The Rayleigh–Taylor instability of a viscous liquid layer resting on a plane wall
The Rayleigh–Taylor instability of a viscous liquid layer resting on a plane wall
复制标题
平面壁上粘性液体层的瑞利-泰勒不稳定性
DOI：
10.1017/s0022112090000878
复制
发表时间：
1990
影响因子：
3.7
通讯作者：
C. Pozrikidis
中科院分区：
文献类型：
--
作者：
L. Newhouse;C. Pozrikidis
考虑了位于具有较高密度的第二种液体下方的平面壁上的液体层的非线性瑞利-泰勒不稳定性。在蠕动流的假设下，将运动研究为表面张力和两种流体粘度比的函数。由层变形引起的流动由格林函数的界面分布表示。针对分布密度推导了第二类 Fredholm 积分方程，并通过连续迭代求解。结果表明，对于较小和中等的表面张力，该层的不稳定性导致形成周期性的粘性羽流阵列，这些羽流渗透到上覆的流体中。这些羽流的形态很大程度上取决于粘度比和表面张力。当上覆流体的粘度与该层的粘度相当或更大时，羽流由狭窄茎顶部的明确界定的前滴组成。当上覆流体的粘度小于该层的粘度时，羽流呈现紧凑的上升流体柱的形式。引导羽流的液滴的大小大致与该层的初始厚度成正比。当表面张力足够小时，环境流体被夹带到领先的液滴中并以螺旋模式循环。上升羽流产生的对流以流线图案可视化，并讨论了残余层变薄的速率以及上升水滴或羽流的速度。
The nonlinear Rayleigh–Taylor instability of a liquid layer resting on a plane wall below a second liquid of higher density is considered. Under the assumption of creeping flow, the motion is studied as a function of surface tension and the ratio of the viscosities of the two fluids. The flow induced by the deformation of the layer is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind is derived for the density of the distribution, and is solved by successive iteration. The results show that for small and moderate surface tension, the instability of the layer leads to the formation of a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of these plumes strongly depends upon the viscosity ratio and surface tension. When the viscosity of the overlying fluid is comparable with or larger than that of the layer, the plumes are composed of a well-defined leading drop on top of a narrow stem. When the viscosity of the overlying fluid is smaller than that of the layer, the plumes take the form of a compact column of rising fluid. The size of the drop leading a plume is roughly proportional to the initial thickness of the layer. When surface tension is sufficiently small, ambient fluid is entrained into the leading drop and circulates in a spiral pattern. Convection currents generated by the rising plumes are visualized with streamline patterns, and the rate of thinning of the remnant layer, as well as the speed of the rising drop or plumes, are discussed.