Analysis and Applied Mathematics Seminar
Theodor Drivas
Princeton University
The Navier-Stokes-End-Functionalized polymer system
Abstract: The problem of minimizing energy dissipation and wall drag in turbulent pipe and channel
flows is a classical one which is of great importance in practical engineering applications.
Remarkably, the addition of trace amounts of polymer into a turbulent flow has a pronounced
effect on reducing friction drag. To study this mathematically, we introduce a new boundary
condition for Navier-Stokes equations which models the situation where polymers are irreversibly
grafted to the wall. For engineering applications, the effects of polymer on drag reduction are
thought to be most pronounced near the boundary and therefore such wall-grafted polymer chains
are often employed as drag-reducing agents. Our boundary condition - derived from a fluid-polymer
stress balance - closes in the macroscopic fluid variables and becomes an evolution equation for the
vorticity along the solid walls. We prove global well-posedness for the resulting system in two spatial
dimensions and show that it captures the drag reduction effect in the sense that the vanishing viscosity
limit holds with a rate. Consequently, we obtain bounds on energy dissipation rate and drag which
qualitatively agree with observations of drag reduction in laminar flow.
Talk is based on joint work with Joonhyun La.
Monday May 6, 2019 at 4:00 PM in 636 SEO