论文标题
几乎纯净的圆形圆柱体中的亚谐波参数不稳定性：弱非线性分析
Sub-harmonic parametric instability in nearly-brimful circular-cylinders: a weakly nonlinear analysis
论文作者
论文摘要
在实验室尺度的法拉第实验中，半月板波对不阈值的小振幅强迫响应，因此可能掩盖了参数波的不稳定性。他们的抑制可以通过诉诸于固定触点角度固定在容器边缘的触点线$θ_s= 90^{\ Circ} $（条件）。但是，在某些应用中，可以通过液体基生物传感器进行调节的弯月板波，可以通过稍微下/过度填充容器（$θ_S\ ne90^{\ circ} $）来控制它们，以调整静态弯月面的形状，同时使固定在纤维上的接触线保持固定。在这里，我们将这种润湿条件称为几乎是纯正的。尽管基于Floquet分析的经典无关理论已经针对固定的接触线进行了重新构建（Kidambi 2013），但考虑到（i）粘性散发以及（ii）静态接触角效应（包括半月板波浪），使这种分析实际上是可怕的，并且仍然缺乏这种全面的理论框架。为了填补这一空白，在这项工作中，我们通过多种时间尺度方法对弱非线性分析进行了形式化，能够预测（i）和（ii）对粘性亚谐波站立波的不稳定性的影响。 Notwithstanding that the form of the resulting amplitude equation is in fact analogous to that obtained by symmetry arguments (Douady 1990), the normal form coefficients are here computed numerically from first principles, thus allowing us to rationalize and systematically quantify the modifications on the Faraday tongues and on the associated bifurcation diagrams induced by the interaction of meniscus and sub-harmonic parametric waves.
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 to a contact line pinned at the container brim with static contact angle $θ_s=90^{\circ}$ (brimful condition). However, tunable meniscus waves are desired in some applications as those of liquid-based biosensors, where they can be controlled adjusting the shape of the static meniscus by slightly under/over-filling the vessel ($θ_s\ne90^{\circ}$) while keeping the contact line fixed at the brim. Here, we refer to this wetting condition as nearly-brimful. Although classic inviscid theories based on Floquet analysis have been reformulated for the case of a pinned contact line (Kidambi 2013), accounting for (i) viscous dissipation and (ii) static contact angle effects, including meniscus waves, makes such analyses practically intractable and a comprehensive theoretical framework is still lacking. Aiming at filling this gap, in this work we formalize a weakly nonlinear analysis via multiple timescale method capable to predict the impact of (i) and (ii) on the instability onset of viscous sub-harmonic standing waves in both brimful and nearly-brimful circular-cylinders. Notwithstanding that the form of the resulting amplitude equation is in fact analogous to that obtained by symmetry arguments (Douady 1990), the normal form coefficients are here computed numerically from first principles, thus allowing us to rationalize and systematically quantify the modifications on the Faraday tongues and on the associated bifurcation diagrams induced by the interaction of meniscus and sub-harmonic parametric waves.
