MEchanics GAthering -MEGA- Seminar: Fluid inertia and the scallop theorem
Abstract In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. Recent works have investigated an asymmetric spherical dimer of oscillating length as a simple model swimmer. Analytical, numerical, and experimental studies have shown a dense (i.e. inertial) dimer swims in Stokes flow. Similarly, numerical study shows a dimer in fluid of intermediate Reynolds number (Re = 1-1000) swims in a direction that varies depending on the degree of fluid inertia, but the reasons for this direction change have not previously been elucidated. Here, we introduce a general model for the inertial flow produced by an oscillating dimer at small amplitudes. We apply the finite element method, using the PETSc library to solve a coupled pair of linear PDEs, to probe the dimer's swim speed with respect to the degree of fluid or solid inertia. The results are compared to asymptotic solutions obtained via the method of reflections. We find the model's predictions match those of the dense Stokes swimmers in the appropriate limit, and that the behavior in inertial fluid is consistent with the previously observed switch in direction.
Biography Nick Derr uses simplified models and high-performance computation to study active systems in biology and physics, especially those with elements of poroelastic flow or fluid-solid interaction. He received a BS from the University of Wisconsin in 2015 and a MASt in Applied Math from the University of Cambridge in 2016. He is a PhD Candidate in Chris Rycroft’s group at Harvard University, and will start as an Instructor in the MIT Math Department this summer.
Biography Nick Derr uses simplified models and high-performance computation to study active systems in biology and physics, especially those with elements of poroelastic flow or fluid-solid interaction. He received a BS from the University of Wisconsin in 2015 and a MASt in Applied Math from the University of Cambridge in 2016. He is a PhD Candidate in Chris Rycroft’s group at Harvard University, and will start as an Instructor in the MIT Math Department this summer.
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- Free
Organizer
- MEGA.Seminar Organizing Committee