Stability of a liquid ring on a substrate
Stability of a liquid ring on a substrate
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DOI：
10.1017/jfm.2012.607
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发表时间：
2013-03-01
影响因子：
3.7
通讯作者：
Kondic, Lou
中科院分区：
文献类型：
--
作者：
Gonzalez, Alejandro G.;Diez, Javier A.;Kondic, Lou
在长波理论的框架下，我们研究了部分润湿衬底上粘性不可压缩流体环的稳定性。我们讨论了在存在接触角滞后的情况下，环达到静态平衡的条件。采用滑移模型对该平衡解进行了线性稳定性分析，以考虑接触线的发散。LSA提供了关于不稳定模式演化的具体预测。为了描述环在更长时间内的演化，我们实现了准静态近似。这一方法假设了一种准静态的演化，并考虑了模式的瞬时增长率的伴随变化，这些模式要么导致环坍塌成单一的中心液滴，要么沿着环的外围分裂成多个液滴。我们将LSA和准静态模型方法的结果与使用互补分离压力模型的非线性数值模拟的结果进行了比较。我们发现这两个模型对破碎过程中形成的液滴的预期数量的预测非常一致。
We study the stability of a viscous incompressible fluid ring on a partially wetting substrate within the framework of long-wave theory. We discuss the conditions under which a static equilibrium of the ring is possible in the presence of contact angle hysteresis. A linear stability analysis (LSA) of this equilibrium solution is carried out by using a slip model to account for the contact line divergence. The LSA provides specific predictions regarding the evolution of unstable modes. In order to describe the evolution of the ring for longer times, a quasi-static approximation is implemented. This approach assumes a quasi-static evolution and takes into account the concomitant variation of the instantaneous growth rates of the modes responsible for either collapse of the ring into a single central drop or breakup into a number of droplets along the ring periphery. We compare the results of the LSA and the quasi-static model approach with those obtained from nonlinear numerical simulations using a complementary disjoining pressure model. We find remarkably good agreement between the predictions of the two models regarding the expected number of drops forming during the breakup process.