June 19 - 30, 2006
The observed swimming behavior of a motile microorganism is the result
of a complex interplay between mechanisms of internal force generation,
the passive elastic properties of its structure, and a surrounding
viscous fluid. In this talk, we will focus on two very different types
of microorganisms: the spirochetes, which are a type of bacteria
characterized by an efficient mode of motility that allows them to
screw through viscous fluids and mucosal surfaces, and spermatozoa,
that undulate as a result of the action of thousands of molecular
motors positioned along the flagellum. We will present mathematical
and computational models that couple the internal force generating
mechanisms of these microorganisms with external fluid mechanics. We
will describe our methodology, which includes both the method of
regularized Stokeslets and the immersed boundary method. We will
discuss recent successes as well as challenges associated with these
models.
The locomotion of most fish and birds is realized by flapping wings or
fins transverse to the direction of travel. Here, we study experimentally
the dynamics of a wing that is flapped up and down but is free to move in
the horizontal direction. In this table-top prototype experiment, we show
that flapping flight occurs abruptly at a critical flapping frequency as a
symmetry-breaking bifurcation. We then investigate the separate effects of
the flapping frequency, the flapping amplitude, the wing geometry and the
influence from the solid boundaries nearby. Through dimensional analysis,
we found that there are two dimensionless parameters well describe this
intriguing problem that deals with this fluid-solid interaction. The
first one is the dynamical aspect ratio that combines four length scales,
including the wing geometry and the flapping amplitude. The second
parameter, the Strouhal number, relates the vertical flapping speed and
its resultant forward flight speed. Overall, we emphasize the robustness
of the thrust-generating mechanisms determining the forward flight speed
of a flapping wing, as observed in our experiments.