Capillary–viscous forcing of surface waves
Capillary–viscous forcing of surface waves
复制标题
表面波的毛细管粘性强迫
DOI：
10.1017/s0022112090003123
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发表时间：
1990
影响因子：
3.7
通讯作者：
J. Miles
中科院分区：
文献类型：
--
作者：
J. Miles
在x = 0时，亲水壁的正弦垂直运动对深层粘性液体表面（x > 0）上的直峰毛细重力波的线性激发的响应是基于以下假设计算的：（i）接触角的动态变化与接触线相对于壁的速度（但不一定同相）;（ii）接触线下方的流体的相对切向速度（滑移）与壁处的剪切成比例，（iii）k 0 lv [Lt ] 1和k 0 lc = O（1），其中k 0是波数，lv是边界层厚度，lc是毛细管长度。的接触角和滑移系数是复杂的函数的频率被发现是线性相关的。物理上的考虑表明，滑移长度ls（壁面处的滑移速度/剪力）与lv相比应该小，这又意味着接触线的运动在参数域中必须小，在该参数域中线性化提供了壁面附近波动的可行描述;然而，分析从（i）和（ii）出发，作为现象学假设，对接触线和滑移系数没有先验限制。目前的结果包括Wilson和Jones（1973）的结果，他们假定壁面处波斜率的振幅和相位是规定的，以及Hocking（1987 a）的结果，他们假定壁面处波斜率的变化与接触线速度同相，并忽略粘性。它们还包括对静态弯月面的动态效应的校正，静态弯月面对于除1/2 π以外的任何静态接触角都是必然存在的，但在先前的分析中被忽略，并且对于密切相关的问题有对应的问题（参见图1）。Hocking 1987 b）的平面波从静止壁的反射。
The linear excitation of straight-crested, capillary–gravity waves on the surface (x > 0) of a deep, viscous liquid in response to the sinusoidal, vertical motion of a hydrophilic wall at x = 0 is calculated on the assumptions that: (i) the dynamical variation of the contact angle is proportional to (but not necessarily in phase with) the velocity of the contact line relative to the wall; (ii) the relative tangential velocity (slip) of the fluid below the contact line is proportional to the shear at the wall, (iii) k0lv [Lt ] 1 and k0lc = O(1), where k0 is the wavenumber, lv is the boundary-layer thickness, and lc is the capillary length. The contact-angle and slip coefficients are complex functions of frequency that are found to be linearly related. Physical considerations suggest that the slip length ls (≡ slip velocity ÷ shear at wall) should be small compared with lv, which, in turn, implies that the motion of the contact line must be small in that parametric domain in which linearization provides a viable description of the wave motion near the wall; however, the analysis proceeds from (i) and (ii), qua phenomenological hypotheses, without a priori restrictions on the contact-line and slip coefficients. The present results include those of Wilson & Jones (1973), who assume that the amplitude and phase of the wave slope at the wall are prescribed, and those of Hocking (1987a), who assumes that the variation of the wave slope at the wall is in phase with the contact-line velocity and neglects viscosity. They also include a correction for the dynamical effects of the static meniscus, which is necessarily present for any static contact angle other than ½π but is neglected in the previous analyses, and have counterparts for the closely related problem (cf. Hocking 1987b) of the reflection of a plane wave from a stationary wall.