Regensburg 2016 – scientific programme
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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 50: Wetting, Nano- and Microfluidics I (joint session CPP/DY, organized by CPP)
CPP 50.4: Talk
Thursday, March 10, 2016, 10:30–10:45, H42
Rayleigh-Plateau instability of slipping viscous filaments in v-shaped grooves — •Martin Brinkmann1,3, Tak Shing Chan1, Ralf Seemann1, Krishna Khare2, and Stephan Herminghaus3 — 1Experimental Physics, Saarland University, Saarbrücken — 2Indian Institute of Technology Kanpur — 3Max Planck Institute for Dynamics and Self-Organisation, Göttingen
Since the seminal works of Rayleigh and Plateau on the break-up of free-standing liquid jets, a large number of studies have addressed the instability of cylindrical interfaces in various experimental settings. The most unstable wavelength λ of a viscous liquid filament wetting the bottom of a v-shaped groove is mainly governed by the slope angle ψ, the contact angle θ of the interface on the solid, and the initial width w of the filament. A linear stability analysis using the method of boundary elements reveals that the characteristic timescale of the decay is affected not only by viscosity, interfacial tension, and geometry. Slip has a substantial effect on the wavelength λ of the fastest growing mode whenever the transverse dimension w of the filaments is comparable or smaller than the Navier slip-length b. In this limit b/w→ ∞ we find λ/w → ∞ while the timescale τ saturates to a finite lower bound, similar to the case of a free-standing viscous liquid cylinder. In the opposite limit b/w→ 0 the corresponding timescale τ of the decay increases only logarithmically with b/w while λ tends to √2 times the neutrally stable wavelength λ∗. A linear stability analysis based on long wavelength approximations of the flows agree with the numerical results only for ‘flat’ filaments 0 <θ−ψ ≪ 1 with λ∗≫ w.