Handling Editor: Evelyn Sander

 

Viscosity movie: a big hit on YouTube

Robert Deegan,
Department of Physics and Center for Study of Complex Systems,
University of Michigan

 

On the morning of May 5, 2004 the web server for the Center for Nonlinear Dynamics (CNLD) was farked. To be "farked" is to be overwhelmed by hits from surfers following a link posted on Fark.com. Overnight the CNLD server received over 50,000 hits, and was paralyzed by the load. The link at CNLD was to a video made by me, Florian Merkt, and Harry Swinney of pattern formation in a vibrated cornstarch solution.

This video was prepared as an entry to Annual Gallery of Fluid Motion competition. At the 2003 Division of Fluid Mechanics meeting the submissions were judged, and mine was found wanting. Disappointed I returned to Texas, put the video on my webpage, and forgot about it until the morning of May 5. The video has since acquired a life of its own. Sometime in 2006 I first learned of YouTube when a friend told me that my video was playing there. The video has been uploaded to YouTube multiple times (my personal favorite is the "blues" version), and has been viewed over 1.5 million times.

Cornstarch is a granular material with grains on the order of 10 microns. When mixed with water it forms a solution that shear thickens, i.e. its viscosity increases with shear rate. For a highly concentrated solution this effect is highly pronounced. Over a narrow window in shear rate the material practically solidifies. (If you have never experienced this yourself, I highly recommend it. You probably already have cornstarch sitting in your kitchen. Mix it with a little water, and stir.) The solution featured in the video is far more dilute than this, and exhibits only a tenfold increase in viscosity.

A vibrated layer of cornstarch in water exhibiting holes. Image by F. Merkt, R.D. Deegan, D. Goldman, E. Rericha, and H.L. Swinney [1].

Our video shows the phenomenon of holes and fingers in a vibrated cornstarch solution. (I recommend watching the video before continuing as it does far better justice to the phenomena that my written words will.) In our experiments a container of this fluid is vibrated vertically. Any vertically vibrated liquid above an acceleration threshold develops surface waves. These waves were first observed by Faraday, and have since been extensively studied for their intrinsic interest and as a model pattern forming system. Using cornstarch adds an extra wrinkle to this scenario: applying a large perturbation to the surface produces a hole, a cylindrical void from the liquid surface down to the bottom of the container that persists indefinitely. This behavior is in striking contrast a Newtonian fluid. Consider for example a cavity created by the impact of an object with a liquid. For a Newtonian fluid the cavity collapses, and all traces of the impact eventually disappear. For a cornstarch solution the application of vibrations stabilizes the cavity so that it remains open indefinitely.

A vibrated layer of cornstarch in water at the onset of delocalization of a hole. These photographs were taken every 0.9 seconds. Time increases from left to right and top to bottom. Image by F. Merkt [1].

Holes are examples of dissipative solitons. A dissipative soliton is a localized state like its classical analogue but is sustained by the input of energy rather than nonlinear focusing. An important distinction from the classical soliton is that dissipative solitons do not require special initial conditions to form. The notion of dissipative soliton is gaining traction in the scientific and mathematical literature, and many examples are now known such as in laser systems, reaction‐diffusion systems, granular materials (see [2] for a recent review). Holes are not the only nor the most popular feature that appears in a vibrated cornstarch solution. As the acceleration is increased, the holes lose stability, and a finger‐like protrusion begins growing on the rim of the hole. The protrusion continues to grow, reaches a maximum height, and falls over. The remnant of this finger seeds the growth of another, and soon the entire surface becomes a writhing mass. The popularity of the video is due to this phenomenon. A surprising number of viewers think it is faked.

The video has inspired a number of people to do their own experiments, and post them on YouTube. I receive a dozen or so requests a year for information on how to duplicate the experiment, and I've now started a collaboration with the San Francisco Exploratorium based on this experiment. Though I now cringe when I hear my clunky narration on the video and feel awkward when I am introduced as someone with a million hit YouTube video, the popularity of the video on YouTube has been a pleasant windfall for me both personally and professionally.

References

[1]		F. Merkt, R.D. Deegan, D. Goldman, E. Rericha, and H.L. Swinney, "Persistent holes in a fluid," Phys. Rev. Letters. 92 184501 (2004).
[2]		N. Akhmediev & A. Ankiewicz, Dissipative Solitons, Springer, New York, 2005.