液晶柱在磁场中的平台不稳定性

Dynamic stabilisation of Rayleigh-Plateau modes on a liquid cylinder

We demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh-Plateau (RP) instability on a liquid cylinder by subjecting it to a radial oscillatory body force. Viscosity is found to play a crucial role in this stabilisation. Linear stability predictions are obtained via Floquet analysis demonstrating that RP unstable modes can be stabilised using radial forcing. We also solve the linearised, viscous initial-value problem for free-surface deformation obtaining an equation governing the amplitude of a three-dimensional Fourier mode. This equation gener…

Plateau-Rayleigh Instability of a Cylinder of Viscous Liquid (Rayleigh vs. Chandrasekhar)

In 1982, in his classical work, L. Rayleigh considered the instability of a cylinder of viscous liquid under capillary force, the so-called Plateau-Rayleigh instability. In this work, in linear approximation, he obtained a dispersion equation describing the increment of this instability as a function of wavelength, the radius of cylinder, the mass density, surface tension, and viscosity of the liquid. Hundreds of authors referred to this work, but none of them used his dispersion equation in its complete form; they used only the asymptotic solutions of his equation for zero and infinitely larg…

具有弹性边界的可变形多孔圆柱的压实

Compaction in a deformable porous cylinder with elastic boundaries

本文建立弹性边界细长多孔介质的流体驱动压实模型，推导孔隙度的主导阶非线性扩散方程，揭示流态与弹性参数的关联，得到亚达西、超达西流等不同流态的区分及紧凑表达式。

圆柱体侵彻颗粒介质的速度场和力的实验研究

Experimental velocity fields and forces for a cylinder penetrating into a granular medium

在这里，我们提出了一个详细的颗粒流特性与力的测量准二维的情况下，一个水平的圆柱体垂直穿透在两个平行的玻璃墙之间的干颗粒物质以恒定的速度。在所研究的速度范围内，圆柱体上的拖曳力与速度V_0无关，而主要与圆柱体直径d成正比。而在圆柱体上的力随着其穿透深度而增加，发现圆柱体周围的颗粒速度分布是固定的，其平均值附近的波动导致颗粒温度分布。平均速度分布和温度分布在圆柱附近都表现出很强的局部化。圆柱引起的平均流扰动在远离圆柱的特征长度λ上呈指数衰减，当圆柱/颗粒尺寸比d/dg足够大时，λ~ d/4 + 2dg主要受圆柱直径的影响。颗粒温度在靠近δ T0 ~ λ/2的薄层内呈现一个恒定的平台T0，在远离δ T0 ~ λ/2的薄层内呈指数衰减，其特征长度λ T为几个颗粒直径（λ T ~ 3dg）。颗粒温度平台T_0的尺度为（V_0^2 d_g/d），它是由流动本身产生的，它是由靠近圆柱体的剪切速率V_0/λ在δ_{T_0}上产生的“颗粒热”与远离圆柱体的颗粒热耗散之间的平衡产生的。

The Plateau-Rayleigh instability in solids is a simple phase separation

A long elastic cylinder, radius $a$ and shear-modulus $μ$, becomes unstable given sufficient surface tension $γ$. We show this instability can be simply understood by considering the energy, $E(λ)$, of such a cylinder subject to a homogenous longitudinal stretch $λ$. Although $E(λ)$ has a unique minimum, if surface tension is sufficient ($Γ\equivγ/(aμ)>\sqrt{32}$) it looses convexity in a finite region. We use a Maxwell construction to show that, if stretched into this region, the cylinder will phase separate into two segments with different stretches $λ_1$ and $λ_2$. Our model thus explains w…

Instability of a horizontal water half-cylinder under vertical vibration

We present the results of an experimental investigation on parametrically driven waves in a water half-cylinder on a rigid horizontal plate, which is sinusoidally vibrated in the vertical direction. As the forcing amplitude is raised above a critical value, stationary waves are excited in the water half-cylinder. Parametrically excited subharmonic waves are non-axisymmetricand qualitatively different from the axisymmetric Savart-Plateau-Rayleigh waves in a vertical liquid cylinder or jet. Depending on the driving frequency, stationary waves of different azimuthal wave numbers are excited. A li…