y-direction (either up or down) into the slide interior until you see tiny moving particles—these are the colloids. Once you zone in on the colloids, increase the magnification to 20X, using either the adjuster on the bottom side of the microscope or the control panel; using both options, the highest possible magnification is 80X. Turn up the light accordingly, as a greater amount of light is needed to illuminate a smaller field of vision to an adequate visibility.

When you achieve desired magnification, lighting and focus, you can take snapshot or a video of the particles visible in Olympus cellSens. However, if you see that many colloidal particles are stuck together, you will have to sonicate test tube (3) again and repeat the procedure of diluting it, preparing another microscope slide, and examining it through the microscope until the proportion of large particles is relatively small. When this is the case, (3) can be used for the colloidal drop experiment.

Since you will be using two different concentrations for the colloidal drop experiment, you will need to weigh out the mass percentage of colloid for the concentrated suspension. First, place wax paper onto an analytical balance and tare. Then, place a glass slide onto the wax paper and tare. Use a pipette to transfer some colloidal suspension onto the glass slide, and take note of the mass (1). Next, insert the glass slide with wet colloidal suspension into the oven, leaving the analytical balance as it is. When all moisture has evaporated from the slide, remove the slide from the oven and place it back onto the wax paper, taking note of the mass (2). Subtracting (2) from (1) results in the mass of moisture evaporated (3). Divide (2) by (3), and obtain the concentration of the colloidal suspension. Now, you can dilute this fluid to prepare another specified concentration of colloidal suspension.

Appendix E: Code Written and Programs Used

Using Jupyter Notebook to make plots

Jupyter Notebook is a platform that operates Python code. All plots in this report were created using Jupyter Notebook. Coding conventions for Python can be found on https://matplotlib.org.

Taking videos using Phantom Camera Control (PCC)

First, press Capture button and then Current Session Reference. Then, adjust Image Range as needed. Make an initial recording of a scale appropriately positioned in the frame. Then, for each subsequent drop recording, press Analyze while also pressing Run on the syringe pump with proper timing.

Tracking Displacement of Drop Using ImageJ

First, set a scale to the video in ImageJ using a snapshot of a scale taken with PCC. Then, load a video onto ImageJ. In the Duplicate menu, select Process → Image Calculator → Divide → Create New Window; 32-bit float.

Next, scroll through the video and stop at the first frame containing the whole drop. Under the Image menu, click Adjust Brightness and select Auto. Then, click on the Wand Tool, and under Enable Thresholding, adjust the thresholding indicator until the interior of the drop is red and there is no red outside the drop.

Exit the thresholding tool, click on the interior of the drop, and press Ctrl-M; notice that the y-coordinate of the center of mass of the drop has been recorded. Go to the next frame and press Ctrl-M again, and repeat this process until the the last frame with the drop intact has been reached (i.e. a frame in which the drop has not yet impacted the glass). Using all of the y-coordinates obtained, input them into Python code, and take the line of best fit to find the impact velocity for a particular height.

Appendix F: Camera Usage

Depending on availability, either use the large or small camera. Using the correct mount, set up the camera on the tripod so that the legs are balanced and stable. Connect the USB cable from the camera to the computer server, and plug the camera into a power socket.

On Phantom Camera Control (PCC), several settings should be remembered:

Frame rate is the frequency at which frames appear in Hertz.

Exposure time is the amount of time the camera’s shutter is open when taking a photo or video. The maximum exposure time is the reciprocal of the frame rate; if the exposure time is too high, information gets cut out from the matrix. Exposure time has an inverse relationship with sample rate.

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