Influence of slow rotation on the stability of a thermocapillary incompressible liquid flow in an infinite layer under zero-gravity conditions for small Prandtl number
Influence of slow rotation on the stability of a thermocapillary incompressible liquid flow in an infinite layer under zero-gravity conditions for small Prandtl number
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DOI：
10.1088/0169-5983/44/3/031416
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发表时间：
2012-06
影响因子：
1.5
通讯作者：
K. Shvarts
中科院分区：
文献类型：
--
作者：
K. Shvarts
研究了失重条件下旋转无限薄液层中热毛细流动的不稳定性。层的两个边界被假定为平面和自由，并受到切向热毛细Marangoni力。边界处的对流热传递受牛顿定律支配，并且边界附近的流体的温度是坐标的线性函数。旋转轴垂直于液体层。旋转是缓慢的，这使得我们可以忽略离心力。所研究的热毛细流动的解析描述，是一个精确的解的Navier-Stokes方程。根据稳定性的线性理论，得到的中性曲线描绘的临界Marangoni数对波数的依赖性在不同的值的泰勒数为小普朗特数（Pr = 0.1）。数值研究了稳定性阈值以外的有限振幅扰动的行为。
Instability of a thermocapillary flow arising in a rotating thin infinite liquid layer under zero-gravity conditions is investigated. Both boundaries of the layer are assumed to be plane and free and are subject to the tangential thermocapillary Marangoni force. A convective heat transfer at the boundaries is governed by Newton's law and the temperature of the fluid near the boundaries is a linear function of the coordinates. The axis of rotation is perpendicular to a liquid layer. The rotation is slow, which allows us to neglect the centrifugal force. The examined thermocapillary flow is described analytically, being an exact solution of the Navier–Stokes equations. According to the linear theory of stability the obtained neutral curves depict the dependence of the critical Marangoni number on the wave number at different values of the Taylor number for the small Prandtl number (Pr = 0.1). The behavior of the finite-amplitude perturbations beyond the stability threshold is studied numerically.