## Fluid Mechanics Seminar: Eliot Fried

- Date: 01/29/2015
- Time: 16:00

*Okinawa Institute of Science and Technology*

University of British Columbia

Slender-body theory via dimensional reduction and hyperviscous regularization.

The classical slender-body theory for viscous flows was initiated by Burgers in 1938 and was developed in the seventies with the primary objective of obtaining the drag force and torque required to sustain the rigid motion of slender bodies in viscous fluids. One important goal of this effort was to provide estimates for parameters such as the effective viscosity of suspensions of solid particles in fluids. Despite the success in describing the viscous flow generated by a single particle of general shape, the treatment of a more realistic number of suspended particles represents a formidable computational challenge. Our approach to slender-body theory, which aims to reduce the computational complexity of the problem, involves replacing slender three- dimensional particles with lower-dimensional objects and the surrounding Newtonian fluid by a quasi-Newtonian second-gradient fluid. In such a fluid, an additional parameter, namely the product of the viscosity and a characteristic length—called the gradient length—enters the flow equation, which resembles the well-known hyperviscous regularization of the Navier–Stokes equation. The central idea underlying our approach is that the aforementioned gradient length represents the effective thickness of the lower-dimensional objects, in the sense that the drag force and torque required to sustain their rigid motion in a hyperviscous fluid are the same as those required to sustain the corresponding motion of a particle with thickness coincident with the gradient length in a Newtonian fluid. Importantly, both the dimensional reduction and the hyperviscous regularization, combined with suitable numerical schemes, can be used also in situations where inertia is not negligible.

Eliot Fried obtained his Ph.D. in Applied Mechanics from the California Institute of Technology in 1991. He received an NSF Mathematical Sciences Postdoctoral Fellowship, a Japan Society for the Promotion of Science Postdoctoral Research Fellowship, and an NSF Research Initiation Award. Professor Fried heads the new Mathematical Soft Matter Unit at the Okinawa Institute of Science and Technology. Previously Professor Fried was at the University of Washington, where he was a Professor of Mechanical Engineering and before that he was Professor of Mechanical Engineering, Professor of Mathematics and Statistics and the Tier 1 Canada Research Chair in Interfacial and Defect Mechanics at McGill University. His research is in soft matter, which is the study of materials made of many atomic or molecular parts, which do not act in a way predicted by any one element within the substance. Understanding these materials, which range from blood and tissue to fuel additives and adhesives, and how to manipulate them, can lead to advances in nearly every field of science and engineering.

Location: ESB 2012