Monday, December 08, 2008

Viscosity - It's only half the story

Most people's introduction to rheology is via fluid mechanics, which certainly is a fine place to start. In the texts, the material property of the fluid that exhibits itself throughout the equation is the viscosity. For simplicity's sake (again, this is quite fine for starters), the viscosity is taken as a constant - an idealization known as a Newtonian fluid. As one's studies advance into more advanced cases, non-Newtonian fluids are studied. In most cases, the viscosity is then allowed to depend on the shear rate. A simple example is the power-law fluid, a strictly empirical and therefore potentially DANGEROUS model (another topic for another day), where the viscosity is proportional to the shear rate raised to a exponential value, h = gn-1 (Yes, it should be g with a dot over it, but coding that is beyond my HTML ability - any pointers?)

Again, all this is fine and nice. But at some point, it needs to be understood that viscosity is a SECONDARY material property, meaning that there are underlying properties that are even more valuable to understand. These are the storage and loss moduli, commonly denoted as G' and G". These properties can be measured in a dynamic state, one where a time dependent strain (such as a harmonic oscillation)is applied to the sample. If your material is a perfect solid, then it should deform in phase with the deformation, while if it is a perfect fluid, it should be 90 degrees behind the deformation (viscosity is proportional to the shear rate, not the shear). Non-Newtonian materials will generally show both of these characteristics to some degree, meaning that by performing dynamic measurements, you can generate curves for G' and G". In other words, viscosity is only half the story. Interpreting these curves is not simple and that is a big part of the reason that rheology is not taught to undergraduates, but there is considerably more information in the curves than a simple viscosity curve can ever show (in most cases being limited to a zero-shear viscosity region and a power-law region.)

As a rheologist, I am often asked for viscosity curves which might be what the client needs, but in most cases, going the extra step and preparing the moduli provides far more information on what is important to the client. Since most of them are not aware of rheology or the power of it, they don't know to ask for it, but are always happy with the results.

You might be curious if you can keep this going and look for even more fundamental properties than the dynamic moduli noted above. In fact you can. Further work shows that the relaxation spectrum, but devising this from the moduli is an ill-posed inverse problem that is difficult to complete. You ultimately end up with a distribution and thereby even more information than you find from just 2 modulus curves.

1 comment:

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