(186z) Stability of Liquid Bridges Coupled by a Hinged-Cantilever | AIChE

(186z) Stability of Liquid Bridges Coupled by a Hinged-Cantilever

Authors 

Xu, X. - Presenter, Cornell University
Steen, P. H. - Presenter, Cornell University


Arrays of liquid bridges in air extending between two substrates can form bonds due to the cohesion of the liquid/gas interfacial tension. In Nature, for example, the palm beetle uses this strategy to defend itself and attaches/detaches on demand in less than a second. Our interest is in the detachment mechanics. A hinged cantilever, supported by liquid bridges, provides a simple configuration for the study of detachment (initiated by bridge instability). The instability of the bridges in this configuration depends on the force/length and pressure/volume responses of the bridges and the nature of their coupling. Here, we report on the stability of coupled liquid bridges pinned at coaxial circular disks. Similar problems on dual bridges coupled by pressure and by force have been studied by Lowry (2000) and by Langbein and Naumann (1995), respectively. The equilibrium states are computed from the Young-Laplace equation with proper boundary conditions. The stabilities, depending on the type of disturbance, are obtained from the system response diagram by applying the Poincare-Maddocks theorem. In the bifurcation diagrams, the equilibrium states of coupled bridges typically undergo a pitchfork bifurcation as the system's control parameter is varied. We report that only the system that undergoes a supercritical pitchfork bifurcation shows multi-stability in the energy landscape and that there are thresholds in the parameter space, beyond which switching between the multi-stable equilibria is feasible. Implications regarding peeling-type detachment of the beetle will be briefly discussed.