These toys dazzle with their color and the patterns formed.
To create their beautiful displays all rely on the formation of droplets.
Droplets, especially controlling the size of droplets is of enormous technological importance:
The mist from an asthma inhaler, the paint sprayed on cars, or the fuel entering the
cylinder of a car’s engine.
To understand how engineer’s control drop size let’s start with this toy, which shows
the essentials of drop formation.
In it a narrow stream of liquid, called a “jet” flows from the opening and them
becomes circular as it flows toward the bottom of the toy.
This circle breaks off to form a “droplet.”
As you can see here the droplets are typically the same size.
This toy motivates the key scientific question: Why does a droplet form at all?
Why doesn’t a jet go forever without breaking up?
To answer that question I’ve put a small hole in this cup and will fill it with a 50/50
mixture by volume of water and glycerol, dyed green.
Glycerol is highly viscous, meaning informally that it is a “thick” liquid, so it will
slow the flow and the formation of drops.
You see a smooth jet exits, but as it travels farther from the cup, the stream gets fuzzy
. . . which you can see better in close up . . . Let’s slow this to see what occurs.
You see the smooth jet at the top, then, as the stream descends, droplets forming — the
fuzziness earlier.
. . notice that just as the liquid exits it forms a uniform cylinder, but as it descends
the cylinder’s sides “wobble,” which increases in intensity so that bulges form
and disappear until this instability, this wobble, slices the jet into drops.
The instability is caused by a liquid’s tendency to minimize its surface area, a tendency
toward the most thermodynamically stable state.
For this jetting liquid that would be a sphere rather than a cylinder.
The surface area to volume ratio of a sphere is double that of an optimized cylinder with
the same radius.
The instability forms quickly: Look at the liquid exiting the cup.
I said it was uniform, but you can now see that the “wobbling” begins soon after
exiting.
The flickering is the wobble, seen better if I zoom in and add guidelines.
. . why, though, doesn’t the cylindrical jet immediately become a sphere?
That’s because the minimization of the surface area competes with another tendency: inertia.
To see that look at one of the bulges that forms and disappears: these are, of course,
failed attempts by the liquid to form a sphere.
Notice what must happen for a sphere (a droplet) to form: some liquid must travel in the opposite
direction of the stream’s flow.
But this flow is opposed by interia, as defined by Newton’s First Law: an object at rest
stays at rest and an object in motion stays in motion with the same speed and in the same
direction unless acted on by an unbalanced force.
So, the flowing liquid keeps flowing downward, pulled by gravity, until the minimization
of surface area forces some liquid to move up by creating these bulges: upward flow occurs
because at ends of the bulge, where the stream is constricted, the pressure is higher than
in the middle, so liquid flows toward the middle.
Although those bulges are large here, recall that “wobbling”near the top: each wobble
moves a bit of liquid up, increasing as the stream descends.
Until eventually, as we see at the bottom of the stream, the surface area wins and droplets
form.
The “wobble” observed at the top of the stream suggests how engineers can create precisely
sized drops.
To create a stream with uniform drops that appear immediately we need to vibrate the
stream at a frequency near that of the “wobble.”
Watch the stream again.
. . notice that the drops form near the bottom of the screen, near the cup no drops form
. . . but, if I repeatedly tap the side of the cup, drops form soon after the stream
exits the cup.
Here’s a clever engineering application of this method to produce drops.
It’s the ink jet printers used to code packaging.
On the bottom of this almond can is a sell-by date, on the ibuprofen an expiration date,
under the cap of this soda a code used, perhaps, in a contest, and on this cleaner a serial
number.
These codes were printed by industrial-strength inkjet printers that throw ink up to an inch
as products move by at speeds up to 2,000 feet per minute.
These industrial printers, known as continuous ink jets or CIJs, create precision droplets
using “tapping” to break a jet into droplets.
Ink from a reservoir is pumped through a nozzle.
The nozzle sprays a jet of ink onto a surface — a box or a container.
The jet so powerful that the printer can print in any direction: from the top as I showed
earlier, or horizontally as shown here.
The letters or images created are composed of dots of ink.
To generate these droplets an oscillator plate — a piezoelectric crystal — vibrates the
nozzle.
This is akin to tapping the cup to break a jet into droplets.
I’ve shown the stream breaking into uniform droplets, but in practice some small droplets
called satellites also form.
To select the right size droplets, the droplets are charged by electrodes, and passed through
high voltage plates.
The larger droplets are more highly charged, so deflect more than the smaller droplets.
These satellites are collected and recycled into the ink supply.
The drops stop and start as needed.
And to create the letters some printers move the nozzle, others change the voltage to redirect
the stream, and some printers have multiple nozzles.
These commercial inkjet printers are only one example of the technological importance
of creating precisely-sized droplets, but it illustrates how all technological applications
that use droplets, rely on the minimization of surface area as the driving force to form
a droplet.
I’m Bill Hammack, the engineerguy.