带电液体射流中的Kortweg de-Vries孤子
Kortweg de-Vries solitons on electrified liquid jets
摘要：
研究了径向电场作用下轴对称波在液体射流表面的传播。射流被假定为无粘性的和完美的传导，和一个字段被设置通过放置在一个完美的圆柱形管的壁保持在一个恒定的电位内同心的射流。一个非平凡的相互作用之间的流体力学和电场的环，导致在形成的电毛细波。本研究的主要目的是描述这种轴对称波的非线性方面的弱非线性制度，这是有效的长波相对于未受干扰的射流半径。这被发现是可能的，如果两个条件成立：外电极半径不是太小，和所施加的电场是足够强的。在这些条件下，长波被证明是色散的，弱非线性理论可以发展到描述的扰动的演变。出现的正则系统是Kortweg de-Vries方程，其系数随着电场和电极半径的变化而变化。有趣的是，最高阶三阶导数项的系数不改变符号并且保持严格正，而非线性项的系数$α$可以针对参数的某些值改变符号。这一发现意味着孤立的电毛细波是可能的;有波的海拔为$α>0$和抑郁的$α<0$。在参数空间中的区域被识别出这样的波被发现。
英文摘要：
The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric field is considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jet concentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivial interaction arises between the hydrodynamics and the electric field in the annulus, resulting in the formation of electrocapillary waves. The main objective of the present study is to describe nonlinear aspects of such axisymmetric waves in the weakly nonlinear regime which is valid for long waves relative to the undisturbed jet radius. This is found to be possible if two conditions hold: the outer electrode radius is not too small, and the applied electric field is sufficiently strong. Under these conditions long waves are shown to be dispersive and a weakly nonlinear theory can be developed to describe the evolution of the disturbances. The canonical system that arises is the Kortweg de-Vries equation with coefficients that vary as the electric field and the electrode radius are varied. Interestingly, the coefficient of the highest order third derivative term does not change sign and remains strictly positive, whereas the coefficient $α$ of the nonlinear term can change sign for certain values of the parameters. This finding implies that solitary electrocapillary waves are possible; there are waves of elevation for $α>0$ and of depression for $α<0$. Regions in parameter space are identified where such waves are found.
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