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| The Florida Palm Beetle has an interesting defense mechanism: When attacked, it exerts a strong adhesive force to suck itself to the ground. This adhesion mechanism consists of a series of connected, fluid- filled channels opening to the outside. The adhesive force is generated by controlling the flow through these channels.
Inspired by this adhesion strategy, van Lengerich, Vogel and Steen (Physica D, 2009) studied networks of channels (pipes) filled with a Newtonian liquid. Each channel ends in a hole where the liquid forms a partial droplet due to interaction with the ambient air. The pressures acting on the droplets depends on the size of each droplet. Interesting dynamical behavior ensues.
Pressure-driven, non-turbulent pipe flow is, of course, well-understood and
adequately modeled by the Hagen-Poiseuille law in case of viscous liquids.
In our investigation we will concentrate on shear-thinning behavior. In order to study the stability of steady droplet con figurations, we devise Lyapunov and Chetaev function techniques since equilibria are generally not hyperbolic. Numerical simulation
will be given in support of our conclusions. Part of this presentation is based
on work done with Ben Jenkins. |
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