MOVING CONTACT LINES AND RIVULET INSTABILITIES .1. THE STATIC RIVULET
MOVING CONTACT LINES AND RIVULET INSTABILITIES .1. THE STATIC RIVULET
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DOI：
10.1017/s0022112080000110
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发表时间：
1980-01-01
影响因子：
3.7
通讯作者：
DAVIS, SH
中科院分区：
文献类型：
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作者：
DAVIS, SH
小溪是位于固体表面上的一条狭窄的液体流，与周围的气体共享一个弯曲的界面。用线性化稳定性理论研究了毛细管的不稳定性。该配方适用于接触（公共或三相）线(i)是固定的，（ii）移动但具有固定的接触角，或（iii）移动但具有接触角的平滑函数的小型静态溪流。将线性化的稳定性方程转化为扰动动能平衡，表明扰动响应完全满足阻尼线性谐振方程。“阻尼系数”包含了整体粘性耗散、沿固体滑动的影响以及在接触线条件下产生的所有动态影响（iii）。“弹簧常数”的符号决定了系统的稳定性或不稳定性，它包含了界面面积的变化，在情况（ii）和（iii）中是相同的。因此，对于小扰动，接触角随接触线速度的变化构成一个纯粹的耗散过程。只要存在一定的积分不等式，上述结果与液固界面的滑移模型无关。最后，得到了(i)、（ii）、（iii）三种情况下稳定性的充分条件。
A rivulet is a narrow stream of liquid located on a solid surface and sharing a curved interface with the surrounding gas. Capillary instabilities are investigated by a linearized stability theory. The formulation is for small, static rivulets whose contact (common or three-phase) lines (i) are fixed, (ii) move but have fixed contact angles or (iii) move but have contact angles smooth functions of contact-line speeds. The linearized stability equations are converted to a disturbance kinetic-energy balance showing that the disturbance response exactly satisfies a damped linear harmonic-oscillator equation. The ‘damping coefficient’ contains the bulk viscous dissipation, the effect of slip along the solid and all dynamic effects that arise in contact-line condition (iii). The ‘spring constant’, whose sign determines stability or instability in the system, incorporates the interfacial area changes and is identical in cases (ii) and (iii). Thus, for small disturbances changes in contact angle with contact-line speed constitute a purely dissipative process. All the above results are independent of slip model at the liquid–solid interface as long as a certain integral inequality holds. Finally, sufficient conditions for stability are obtained in all cases (i), (ii) and (iii).