Extensional fall of a very viscous fluid drop
Extensional fall of a very viscous fluid drop
复制标题
DOI：
10.1093/qjmam/53.4.565
复制
发表时间：
2000-11
影响因子：
0.9
通讯作者：
Y. Stokes;E. Tuck;L. Schwartz
中科院分区：
文献类型：
--
作者：
Y. Stokes;E. Tuck;L. Schwartz
具有大粘度μ和大密度p的有限流体液滴最初在重力g的作用下静止悬挂在固体边界的下侧。初始配置可以是一般边界形状，具有（垂直）最大长度L（0）= L 0和（水平）最大宽度w 0。随后的运动、作为时间t的函数的液滴长度L（t）和边界形状由细长液滴近似理论（对于w 0 <L 0）和精确有限元计算确定。用拉格朗日法和欧拉法推导了细长液滴理论。确定了壁边界层，并对细长液滴理论中出现的Trouton粘度进行了经验修正，以解释这一层。当忽略惯性时，在有限时刻t = t * = O（μ/（ρgL 0））存在一个临界点，当t → t * 时，L（t）→ ∞，这个临界点与液滴脱离和进入自由落体的时间有关。当断点福尔斯落在壁面边界层之外时，它的位置以及由此得到的福尔斯下落的原始液滴的分数可以直接从细长液滴理论得到，并通过有限元计算得到确认。
A finite drop of fluid with large viscosity μ and density p is initially at rest hanging under gravity g from the underside of a solid boundary. The initial configuration may be of a general boundary shape, with (vertical) maximum length L(0) = L 0 and (horizontal) maximum width w 0 . The subsequent motion, drop length L(t) as a function of time t, and boundary shape is determined both by a slender-drop approximate theory (for w 0 « L 0 ) and by an exact finite-element calculation. The slender-drop theory is derived both by Lagrangian and Eulerian methods. A wall boundary layer is identified, and empirical corrections made to the Trouton viscosity appearing in the slender-drop theory to account for this layer. When inertia is neglected, there is a crisis at a finite time t = t * = O(μ/(ρgL 0 )), such that L(t) → ∞ as t → t * , this time being related to the time of break-off and entry of the drop into free fall. When the break point falls outside the wall boundary layer, its location and hence the fraction of the original drop which falls can be obtained directly from the slender-drop theory, and is confirmed by the finite-element computations.