Multiscale mesoscopic dynamics and thermodynamics

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The principal objective of newly emerging field of nano- and bio-engineering is to construct macroscopic objects with a desired macroscopic behavior by controlling their microstructure at nanoscale. Bridging the scales requires new knowledge and new techniques in both experiments and modeling. I have been contributing to the multiscale modeling of complex macroscopic systems since 1980. I have organized the first founding international workshop (IWNET) devoted to this subject in 1996 in Montreal (6th IWNET workshop took place in 2012 in Norway, 7th will take place in 2015 in Holland - see [M. Grmela, H.C. Oettinger, J. NonNewtonian Fluid Mech. vol.194, 60 (2013) for the history of IWNET meetings). The novel approach has recently been reviewed in M. Grmela, "Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering" Advances in Chemical Engineering, vol.39, 76-129 (2010). My objective in the proposed research is to develop it further, to apply it to new examples of complex fluids and complex solids, and to bring to the multiscale modeling new students and new colleagues.More specifically, in the part of the research that is oriented toward fundamental aspects of modeling, I intend to focus on the geometrical setting providing unified mathematical framework for equilibrium and nonequilibrium thermodynamics as well as for equilibrium and nonequilibrium statistical mechanics of driven complex systems on micro, meso and macro scales. The geometrical formulation greatly facilitates translation of the physical insight gained in experimental observations into mathematically well formulated model that then provides a basis for understanding and guides further investigations.In applications (that also serve as a source of motivation for the general theory) I will continue to investigate rheological properties of complex fluids. In particular, the suspension models, that I have been investigating recently with my colleagues and students in École Centrale de Nantes and in University of Grenoble, will be extended to soft colloids. Many biological fluids belong to this category. New significant features of soft colloids is complexity and variability of shapes of suspended particles (e.g. blood cells) and strong particle-particle interactions. In biological applications I will also continue (in collaboration with colleagues in École Polytechnique of Montreal, Czech Technical University, University of Torino, and University of Florence) investigations of coupling of chemical kinetics (modeling for example growth-related processes in bones) with mechanics (modeling for example mechanical deformations of bones). Other areas of applications include heat transfer in polymer nanocomposites (in collaboration with students and colleagues in Ecole Polytechnique and University of Liege), dynamics and thermodynamics of yield-stress fluids (in collaboration with I. Peshkov - my post doctoral student who is now at University of Marseille), and numerical simulation methods seen as physically meaningful modifications of models (in collaboration with students and colleagues in University of Marseille, École Centrale de Nantes, and University of Grenoble).