(4el) Materials Processing and Structure Formation in Compositionally Inhomogeneous and Reactive Complex Fluids

In rheology and soft matter physics, there are unique opportunities to turn low-cost raw materials into high-value products by careful processing of the microstructure. Demixing instabilities and reversible/irreversible polymerization reactions are especially powerful tools in this respect, but for systems under non-linear and non-equilibrium flow conditions they are also challenging to control and costly to optimize. My independent research program will address this challenge by developing and applying new microscopically-derived constitutive models for compositionally inhomogeneous and chemically reacting flows. These models will be used to interrogate the relationship between processing protocol, chemical functionality, and microstructure formation in order to inform raw material selection and processing strategies in both established and developing technology areas. Application areas of interest include sustainable food production, consumer products, and conventional polymer processing.

The modeling approach at the core of my proposed independent research program integrates a multi-fluid framework for compositionally inhomogeneous flows with microscopically-derived population balance constitutive equations for materials undergoing reversible/irreversible polymerization reactions. This framework minimizes dependence on phenomenological or inscrutable parameters and therefore allows a more direct link between the model predictions and the chemical/mechanical properties of the system. A principal cost of this robust and detailed modeling approach is that the full governing equations will often be computationally intractable for complex flow conditions. To overcome this, we will employ well-established mathematic methods for controlled approximations (asymptotic methods, moment closures, Galerkin approximations, etc.) to develop and validate simplified models for subsequent use. Integrating suitably simplified models into existing computational fluid dynamics packages, we will compare predictions against experimental data and perform in-silico experiments to explore and interpret how changes in material composition (miscibility, reactivity, polydispersity, etc.) and processing protocols (deformation, heat, light, etc.) determine the final microstructure of the system. This work will inform a more optimal selection of raw materials and processing protocols, making more efficient use of available resources and helping expand emerging technologies to wider markets.

This research program draws on my expertise in constitutive modeling, multi-fluid models, population balances, and controlled approximation schemes. In my PhD work, I studied shear induced demixing in polymer solutions and polydisperse polymer melts. For polymer solutions, I applied asymptotic methods and Liapunov stability analysis to a standard viscoelastic two-fluid model to better understand the non-linear dynamics of flow-induced demixing instabilities. This work showed that unsteady flow conditions generate migration-induced stresses at a phase boundary and arrest normal coalesence phenomena [3]. For polymer melts, I developed a new non-linear constitutive equation that extends the microscopic picture of double reptation to the non-linear stress relaxation processes of the Rolie Poly constitutive equation [2]. This constitutive equation was then embedded in a multi-fluid model to show that shear induced demixing transitions can occur in polydisperse melts, leading to dramatic changes in the material composition [7]. In my postdoctoral work, I developed tools for incorporating population balance equations into non-linear constitutive equations for systems of linear chain polymers undergoing reversible and irreversible polymerization reactions [8, 12, 13]. This work provided unprecedented insight to the role of flow-induced scission in shear banding instabilities [13] as well as CFD-friendly non-linear constitutive equations for fast-breaking [8, 13] and semi-slow-breaking [12] systems of well-entangled wormlike micelles. My research perspective has also been shaped by my experiences with industry: I was an intern with the safety and graphics R&D lab at 3M for three years during my undergraduate, and my postdoctoral research has been done in close collaboration with researchers at Unilever. These experiences have given me an appreciation for the needs and perspectives of industry, especially as it pertains to the importance of (1) anticipating and adapting to evolving regulatory frameworks and consumer preferences and (2) optimizing throughput without compromising process stability or product quality. As a faculty member, my experiences and expertise will provide the foundation for a research program that maintains strong ties with industry collaborators and tackles both emerging and established challenges in the areas of sustainable food production, consumer products, and conventional polymer processing.

Teaching Statement

In my view, teaching and mentorship outcomes should be considered co-equal to research output in the priority hierarchy of a well-balanced chemical engineering department. This strong commitment to teaching and mentorship was exemplified by my instructors and advisors at every institution I have been a part of, to my great personal and professional benefit. As a faculty member, it would be my privilege to model this commitment to student life/learning outcomes for the next generation of chemical engineers. Moreover, I believe that my past experiences in teaching and mentorship demonstrate the capacity to match my ambition in these respects.

As a fourth-year PhD student (2016), I was awarded the CSP teacher/scholar fellowship at UCSB to co-teach an undergraduate numerical methods course with professor Mike Gordon. The course covered root finding for linear and non-linear systems of equations, optimization, curve fitting, numerical differentiation/integration, and ODE methods, all with an emphasis on problems relevant to chemical engineering. The course also served as an introduction to computer programming with weekly recitations in the computer lab. I was given a lot of responsibility and freedom as a co-instructor; I prepared and delivered half of the lectures, wrote half of the problems for homeworks and exams, and held office hours. Prior to this teaching appointment I also had considerable tutoring experience, including participation in the ESTEEM program for first-generation college students at UCSB. In the future, I look forward to teaching whatever courses are assigned to me: I am qualified and capable to teach any course in the core chemical engineering curriculum, though my own interests and experiences are inclined towards courses that are more math/theory intensive (e.g. numerical methods, fluid mechanics, transport, thermodynamics, reaction kinetics, mass/energy balances, etc.). I am also interested in developing new courses to meet the department’s needs, especially where there are opportunities to expand course offerings in fluid mechanics, rheology, polymer physics, and advanced mathematics for engineers.

My philosophy of mentorship is primarily shaped by the mentorship that I have received over the years. The mentors in my life – advisors, post-docs, and industry contacts – have provided direction at critical junctures, advocated on my behalf, and connected me to valuable professional opportunities that I otherwise would not have been aware of. But more importantly, my mentors took the time to understand what was important to me and connect me with the resources that I needed in order to be successful in both my personal and professional life. This is the wholistic approach to mentorship that I have tried to take when interacting with younger graduate and undergraduate students who are trying to find their place in the field of chemical engineering. As a faculty member, I will look forward to the more regular and structured opportunities for advising and mentoring students and post-docs, advocating on their behalf and helping them navigate matters of career development and work/life balance.

Publications

[13] Peterson, J. D. and L. G. Leal, "Predictions for flow-induced scission in well-entangled living polymers: the 'Living Rolie Poly' model", Accepted for publication in the Journal of Rheology

[12] Peterson, J. D. and M. E. Cates, "Constitutive Models for Living Polymers Beyond the fast-breaking Limit", Journal of Rheology 65(4) pp. 633 – 662

[11] Li, Y. et. al. "Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19." arXiv preprint arXiv:2010.11783 (2020), submitted to Royal Society Open Science.

[10] Peterson, J. D. and R. Adhikari, "Efficient and flexible methods for time since infection models." arXiv preprint arXiv:2010.10955 (2020), under review at Phys. Rev. E

[9] Adhikari, R., et al. "Inference, prediction and optimization of non-pharmaceutical interventions using compartment models: the PyRoss library." arXiv preprint arXiv:2005.09625 (2020).

[8] Peterson, J. D. and M. E. Cates, "A full-chain tube-based constitutive model for living linear polymers." Journal of Rheology, 64 (6) pp. 1465 - 1496

[7] Peterson, J. D., G. H. Fredrickson, and L. G. Leal. "Shear Induced Demixing in Bidisperse and Polydisperse Polymer Blends: Predictions From a Multi-Fluid Model." Journal of Rheology 64 (2020)

[6] Andriano, L.T. et. al., "Microstructural characterization of a star-linear polymer blend under shear flow by using rheo-SANS", Journal of Rheology 64 (2020)

[5] Gillissen, J. J., C. Ness, J. D. Peterson, H. J. Wilson, and M. E. Cates. "Constitutive model for shear-thickening suspensions: Predictions for steady shear with superposed transverse oscillations." Journal of Rheology 64.2 (2020): 353-365.

[4] Gillissen, J.J., C. Ness, J.D. Peterson, H. J. Wilson, and M. E. Cates. "Constitutive model for time-dependent flows of shear-thickening suspensions." Physical Review Letters, 123.21 (2020)

[3] Peterson, J. D., G. H. Fredrickson, and L. G. Leal. "Does shear induced demixing resemble a thermodynamically driven instability?" Journal of Rheology 63.2 (2019): 335-359.

[2] Boudara, V., J. D. Peterson, L. G. Leal, and D. J. Read. "Nonlinear rheology of polydisperse blends of entangled linear polymers: Rolie-Double-Poly models." Journal of Rheology 63.1 (2019): 71-91.

[1] Peterson, J. D., M. Cromer, G. H. Fredrickson, and L. G. Leal. "Shear banding predictions for the two-fluid Rolie-Poly model." Journal of Rheology 60.5 (2016): 927-951.