The International Workshops on Numerical Methods in Non-Newtonian Fluid Mechanics have been held roughly biennially, alternating between North America and Europe since 1979. This proposal is for partial support of the sixteenth workshop in this series. The funds will primarily be used for travel support for young researchers, researchers from under-represented groups in science, as well as researchers who have not previously been part of the community. This support will broaden participation in the Non-Newtonian flows community and maintain its intellectual vitality by bringing in new members.
Intellectual Merit: The primary motivation for the original workshop in 1979 was the recognition in the community that the mathematical models that had been developed to describe flowing complex fluids (specifically polymer solutions and melts) were much more difficult to solve computationally than were more traditional flow problems with Newtonian or generalized Newtonian fluids. Modeling of such fluids is important for applications ranging from polymer processing to blood flow in biomedical devices. Topics covered in recent workshops include numerical methods for solution of the differential or integrodifferential equations arising from continuum models of flowing complex fluids as well as also mathematical analysis of models of flowing complex fluids and the phenomenological and statistical mechanical framework for describing them. Additionally, an important aspect of the workshops in recent years has been mesoscopic and multiscale simulation methods. Finally, we emphasize that the workshop addresses not just numerical methods but also the physical phenomena and engineering processes whose prediction and understanding motivate those methods. Despite the name of the workshop, presentations of experimental work are essential, as motivation and validation for the newest generations of methods.
Broader Impacts: This series of workshops is truly international attendees from 12 nations around the world are already registered for the present workshop. The informal format, and in particular the fact that attendees all eat meals together promotes close interaction between them. The travel grants provided through this grant will promote participation from young people and members of underrepresented groups in science. The selection process for the grants will also give weight to applicants whose primary research field has not been non-Newtonian fluid mechanics, with the aim of achieving intellectual growth in the field by cross-fertilization of ideas brought by researchers from outside the field.
Dissemination of the advances reported in the workshop will be achieved via a special issue of Journal of Non-Newtonian Fluid Mechanics and manuscripts that will contain peer-reviewed articles based on research presented at the workshop.
The International Workshops on Numerical Methods for Non-Newtonian Flows have been held roughly biennially, alternating between North America and Europe, since 1979. The primary motivation for the original workshop in 1979 was the recognition in the community that the mathematical models that had been developed to describe flowing complex fluids (specifically polymer solutions and melts) were much more difficult to solve computationally than were more traditional flow problems with Newtonian or generalized Newtonian fluids. Modeling of such fluids is important for applications ranging from polymer processing to blood flow in biomedical devices and a specific issue that motivated the original workshop was the "high Weissenberg number problem", the difficulty of obtaining a converged numerical solution to a flow problem involving a complex fluid in the regime where the characteristic time of the fluid is larger than the characteristic time for the flow. Due in part to advances over the years, many of which were introduced at these workshops, the high Weissenberg number problem is much better understood and it is now possible to make numerical predictions in many situations of practical interest. Nevertheless, flowing complex fluids remain difficult to simulate, essentially for the reason identified so many years ago -- the time scales for evolution of microstructure in the material are comparable to or longer than the time scales for its deformation during a process of interest -- indeed this is precisely the reason that such fluids are so interesting and important in many applications. Attention has shifted in recent workshops from purely continuum descriptions of complex fluids to mesoscopic or multiscale descriptions that increasingly incorporate microscopic details such as the motions of individual polymer chains or nanoparticles in a solution. Additionally, the community has become interested in other complex fluids such as blood and micellar surfactant solutions, which display new phenomena and demand new computational advances. The XVIth International Workshop on Numerical Methods for Non-Newtonian Flows was held June 13-16, 2010 in Northampton, Massachusetts, USA. 62 participants from 13 countries attended -- the strongly international aspect of these workshops has always been one of their most attractive features, and it is gratifying to see this important and valuable tradition continue. 37 of the attendees were from the US, and 9 were women. There were 40 talks and a dozen posters, covering a wide range of topics. Organization of the individual sessions was determined by the content of the submitted abstracts – there were no a priori restrictions placed on the subject matter, so the content of the workshop was entirely determined by the interests and activities of its attendees. This grant provided support for travel of young U.S. investigators to the workshop as well as a small amount of money for expenses in running the workshop. A summary of the technical sessions for the workshop is as follows: I: models and simulation methods for blood flow II: mesoscale simulation methods III: micro-macro and systems-level simulations IV: Complex fluid suspensions V: Interfacial flows of complex fluids VI: Flow of micellar surfactact solutions VII: turbulence in complex fluids VIII:elasticity-driven flow instabilies IX: Finite element and finite volume methods X: General session In the original proposal, 90+% of the budget was for the travel grants, with emphasis in awarding these grants going to young researchers and researchers new to the Non-Newtonian fluid mechanics community. We ended up being able to support nine researchers, all at assistant professor level or lower, including two women assistant professors. As noted, this workshop was part of a biannual series. Site proposals for the next workshop were solicited in advance of this workshop. Two outstanding proposals were received and at the workshop a committee comprised of the present and previous organizers chose the winning proposal. The next workshop will be held in Nantes, France in April 2012; Francesco Chinesta and Roland Keunings are the organizers. Dissemination of the advances reported in the workshop was facilitated by arranging with Elsevier Publishers for publication of a special issue of the Journal of Non-Newtonian Fluid Mechanics, edited by the workshop organizers and containing articles based on the presentations given at the workshop. This special issue appeared in Spring 2011 and included six articles. The primary intellectual merit of the conference support lay in its facilitation of attendance for young researchers – the intellectual vitality of a field depends on young people continuing to enter it, bringing their energy and new ideas. Broader impacts lay the key role such workshops have in dissemination of ideas throughout the international research community.
