(6et) Constitutive Modelling for Complex Fluids in Complex Flows

From dry powders to entangled polymer melts, the processing of complex fluids at industrial scales is often limited by flow instabilities that are poorly understood on a fundamental level. In my research, I seek to address this problem by developing and applying improved constitutive models for complex fluids. For such systems, the coupling between flow and microstructure is generally complex, non-linear, and non-equilibrium, with underlying physics spanning many length-scales and time-scales. In my approach to the subject, I combine new ideas and insights with existing theories to produce a microscopically faithful continuum description of a fluid’s response to deformation and flow. Thereafter, I use insights from physical intuition and numerical simulations to guide well-controlled simplification strategies (asymptotic expansions, pre-averaging approximations, galerkin expansions, moment expansions, etc.) until I reach a suitable balance between fidelity to the full model and computational tractability in complex flows. These simplified models are then applied to study flow instabilities observed in benchmark problems. Initial directions for future work will include polydisperse entangled polymers, dense granular suspensions, and dry fibers.

Selected Research Experience:

Constitutive modelling of wormlike micelles: Department of Applied Maths and Theoretical Physics, University of Cambridge (advised by Mike Cates)

My postdoctoral research focuses on developing and applying simplified constitutive models for the linear and non-linear rheology of wormlike micelles. Wormlike micelles are an important component of many consumer goods (hand-soap, shampoos, detergents, etc.) and industrial processes (e.g. advanced oil recovery). However, the rheology of wormlike micelles is notoriously sensitive to minute changes in formulation, and this creates problems for industrial-scale production. Improved constitutive models could reduce waste and down-time by helping to diagnose and correct problems with the formulation in real-time. By combining existing tube-based constitutive models (e.g. the Rolie Poly model) with a complete population-balance model for scission and reformation kinetics, we have produced a model that directly connects molecular-scale information to linear and non-linear rheological measurements. On some levels, this approach is conceptually similar to what has been done by others – however, by including previously-neglected physics we have upended several well-established results in the existing literature. For example, by incorporating the entire polydisperse molecular weight distribution in our population balances, we show that flow-induced breaking is not generally responsible for shear banding instabilities in wormlike micelles and that a Doi-Edwards type instability is more likely to be at play.

Constitutive modelling of polydisperse blends: Department of Chemical Engineering, University of Santa Barbara (advised by Gary Leal and Glenn Fredrickson)

In one component of my PhD studies, I developed a simplified constitutive model for polydisperse entangled linear polymer melts. Whereas monodisperse polymer melts have been a historical focal point of constitutive modelling efforts, industrially relevant polymers are highly polydisperse in their composition. It is well known that high polydispersity improves processability, but the precise mechanism by which this is achieved is not at all well-understood. By generalizing the ‘double reptation’ ansatz to non-linear modes of stress relaxation (e.g. chain retraction and convective constraint release), we have produced a simple constitutive model of polymer blends that retains a seemingly reasonable approximation for the effects of microscopic couplings between chains of differing lengths. When applying this model to complex flows, we find (as is seen in experiments) that adding a small fraction of short chains dramatically extends the window of stable processing conditions. This work has created new opportunities to understand how changes in melt formulation influence the processability of polymer melts.

Publications:

• D. Peterson, M. E. Cates, L. G. Leal, “Constitutive modelling of wormlike micelles”, in prep.
• D. Peterson, C. Sasmal, V. Boudara, D. J. Read, L. G. Leal, “Nonlinear rheology predictions of bidisperse polymer blends in a complex flow”, in prep.
• J. Gillessen, C. Ness, J. D. Peterson, H. J. Wilson, M. E. Cates, “A tensorial constitutive model for dense frictional suspensions”, in prep.
• D. Peterson, G. H. Fredrickson, L. Gary Leal, “Does shear induced demixing resemble a thermodynamically driven instability?” Journal of Rheology, 63(2) pp. 335 – 359
• Boudara, J. D. Peterson, L. Gary Leal, D. J. Read, “Nonlinear rheology of polydisperse blends of entangled linear polymers: Rolie-Double-Poly models”, Journal of Rheology, 63(1) pp. 71 – 91
• D. Peterson, M. E. Cromer, G. H. Fredrickson, L. G. Leal, “Shear banding predictions for the two-fluid Rolie-Poly model”, Journal of Rheology 60(5) pp. 927 - 951

Recorded Talks (available online):

“Modelling polymer blends in flow,” Joseph D. Peterson, Glenn H. Fredrickson, L. Gary Leal. Thesis defense (2018). https:/bit.ly/2IRJPmf

“Two-fluid models for polymer melts and solutions,” Joseph D. Peterson, Glenn H. Fredrickson, L. Gary Leal. KITP dense suspensions workshop (2018). (talk begins at 1:00:58) https://bit.ly/2xe7OFl

Teaching Interests:

During my PhD Studies, I was awarded a departmental fellowship to be a co-instructor for an undergraduate chemical engineering course. Because my research is heavily math-oriented, I chose to co-teach the numerical methods class for chemical engineers. This was a great learning experience for me, and I look forward to future opportunities to engage with students in the classroom setting. Although I enjoyed teaching a subject relevant to my own research, I would also welcome the challenge of teaching other subjects as well: my background and training as a chemical engineer makes me qualified to teach any core subject in the discipline (thermo, transport, kinetics, process control, etc).