# Chaos, Twist Maps and Big Business

##### July 26, 2004

Obscure mathematical ideas developed back in the 1980s could solve current problems of mixing fluids at the microscale, and revolutionise the technology, reports an article in Science this week (23 July 2004).

The need to mix fluids at the microscale affects a whole range of developing technologies – from inkjet printers to DNA analysis – and finding ways to do it is becoming big business. Millions of dollars have already been poured into 'lab-on-a-chip' projects, but making miniature labs is not just a question of scaling things down.

When you pour cream into your coffee via the back of a spoon, it forms a delicious layer on the top, through which you sip your coffee. Should you want to mix the layers together, however, you simply pick up the spoon and stir, creating turbulence in the fluids that causes them to mix.

But it’s a different story when the amount of fluids you are trying to mix is very, very small. Tiny volumes behave in strange ways and getting them to mix is extremely difficult. This is where a powerful mathematical idea that involves chaos theory – ‘chaotic mixing’ – becomes useful, since it provides a key mechanism for mixing at such small scales.

Professor Steve Wiggins, a mathematician at Bristol University, and his colleague Professor Julio Ottino, a chemical engineer at Northwestern University, USA, pioneered ideas of chaotic mixing back in the 1980s. Recently they stumbled on even earlier, highly abstract, ideas – the exotically named ‘linked twist maps’. These, they suddenly realised, could be applied to the problems of mixing tiny volumes.

A common design for many micromixers currently in use is a construction that has several segments, each with different geometrical characteristics. Twist maps describe the swirling motion particles undergo as they movedown the length of one segment, while ‘linked twist maps’ describe particle motion through multiple segments. As a result of their structure, Wiggins and Ottino found that linked twist maps can be designed to give exceptional mixing properties at the microscale.

This discovery has provided Wiggins and Ottino with a new method for the design of micromixers, and the potential to revolutionise the technology.

Professor Wiggins said: “Chaotic mixing is probably a long way from the thinking of those who develop new designs for mixing fluids at this scale. But this is an area where seemingly abstract mathematical work could have a direct impact on the bottom line.”

Design strategies are mainly based on a ‘trial-and-error’ procedure. This can be prohibitively expensive and negatively impact on commercial viability, due to uncertainties in the fabrication processes.

Source: University of Bristol

Explore further: Companies exploit live-streaming apps Periscope, Meerkat

## Related Stories

#### Companies exploit live-streaming apps Periscope, Meerkat

August 5, 2015

Companies have learned to use Facebook, Instagram and other social media to drum up business and now they're finding ways to exploit two new apps, Periscope and Meerkat.

#### Sapphire talk enlivens guesswork over iPhone 6

July 27, 2014

Sapphire screens for the next iPhone? Sapphire is second only to diamond in hardness scratch-proof properties, used in making LEDs, missiles sensors, and on screens for luxury-tier phones. Last year, the budget-conscious ...

#### Our latest scientific research partner was a medieval bishop

June 8, 2015

There was something unusual about our recent research collaboration on the science of light, colours and the perception of rainbows: one member of the team wrote his best science in the 1220s.

#### DNA double helix does double duty in assembling arrays of nanoparticles

May 25, 2015

In a new twist on the use of DNA in nanoscale construction, scientists at the U.S. Department of Energy's (DOE) Brookhaven National Laboratory and collaborators put synthetic strands of the biological material to work in ...

#### New retail strategy opens with Apple Watch launch

April 23, 2015

Apple Watch is coming, but don't expect long queues of people waiting to snare a limited supply of the new devices.

March 25, 2015

Facebook's Messenger app is evolving into a multitasking tool equipped to send an animated fist bump to a friend at one moment and then get a little business done in the next.

## Recommended for you

#### Team extends the lifetime of atoms using a mirror

October 13, 2015

Researchers at Chalmers University of Technology have succeeded in an experiment where they get an artificial atom to survive ten times longer than normal by positioning the atom in front of a mirror. The findings were recently ...

#### Measurements of dinosaur body temperatures shed new light on 150-year debate

October 13, 2015

Were dinosaurs really fast, aggressive hunters like the ones depicted in the movie "Jurassic World"? Or did they have lower metabolic rates that made them move more like today's alligators and crocodiles? For 150 years, scientists ...

#### With this new universal wireless charger, compatibility won't be an issue

October 13, 2015

A wireless charger that's compatible with different consumer electronics from different brands is one step closer to becoming a reality thanks to research by electrical engineers at the University of California, San Diego.

#### Quantum coherent-like state observed in a biological protein for the first time

October 13, 2015

If you take certain atoms and make them almost as cold as they possibly can be, the atoms will fuse into a collective low-energy quantum state called a Bose-Einstein condensate. In 1968 physicist Herbert Fröhlich predicted ...

#### Pebbles on Mars likely traveled tens of miles down a riverbed, study finds

October 13, 2015

While new evidence suggests that Mars may harbor a tiny amount of liquid water, it exists today as a largely cold and arid planet. Three billion years ago, however, the situation may have been much different.

#### Researchers create light emitting diodes from food and beverage waste

October 13, 2015

Most Christmas lights, DVD players, televisions and flashlights have one thing in common: they're made with light emitting diodes (LEDs). LEDs are widely used for a variety of applications and have been a popular, more efficient ...