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November 3, 2011

One apparent selling point of ketchup is its thickness, which is indicated by the slowness of its pouring out of the bottle.[1] This quality was used in an effective television commercial for Heinz Ketchup that featured the song, "Anticipation," by Carly Simon.[2] Seeing that commercial inspired my wife and me to make a midnight run to the local burger joint. I don't think the ketchup (or is it, catsup?) there was Heinz. The scientific instrument that's used to measure things such as the slowness of pouring of ketchup is a rheometer, and the science of flow is called rheology.

As I wrote in a previous article (The S-Curve, August 1, 2011), flow has been considered to be an important physical principle since the time of the Greek philosopher, Heraclitus of Ephesus (c. 500 BC). Heraclitus' philosophy is usually summarized by the expression, παντα ρει (everything flows), that Heraclitus did not himself say. This expression is contained in the logo for the The Society of Rheology.

The Roman philosopher, Lucretius (c. 99 BC - c. 55 BC), wrote about rheology in his book, De Rerum Natura (On the Nature of Things),[3-4]
"We see how quickly through a colander
The wines will flow; how, on the other hand,
The sluggish olive-oil delays: no doubt,
Because 'tis wrought of elements more large,
Or else more crook'd and intertangled. Thus
It comes that the primordials cannot be
So suddenly sundered one from other, and seep,
One through each several hole of anything."

This section of text also reveals Lucretius' belief in atomism, and his explanation comes quite close to the actual mechanism for some macromolecules.

Quite a few centuries later, the remarkable physicist, Isaac Newton, proposed his theory of viscosity in the Principia,[5-6]
"The resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another."

Viscosity is the scientific term for Newton's "lack of slipperiness."

Using a colander as a rheometer, as described by Lucretius, is close to the truth. Some rheometers function by measuring the time for fluid to flow through a pipe or capillary. My wife used this type of rheometer in an undergraduate research project. Other rheometers examine the force transmitted through the fluid from a moving surface to another surface. There are high-tech variations on both these methods.

Although the viscosity of industrial products can be examined on a batch basis by such laboratory instruments, there's much advantage to making measurements on materials as they are being processed, in real time, so that manufacturing conditions can be made immediately to improve product yield. There's also an advantage in making measurement devices very small to prevent generation of too much waste.

Scientists at the University of Sheffield's Department of Chemical and Biological Engineering have collaborated with mathematicians in their School of Mathematics and Statistics to develop a new type of microrheometer. A description of the device has been published in the latest issue of Measurement Science and Technology.[7-8]

Collaboration with mathematicians was essential, since the accurate measurement of fluid properties depends a lot on the interaction between the fluid and the measurement device. Newtonian flow, in which the shear stress vsstrain rate curve is linear, is an idealized case that's rarely found in practice. Polymers and mixed colloidal fluids are non-Newtonian.[8]

Examples of non-Newtonian flow are blood in arteries and veins and inkjet printing.[8] To get accurate measurements of these, you need to solve what's called an inverse problem; that is, your sensor is giving you some numbers, and you need to relate these to viscosity. Says Julia Rees of Sheffield's Department of Applied Mathematics, a co-author of the journal paper,
"We can produce equations to measure a liquid's total viscosity, but the rheology of most liquids is very complicated. Instead, we look at properties in a liquid that we can measure easily, and then apply maths to calculate the viscosity. The sensor device we have developed will be able to make these calculations for companies using a straightforward testing process."[7]

As can be seen in the figure, the agreement between the calculated and measured values is excellent. The device can be scaled to extremely small dimensions, and it can be etched into a microchip. Nanofluidic devices are useful for measurement of small biological specimens of just a few microliters. Scaling to lower dimension has another beneficial effect. The large surface to volume ratios in microfluidic channels leads to large viscous friction effects. These inhibit turbulence, making the flow more laminar and more predictable.[8]

University of Sheffield Microrheometer

Predicted and measured velocity magnitude profiles of the microrheometer.
The agreement shows that the sensor output can be related to the actual viscosity.

Image: Julia M. Rees/University of Sheffield (cropped to fit page)


  1. Heinz Ketchup commercial, "The Slowest in the West" TV ad, 1971, via YouTube.
  2. Heinz Ketchup "Carly Simon - Anticipation" TV ad, 1979, via YouTube.
  3. Lucretius, "On the Nature of Things," Translated by William Ellery Leonard, Book II, ll. 391-397, via Classics.MIT.edu.
  4. TITI LVCRETI CARI DE RERVM NATVRA LIBER SECVNDVS, Book II, ll. 391-397, Latin Text, via The Latin Library.com.
    "Et quamvis subito per colum vina videmus
    perfluere, at contra tardum cunctatur olivom,
    aut quia ni mirum maioribus est elementis
    aut magis hamatis inter se perque plicatis,
    atque ideo fit uti non tam diducta repente
    inter se possint primordia singula quaeque
    singula per cuiusque foramina permanare."
  5. Roger I. Tanner and Kenneth Walters, "Rheology: an historical perspective," Elsevier, 1998, 255 pages.
  6. I.S. Newton, "Philosophiae Naturalis Principia Mathematica," 1st Ed., 1687, Bk 2, Sect. IX, Latin text via Project Gutenberg.
    "Resistentiam, quae oritur ex defectu lubricitatis partium Fluidi, caeteris paribus, proportionalem esse velocitati, qua partes Fluidi separantur ab invicem."
  7. New device measures viscosity of ketchup and cosmetics, University of Sheffield Press Release, October 21, 2011.
  8. H. C. Hemaka Bandulasena, William B. Zimmerman and Julia M. Rees, "An inverse method for rheometry of power law fluids," Measurement Science and Technology, vol. 22, no. 12 (December 2011), Document No. 125402.

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