Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

In lab-scale Faraday experiments, meniscus waves respond harmonically to small-amplitude forcing without threshold, hence potentially cloaking the instability onset of parametric waves. Their suppression can be achieved by resorting a contact line pinned at container brim with static angle $\theta_s=90^{\circ}$ (brimful condition). However, tunable are desired in some applications as those liquid-based biosensors, where they controlled adjusting shape slightly under/over-filling vessel ($\theta_s\ne90^{\circ}$) while keeping fixed brim. Here, we refer this wetting condition nearly-brimful. Although classic inviscid theories based on Floquet analysis have been reformulated for case (Kidambi 2013), accounting (i) viscous dissipation and (ii) effects, including waves, makes such analyses practically intractable comprehensive theoretical framework is still lacking. Aiming filling gap, work formalize weakly nonlinear via multiple timescale method capable predict impact sub-harmonic standing both brimful nearly-brimful circular-cylinders. Notwithstanding that form resulting amplitude equation fact analogous obtained symmetry arguments (Douady 1990), normal coefficients here computed numerically from first principles, thus allowing us rationalize systematically quantify modifications tongues associated bifurcation diagrams induced interaction