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Abstract: A recent experiment showed that cylindrical segments of water filling ahydrophilic stripe on an otherwise hydrophobic surface display a capillaryinstability when their volume is increased beyond the critical volume at whichtheir apparent contact angle on the surface reaches ninety degrees Gau et al.,Science, 283, 1999. Surprisingly, the fluid segments did not break up intodroplets - as would be expected for a classical Rayleigh-Plateau instability- but instead displayed a long-wavelength instability where all excess fluidgathered in a single bulge along each stripe. We consider here the dynamics ofthe flow instability associated with this setup. We perform a linear stabilityanalysis of the capillary flow problem in the inviscid limit. We first confirmprevious work showing that that all cylindrical segments are linearly unstableif and only if their apparent contact angle is larger than ninety degrees. Wethen demonstrate that the most unstable wavenumber for the surface perturbationdecreases to zero as the apparent contact angle of the fluid on the surfaceapproaches ninety degrees, allowing us to re-interpret the creation of bulgesin the experiment as a zero-wavenumber capillary instability. A variation ofthe stability calculation is also considered for the case of a hydrophilicstripe located on a wedge-like geometry.

Author: Raymond L. Speth, Eric Lauga



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