Tikalon Blog by Dev Gualtieri

Drip, Drip

August 6, 2018

During my childhood in the 1950s and 1960s, cable television wasn't the ubiquitous medium that's known today. There were just your few local broadcast television stations that tried to fill the many hours of the day with the limited content available. Most signed-off near midnight to the tune of the national anthem, accompanied by patriotic military images. These sign-off sequences were happily supplied by the US military as a method to promote recruitment and public funding. As a broadcast engineer for one such television station as a summer job during my college days, I watched quite a few of these.

Since advertisers were reluctant to air commercials on such marginal fare as "Queen for a Day," and "The Million Dollar Movie," the planned commercial segments were filled with public service announcements (PSAs). These included such themes as fire prevention with Smokey Bear, anti-smoking, and weeping American Indians imploring you to "keep America beautiful."

Smokey Bear, champion of forest fire prevention in the US.

The Smokey character was supplemented by the more cartoonish, Woodsy Owl in 1971.

Woodsy's goals are summarized in his two mottoes, "Give a hoot—don't pollute!" and "Lend a hand—care for the land!"

(Via Wikimedia Commons)

One such PSA of that era that caught my attention was an environmentalist spot about water conservation. It featured a dripping water faucet, and claimed that this seemingly small leakage amounted to a water waste of a gallon a day. Of course, I needed to check this myself. As astronomer, Carl Sagan, said, "extraordinary claims require extraordinary evidence."

As an experimental scientist, I should have just grabbed a gallon bottle and headed to the sink. However, I remembered one of my high school chemistry laboratory experiments in which we calibrated our eye droppers (miniature bulb pipettes). There are about 20 drops per milliliter, a quantity that depends on the surface tension of the liquid, and the orifice. The drip rate would depend on the hydraulic head. A drop per second is 3 milliliters per minute, or 90 milliliters per hour, and 2,160 milliliters in a day. A US gallon is 3,785 milliliters; so, there was some exaggeration.

Dripping faucets were a problem in the past, simply because the available gasket material, rubber, deforms over time. Today, faucet washers are made from neoprene, which is a much more resilient material. My house even has some "washerless faucets" that are made from closely fitting ceramic disks with triangular cutouts for metered water flow.

There are a few techniques to mitigate the plink-plink sound of the water drops of a dripping faucet before the washer is replaced, some of which I've done myself.[1]

• Wrap a towel around the faucet and direct the other end into the drain.
• Attach a piece of string, sewing thread, or dental floss, to the faucet so that the drip slides down the fiber into the drain.
• As above, but with an inexpensive necklace chain. The water will fill the loops in the chain to provide a smooth water path.
• Place a tall bottle under the faucet so that the water slides down the outside of the bottle.
• For a double basin sink, as the one in my own kitchen, direct the drips to slide down the basin divider.
• Submerse the faucet in a tall tumbler filled with water. The excess water from the drips will slide down the side of the container.
• Use the shutoff knob, typically positioned under the sink.

The shutoff valve solution is not recommended, since replacement of this valve or its washer is more of a problem than replacing a faucet washer.

Backjet of a water droplet after impacting a water surface.

(Wikimedia Commons image by Roger McLassus)

By now, everyone has seen at least one of the many available images of water droplets hitting a water surface, an example of which is shown above. In 1908, English physicist, Arthur Mason Worthington (1852-1916), took the first high speed photographs of impacting water droplets. This topic was of just academic interest until to advent of inkjet printing.

Whether or not a scientist tolerates the "plink" sound of a water droplet hitting basin bottom, he should still be interested in how the sound is made. The droplet is small, the gravitational energy supplied by fall from such a short height is small, but the sound is irritatingly loud and it has a fairly precise audio spectrum. Not surprisingly, you don't get research funding to study dripping faucets, so droplet sound production has only now been analyzed by a team of engineers from Cambridge University (Cambridge UK). Their research is reported in an open access paper in Scientific Reports.[2-5]

following in the hundred year tradition of Arthur Worthington, the experiment involved high speed photography of the droplet after it impacts the water. The researchers then correlated the images with the sound that's produced. As the authors state in their paper, this is the first time that modern high-speed video and audio capture techniques have been applied to this problem.[2] Says lead author, Anurag Agarwal of the Cambridge University Department of Engineering,

"A lot of work has been done on the physical mechanics of a dripping tap, but not very much has been done on the sound... But thanks to modern video and audio technology, we can finally find out exactly where the sound is coming from, which may help us to stop it."[3]

As first revealed by the Worthington photos, a droplet's impact on a water surface causes the formation of a cavity, and this cavity quickly recoils because of surface tension. The result of this recoil is a rising column of water, and the recoil is so rapid that a small air bubble is trapped underwater.[2-3] Further experiments in the few decades after that showed that a minimum drop height is required for sound production, and they indicated that sound production was associated with the air bubble.[2]

A 1959 paper by Franz did a more thorough study using hydrophone recordings synchronized to photographic images to show that the droplet's initial contact and the bubble entrainment were important to sound generation.[6] A short audio pulse was produced by impact, followed by a louder pulse after a delay as the crater forms.[6] While the data were suggestive, the photography was at too low a frame rate to reveal the physical mechanism for sound generation.[2]

Further work by Pumphrey and Crum in 1989 confirmed what Franz had discovered, and they found the underwater bubble would only form within a certain range of impact velocities for a given droplet diameter.[7] In his 1991 Master's thesis, Jacobus found a linear correlation between the sound energy emitted by a drop impact and the temperature difference between the drop and the body of water that it impacted.[2]

Some scientists are inspired by dreams, but Agarwal was inspired to this research by sleeplessness caused by a roof leak. Says Agarwal,

"While I was being kept awake by the sound of water falling into a bucket placed underneath the leak, I started thinking about this problem... The next day I discussed it with my friend and another visiting academic, and we were all surprised that no one had actually answered the question of what causes the sound."[3]

The research team used an ultra-high-speed camera, a microphone and a hydrophone to record both the audio signals and droplet shape as it impacted a tank of water.[3] They discovered that the initial splash, the formation of the cavity, and the jet of liquid produce very little sound, while the trapped air bubble produced the audible "plink."[3] The air bubble forces vibration of the water surface, and the water surface produces sound in the air above.[3] The recorded audio spectrum aligns with the theoretical natural oscillation frequency of the air bubble, and these oscillations were observed in the video record.[2]

Video clip showing the oscillation of the trapped air bubble caused by impact of a water droplet on a water surface. The acoustic wave propagates to the water surface to produce a sound in the air above.

(Portion of an ultra slow-motion video by the University of Cambridge video, via eurekalert.org.)[4]

The amplitude of the "plink" sound is only significant when the trapped air bubble is close to the bottom of the cavity caused by the impacting drop. This leads to the most efficient coupling of sound from the underwater bubble to the air.[3] Changing the surface tension of the surface, as by adding dish soap, will stop the "plink" sound.[3] The authors write that their research will enable a method for synthesis of water droplet sounds in video games and movies.[3]

Drip, Drip

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