Kenneth Langley and Dr. Tadd Truscott, Department of Mechanical Engineering
Introduction
If an egg spinning on a counter-top passes through a shallow pool of milk, a thin film of milk will be drawn up the sides of the egg and sprayed on the counter-top. This phenomenon is not limited to eggs or milk. In fact, when any axis-symmetric object is spun in a shallow bath of fluid, this phenomenon occurs in which fluid flows up the object and is then ejected at the maximum radius. This phenomenon lends itself well as a pump for moving fluids from very shallow areas to other regions and can even be used to make droplets of specific sizes quickly, as opposed to using gravity and capillary tubes. Several industrial processes use this phenomenon to produce small droplets of liquid. For instance, typical off-the-shelf humidifiers use a spinning cone to draw fluid up the cone from a bath to spray small droplets that evaporate quickly, thus humidifying the air. This phenomenon is quite complex and previous research efforts have not fully explained the physical mechanisms that cause it.
Prior to the commencement of this research, there has been little investigation into the mechanisms that govern this phenomenon. In May 1998, Gutierrez [1] introduced the phenomenon and gave a brief explanation of why the phenomenon occurs using introductory physics focusing mainly on the distance a droplet travels after detachment. In May 2006, Martinez [2] furthered the findings of Gutierrez by investigating the effect of the Coriolis force on the fluid as it flows up the lower portion of a sphere. Additionally, Martinez investigated the effect of geometry and fluid viscosity on the phenomenon.
Both of these previous studies have neglected to investigate the mechanisms that govern this flow and the change in fluid ejection with increased angular velocity. Therefore, the purpose of this research is to experimentally explore the effects of fluid properties, object geometries, and angular velocities on this unique flow.
Experimental Methods
Experiments were performed to determine the effect of object size, fluid viscosity, and angular velocity on the modes of ejection and the flow rate of the fluid being ejected. In all, 4 sizes of spheres were used in the experiment with diameters of 3.5 cm, 3.8 cm, 5.7 cm, and 10.2 cm. These objects were tested in 5 different fluids: milk, water, 10% glycerin-water mixture, 20% glycerin-water mixture, and 50% glycerin-water mixture.
Experiments were conducted in the Splash Lab located in the Fletcher Building on the BYU Campus. A Parker Compumotor with a maximum angular velocity of 50 revolutions per second with a resolution of 25,000 steps per revolution was used to spin the spheres. The motor was mounted on a frame constructed from t-slotted aluminum extrusions and was allowed to move vertically through the use of a linear screw slide, which enabled control of the immersion depth of each object.
The mass flow rate was measured by capturing all of the fluid that was ejected from the sphere in one minute using a custom designed container made from clear acrylic. Since the flow rate is highly dependent on several parameters namely, immersion depth, sphere diameter, angular velocity, and fluid viscosity, measurements were taken at three fixed immersion depths, in four fluids of varying viscosity, and with three spheres of different diameters.
Images of each experiment were captured either using high-speed video or high-speed flash photography. A Photron SA3 high-speed camera with a frame rate of 1000 fps was used to capture the high speed videos, and a Canon Rebel DSLR camera was used to photograph the phenomenon in conjunction with 3 flashes with a flash duration of ~1/20,000 of a second.
Results and Discussion
The initial experiments were focused on the characterization of the modes of ejection. Four modes of ejection have been identified. As seen in Figure 1, these modes are droplets, jets, sheets, and sheet break-up. The mode of ejection is determined in large part by the angular velocity of the sphere. As the angular velocity increases, the ejection will change from droplets to jets and then to sheets, and finally the fluid will be ejected as sheet break-up.
The ejection of the fluid is a result of a force difference between the surface tension forces attempting to keep the fluid in the same body and the inertial forces due to the rotation of the sphere. The nondimensional ratio of inertial effects over surface tension effects known as the Weber number lends itself to characterizing when the different modes of ejection occur. A Weber number at the point of ejection of approximately 5 marks the transition from jets to sheets. A sheet will persist until the Weber reaches approximately 10 at which time sheet breakup will occur.
In order to find the local Weber number at the point of ejection it is necessary to know the thickness and the velocity of the fluid at that point. The velocity of the ejecting fluid was determined by measuring the streak length of particles in images from high-speed videos. As anticipated, the velocity of the fluid at the point of ejection is approximately equal to the tangential velocity of the sphere at that point. Based on this velocity and mass flow rate, the ejecting fluid varied between 15 and 30 microns thick.
In conclusion, 4 modes of ejection have been characterized: droplets, jets, sheets, and sheet break-up. The ejection mode will transition from jets to sheets when the local Weber number at the point of ejection is near 5, and the transition from sheet to sheet break-up occurs when the Weber number is near 10. Future work includes verification of the experimental results with a theoretical model that is being developed, presentation at a professional conference and preparation and submission to a scholarly peer-reviewed journal.
References
- G. Gutierrez, ”Fluid flow up the wall of a spinning egg,” American Journal of Physics, vol. 66, pp. 442, 1998.
- J. C. Martinez, ”Fluid flow up a spinning egg and the Coriolis force,” European Journal of Physics, vol. 27, pp. 805, 2006.