Project OverviewThe goal of this project was to characterize the behavior of droplets on the inside and outside of open tubes under various gravity conditions with the help of simulation software. Various starting topologies (Fig. 2) were used with a droplet pinned at the end of an open tube. The bond number was increase while holding contact angle constant. We were able to determine conditions under which several distinct topologies could be expected and create a “regime map” for the inside and outside of tube ends (Fig. 1).

Fluid Surface Energy Simulations ● Simulations were performed using Surface

Evolver-Fluid Interface Tool (SE-FIT®). This software uses Ken Brakke’s surface energy minimizing software called Surface Evolver2.

● The fluid surface is represented as a simplicial complex3, i.e. a mesh of points and line segments where connections are made only at vertices as seen in the figure below.

AcknowledgementsThank you to the Oregon Space Grant Consortium, Dr. Mark Weislogel, Dr. Yongkang Chen, Marc Wasserman, Jacob Brauer, Josh Mak, Parker Southwick, Tara Prevo, and Zachary Reed.

Oleg Krishcko

THE TOPOLOGY AND STABILITY OF DROPS AT OPEN TUBE ENDS

Applications● Such fluid configurations are common in

applications from fuel tank filling to pipetting and are particularly of interest in a variety of g environments: Earth, Moon, Mars, spin stabilized spacecraft, low-g spacecraft such as the ISS, etc.

● Fluid system designs may need to take such configurations into account especially in low-g since droplet size becomes very large.

Conclusion and Future Work● These regime maps could be used to determine

expected topologies at various bond numbers which are useful for fluids system design in various gravitational environments (Earth, Moon, Mars, Low-g spacecraft, etc.)

● Some areas, such as where topologies intersect, need refining.

● Bond numbers should also be changed from near unstable values downward in order to observe potential hysteresis in the topology transitions.

● We also plan to run experiments to verify these results and observe some of these interesting topologies.

Topology Regime Maps

Tube Ending Starting Topologies

Bond Number and Contact AngleBond number is a quantified look at how gravity affects a system that would normally be dominated by capillary forces1. Contact angle is the angle between the fluid surface and the wall it is in contact with, as shown below to the right.

This research was supported in in part through NASA/Oregon Space Grant Consortium.

PARTNER

Topology Transition (example)Changes in topology are observed when bond number is increase for certain contact angles. The example below shows a transition from annular interior droplet to interior plug for a contact angle of 50° when the fluid volume is large relative to the radius. This case is not shown in the regime map above since it does not include other topologies of interest, but serves as a good visual example of the topology change in the tube end.

Bond Number Increasing

ReferencesYongkang Chen, Mike Bacich, Cory Nardin, Albert Sitorus, Mark M. Weislogel. The Shape and Stability of Wall-Bound and Wall-Edge-Bound Drops and Bubbles. Microgravity sci. technol. XVII-4, 2005.K. A. Brakke. The Surface Evolver. Experimental Mathematics, 1:141–165, 1992. The manual and code are available at http://www.susqu.edu/facstaff/b/brakke/.Mark M. Weislogel, Yongkang Chen, et al. at Capillary Fluidics Lab, Portland State University. The manual and code are available at https://www.se-fit.com/

FIGURE 1. These graphs show the various topological regimes that a droplet on the end of an open tube may be expected to be in for a given bond number and contact angle. The left graph shows regimes for droplets on the inside of open tubes, the right graphs is for the a droplet on the outside of an open tube. On earth, these configurations are small since the gravity term in the bond number is large, however, In low-g environments these droplets can be very large.

Bond Number (Bo) Contact Angle (𝜭)

FIGURE 2. Side and top views for various starting topologies in SE-FIT. Blue mesh face represents the fluid surface, the vertical lines represent the tube walls.