Gooey Sweet Rheology

Foods always make for fun and interesting rheology experiments. Witness the ongoing (and incorrect) characterization of ketchup as thixotropic [1]. Talking about viscoelastic and other complex rheological behaviors of polymeric materials really won't grab the attention of too many people, even those with a technical background. But mention the unusual flow properties of food and suddenly everyone perks up.

And so it is with a new research paper (open access with registration until 3/29/16) on the rheology of caramels and how it changes with the recipe.

It's a nice little piece of work, the most surprising result being that even though there are 6 ingredients [2] in the recipe, the rheology can be simplified using standard techniques that greatly reduce the number of variable that we need to be concerned with.

What I really didn't like about the work however, was the comparison of caramel to rubber, or specifically to what they call "Ferry 'type VII'" materials. Can I see a show of hands of how many people know what that means? Anyone? Anyone? Yep, only the SOR (Society of Rheology) members got it.

John Ferry wrote a book, Viscoelastic Properties of Polymers which is canonic. I can't imagine anyone being serious about rheology and not having read the book - it is that good. In it, Ferry shows some "ideal" rheological curves for 8 different types of non-Newtonian systems, ranging from dilute solutions of polymers all the way to highly crystalline systems. One such plot is this:

which shows the curves, designated by Roman numerals, which is where the 'type VII' came from.

But no one ever calls something a Ferry "type x" [3] material. It's not wrong, it's not incorrect, it's just improper and shows a newness to the field. And so to call a caramel as a rubber is also improper. It may have some elastic behavior that mimics rubber, but it is not a rubber. A rubber has an entirely different chemical structure that I won't go into today.

But worse yet is think of this characterization of caramel as a "rubber" falling into the wrong hands, such as those of The Food Babe. She already made name for herself by associating an ingredient in Subway's bread with also being used in yoga mats, so imagine what could happen in a case like this where the researchers already have made the connection to rubber.

When caramels are outlawed, only outlaws will have caramels. But at least we have a good understanding of how to prepare them.



[1] Well, maybe incorrect isn't the correct word, as ketchup is thixotropic, but that characteristic isn't what makes it so hard to get it out of the bottle. It's the yield stress that drives the us nuts.

[2] Or maybe you can call it 4 since 2 of them were held constant. Apparently the researchers are not familiar with Designed Experiments for formulations or similar types of analysis.

[3] Or should that be Ferry 'type X', since they are all Roman numerals?

Previous Years

February 18, 2013 - Viscoelasticity in the Bathroom

February 18, 2011 - How to (not) Become a Polymer Engineer

February 18, 2010 - A Concept Kitchen

Rheology and Memristors

Viscoselasticity in polymers is often modeled with mechanical elements, specifically springs and dashpots (think of a dashpot as a being like those cylinders that prevent doors from closing too quickly so as to not pinch fingers).

These elements can be connected in series such as in a Maxwell fluid shown on the left. This was proposed by James Maxwell of electromagnetic fame (more on that in a minute).

They can also be connected in parallel, such as in a Kelvin-Voight material.

Of course, there is no reason to limit any model to just two elements, and a Generalized Maxwell model will have a number of serially-connected springs and dashpots that are connected in parallel.

While knowing about these models is part of a good theoretical understanding of viscoelasticity (including knowing full well that these models, like all models, have limitations while still being useful), this can also be helpful when explaining viscoelasticity of people not trained in the subject. Mechanical/civil/aeronautical/... engineers and physicists catch on quickly, while electrical engineers can struggle. Fortunately, this struggle can easily be resolved by using mechanical-electrical analogies. A dashpot is analogous to a resister - energy is irrecoverably lost, while a spring is analogous to a capacitor as they both store energy. Viscoelasticity is simply an RC-circuit. I've made this analogy to electrical engineers many times and it works quite well.

But the analogy can be problematic at times. Electrical engineers also work with another basic circuit element, an inductor. Inductors resist the change of electrical flow by taking advantage of a nearby magnetic field. While mass/inertia/momentum can be considered analogs to inductance and we can describe a flowing polymer in unsteady conditions as an RCL circuit, the next element is where the analogy completely breaks down.

The next element? Beyond the resistor, capacitor and inductor? Maxwell (him again) first described those three as basic, circuit elements back in the 1800's, often using the electromechanical analogy described above. And for the longest time, those three elements were all that were known to exist, at least as passive devices. However, in 1971, Prof. Leon Chua, using symmetry arguments, proposed a forth basic circuit element - the memristor. This device, showing both a memory and resistance (hence the name), would show decreasing resistance as more current had flowed through the device, and it would also remember what its resistance was when the device was turned off. After restarting the element, the resistance would be the same as before. Changing the direction of current flow would reset the device to its initial resistance. As with the inductor, all of this is possible by a coupling the current to a nearby magnetic field.

Going from theory to practice took some 37 years. Or did it? Apparently a controversy exists. I'm not in any position to say who's right and who's wrong. Regardless of the physical existence of the device, it exists theoretically. But even trying to describe a mechanical analog of a memristor is complicated. HP Senior Fellow Stan Williams describes it as:

" An analogy for a memristor is an interesting kind of pipe that expands or shrinks when water flows through it. If water flows through the pipe in one direction, the diameter of the pipe increases, thus enabling the water to flow faster. If water flows through the pipe in the opposite direction, the diameter of the pipe decreases, thus slowing down the flow of water. If the water pressure is turned off, the pipe will retain it most recent diameter until the water is turned back on. Thus, the pipe does not store water like a bucket (or a capacitor) � it remembers how much water flowed through it."

And I further doubt that a polymeric analog of a memristor exists. While the whole idea of decreasing resistance with flow is quite analogous to shear thinning, the analogy fails on two fronts: polymers will lose the decreased viscosity upon cessation of flow (the rate of such loss being related to "the" relaxation time of the polymer), and switching flow directions will not reset the viscosity. Thank goodness, as dynamic mechanical analysis, where rheologists measure viscosity by imposing oscillatory shear on a sample, would not exist if it did.

Like all analogies, there are limits on their applications and if pushed too far, they break down. The analogy of a memristor to any part of a non-Newtonian fluid is just not going to happen, regardless of whether or not a memristor actually exists.

Previous Years

July 6, 2011 - "Scientists Develop Bioplastic"

July 6, 2010 - Ruminations on a Furnace Filter

Sir Sam Edwards, RIP

The field of polymer science lost one of its giants last week with the passing of Sir Sam Edwards. [*]

Edwards most lasting contribution will likely be the Doi-Edwards theory which describes the reptation of polymers. Small molecules in a liquid can easily slip past each other just like people in a crowded party can move around. But polymer chains do not have it so easy. Continuing the crowded party analogy, a polymer chain would be like a conga line. The big difference is that individual people can move in pretty much any direction, but the conga line can only follow where the head of the line goes. This snake-like motion is what is referred to as "reptation" (coming from the same Latin root as the word "reptile", meaning to crawl).

If there is only one conga line (analogous to a dilute polymer solution), the line can move around easily. But for a liquid made up exclusively of polymer molecules, you have a whole room of conga lines. The only way anyone of them is going to move is to get some cooperation from neighbors, and that will take some time. That is why polymers have such a high viscosity.

The Doi-Edwards theory was able to model this reptation motion and found that the viscosity of a polymer melt increases with the molecular weight to the third power. As in the number 3. As in 3.0, or 3.00 or 3.000 etc.

Why the big deal on 3? Well, the theory is close to the data, but not not quite. The data, for numerous systems, shows that the exponent should be 3.4, not 3.0. And everybody knows this. Everybody has seen this famous plot on the right, showing the same slope for all those polymers. That was a big gap to try and close.

Shortly after the Doi-Edwards theory was published, I was fortunate enough to attend a lecture of Sir Edwards where he tried to soft-shoe and hand-wave over the difference. (I don't think he did too well.) Regardless, reptation has been clearly document via experimentation, and Doi-Edwards is still widely used as the basis for modelling polymer dynamics, so it all to the good. Whoever does find the missing 0.4 (if it hasn't been found already) will not receive the same recognition. That's how it goes.



[*] Dame Athene Donald seems to be the only one to have noticed this passing. There is a post in her blog and an article in the Guardian, but Google comes up empty when I search for an obituary. Strange indeed for such a large figure of science.

Previous Years

May 12, 2014 - Dow Chemical's biggest critic has forgotten college mathematics

May 12, 2011 - Polypropylene Pricing

May 12, 2010 - The World's Smallest Rheologist?

Don't be a Rheology Fool

'Nuff said.

Previous Years

April 17, 2013 - Polymers from Elemental Sulfur

April 17, 2012 - Some Novel Polymer Chemistry Reactions

April 17, 2007 - Rapid announcements across a campus - the Tragedy at VTU