Stokes flows are laminar fluid motions that are dominated by high
dissipation, and due to its simple nature, chaotic dynamics is often not
expected in Stokes flow. In this talk we report interesting dynamics due
to
fluid-structure interaction and fluid-interface interaction in Stokes
flow.
When an elastic fiber is moving in a Stokesian fluid, it may become
susceptible
to buckling instability when moving in the neighborhood of a hyperbolic
point
of the flow. When the stagnation point is part of a spatially-extended
cellular flow,
it is found that fibers can move as random walers across time-independent
closed-streamline flow. It is also found that the flow is segregated into
transport regions around hyperbolic stagnation points and their manifolds,
and
closed entrapment regions around elliptic points.
Another example is a viscous drop immersed in Stokes flow with
time-varying
rotation. Due to the fluid-interface interaction, the drop dynamics
becomes
chaotic even in the Stokesian regime. The chaotic dynamics is found to
arise
from a cascade of period-doubling bifurcations. We will further discuss
how
this findings can be useful in designing micro-fluidic mixers.
These work is collaborations with Michael Shelley (NYU) and Jerzy
Blawzdziewicz
(Yale University).
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