I ran across an article in the Journal of Rheology with just such a title (subscription require), but since it was written 80 years ago in 1932, the "future" is now the present (or maybe even the past). When this article was written, the term rheology had only been around for dozen years, so the subject was quite new. The article has aged quite as most of it is now incorporated in textbooks, but a couple of passages caught my eye and are worth a comment or two. The first was this: "In practice, the results can be applied to ordinary inhomogeneous materials, if their structure is sufficiently fine grained so that the structural units are small compared to the dimensions of the narrowest passages through which flow of any kind takes place." I say this is eye catching as it is a concept that many people today still fail to grasp. I've lost track of all the papers that have modeled fluid mechanics on such small scales that the whole idea of fluid continuum breaks down, and yet the researchers continue to use it. 80 years on and too many people fail to understand this basic concept.
As for specific "future" problems, the author proposed a dozen of which a few are interesting: "(5) Consider the effect of the temperature rise due to dissipation of energy in shearing a plastic material. There were not many plastics around in 1932, so I was surprised to see that extruders back then were so well equipped that they could detect the heat from shearing.
This next one shows that we've had a change in perspective over time: "(6) Investigate mathematically the change of consistency with working, as well as thixotropic and other irreversible effects" So thixotropy was considered irreversible back then? That is not in alignment with current definitions which in fact require that the effect be instead reversible.
And this last one shows how some thing never change: "(10) Rationalization of the pour-point: correlate if possible the customary ASTM observations on pour-point, penetration, and other consistency phenomena with the intrinsic rheological constants of the material." People have been developing endless additional ad hoc tests since and still want them correlated to the fundamental underlying principles. Melt Flow Index, Ring and Ball Softening Point, Probe Tack (and Loop Tack and Rolling Ball Tack and __________ Tack) - the list goes on and on. Problem #10 here is still a "future" problem of theoretical rheology.
The case of continuum breakdown is treated in the vast literature on boundary lubrication. As for polymer flow in such instances, a good place to start is with my favorite term in polymer physics: Pincus blobs.
Thanks for sharing this interesting article, John!
The early rheologists' insight in the "continuum limit" originated from their theoretical physical + chemical engineering background. They had clear pictures and the concept of length/time scale before treating every problem.
As far as I know the concept of thixotropy referred to reversible yield-reconstruct cycle from the beginning. The phrase "other irreversible effects" may be only a counterpart of the word "working". The "working" effect include both "work hardening" and "work softening", which are the irreversible version of "anti-thixotropy" and "thixotropy". But still the sentence looks strange.
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