"All models are wrong but some are useful"
~ George Box
"All models are wrong but some are useful"
~ George Box
The homepage serves as an annotated bibliography for some of our group's recent projects, complete with recorded presentations. Navigate the webpage to learn more!
Do shear stresses decrease when flow causes polymers to get shorter? To explore this, we develop new tools for "reactive rheology", applying population balance equations to the constitutive equation. What we find, in short, is that polymers do not get shorter unless they are more stressed... in which decreasing length always corresponds (perhaps surprisingly) to increasing stress.
For more than three decades, we have had practical engineering approaches to modeling the linear rheology of living polymers, but unquantified sources of uncertainty were present in the analysis due to phenomenological approximations or statistical noise in the data. Here, we present a new method that allows numerically converged solutions of the true reptation/reaction model for the first time.
For a fluid at rest, a mixture of polymer chains with differing lengths but similar chemistry (e.g. all PS monomers) is thermodynamically stable. When flow is applied, however, stresses are divided unequally between long/short chains and a demixing instability can ensue! We develop a multi-fluid model to explore this in more detail, and we validate a back-of-the-envelope calculations that shows these demixing instabities are enhanced by high entanglement and high polydispersity.
By now, we are all arm-chair experts in epidemiology, well-versed in the standard SIR model. But where does this artifically discrete and memoryless "infected" compartment come from - and is there a better way to build these models?