Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers
Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers
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DOI：
10.1017/s0022112003004476
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发表时间：
2003-06-25
影响因子：
3.7
通讯作者：
Frenkel, AL
中科院分区：
文献类型：
--
作者：
Halpern, D;Frenkel, AL
考虑了界面上有不溶性表面活性剂单层的两层体系的蠕动流动。本文在Stokes近似下发展了平面Couette-Poiffille流的线性稳定性理论。为了分离马兰戈尼效应，重力被排除在外。由于界面表面活性剂的剪切流不稳定性，发现较早的长波（Frenkel和Halpern 2002），研究包括所有波长，并在整个参数空间的Marangoni数M，粘度比m，界面速度剪切s，和厚度比n（大于或等于1）。简正波的复波速解一个二次方程，增长率函数在所有波数和所有参数值下都是连续的。当M > 0，s不等于0，m < n（2），n > 1时，只要扰动波足够长，小扰动就会增长。然而，在以下意义上，不稳定性不是长波：不稳定波不一定比两层厚度中较小的一层长得多。另一方面，有参数制度的不稳定性有一个中波字符，流动是稳定的，在足够大和足够小的波长和不稳定的之间。研究了参数空间中的临界（失稳）流形。此外，它示出，对于某些参数限制的色散函数的收敛是非均匀的相对于波数。这是用来解释参数的不连续性的长波增长率指数发现较早。
Creeping flow of a two-layer system with a monolayer of an insoluble surfactant on the interface is considered. The linear-stability theory of plane Couette-Poiseuille flow is developed in the Stokes approximation. To isolate the Marangoni effect, gravity is excluded. The shear-flow instability due to the interfacial surfactant, uncovered earlier for long waves only (Frenkel & Halpern 2002), is studied with inclusion of all wavelengths, and over the entire parameter space of the Marangoni number M, the viscosity ratio m, the interfacial velocity shear s, and the thickness ratio n (greater than or equal to 1). The complex wave speed of normal modes solves a quadratic equation, and the growth rate function is continuous at all wavenumbers and all parameter values. If M > 0, s not equal 0, m < n(2), and n > 1, the small disturbances grow provided they are sufficiently long wave. However, the instability is not long wave in the following sense: the unstable waves are not necessarily much longer than the smaller of the two layer thicknesses. On the other hand, there are parametric regimes for which the instability has a mid-wave character, the flow being stable at both sufficiently large and small wavelengths and unstable in between. The critical (instability-onset) manifold in the parameter space is investigated. Also, it is shown that for certain parametric limits the convergence of the dispersion function is non-uniform with respect to the wavenumber. This is used to explain the parametric discontinuities of the long-wave growth-rate exponents found earlier.