Dynamics and stability of an annular electrolyte film
Dynamics and stability of an annular electrolyte film
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DOI：
10.1017/s0022112010001254
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发表时间：
2010-05
影响因子：
3.7
通讯作者：
D. Conroy;R. Craster;O. Matar;D. Papageorgiou
中科院分区：
文献类型：
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作者：
D. Conroy;R. Craster;O. Matar;D. Papageorgiou
我们研究了在存在静电和电动效应的情况下，在均匀圆柱管内和在芯-环排列中，围绕第二电解质核心流体的电解液膜的演化。研究了岩心流体电解质为理想导体时的极限情况。我们对薄环形极限进行了渐近分析，得到了界面位置的非线性演化方程，该方程考虑了静电和动电效应，适用于随膜厚变化的小德拜长度，即电荷分离发生在与环状层厚度成比例的距离上。在德拜-胡克尔极限(对小势能有效)和完全非线性的泊松-玻尔兹曼方程中推导和研究了该方程。这些方程由电毛细管数、无因次标度反德拜长度和界面与壁面静电势之比来表征。我们利用线性稳定性分析探讨了电动力学对界面动力学的影响，并对周期边界条件下的初值问题进行了广泛的数值模拟。对可能发生的全奇异有限时间破裂事件进行了联合非线性分析。根据参数区域的不同，电动力学要么稳定薄膜，要么使薄膜不稳定，在后一种情况下，导致薄膜在有限时间内破裂。在这种情况下，最终的薄膜形状可以具有环形或线状破裂；破裂动力学被发现是自相似的。相反，在没有静电效应的情况下，薄膜不会在有限的时间内破裂，而是演变成非常长寿命的准静态结构，这些结构被这些非常缓慢演变的液滴和叶的突然重新分布所打断。目前的研究表明，电动效应可以调节以在有限的时间内破裂薄膜，并且破裂时间可以通过改变系统参数来控制。在大规模反德拜长度的极限下，还发现了一些有趣而新颖的行为，即由于不稳定的毛细作用力和稳定的电动作用力之间的平衡，出现了稳定而光滑的非均匀稳态薄膜形状。
We investigate the evolution of an electrolyte film surrounding a second electrolyte core fluid inside a uniform cylindrical tube and in a core-annular arrangement, when electrostatic and electrokinetic effects are present. The limiting case when the core fluid electrolyte is a perfect conductor is examined. We analyse asymptotically the thin annulus limit to derive a nonlinear evolution equation for the interfacial position, which accounts for electrostatic and electrokinetic effects and is valid for small Debye lengths that scale with the film thickness, that is, charge separation takes place over a distance that scales with the annular layer thickness. The equation is derived and studied in the Debye-Hückel limit (valid for small potentials) as well as the fully nonlinear Poisson–Boltzmann equation. These equations are characterized by an electric capillary number, a dimensionless scaled inverse Debye length and a ratio of interface to wall electrostatic potentials. We explore the effect of electrokinetics on the interfacial dynamics using a linear stability analysis and perform extensive numerical simulations of the initial value problem under periodic boundary conditions. An allied nonlinear analysis is carried out to investigate fully singular finite-time rupture events that can take place. Depending upon the parameter regime, the electrokinetics either stabilize or destabilize the film and, in the latter case, cause the film to rupture in finite time. In this case, the final film shape can have a ring- or line-like rupture; the rupture dynamics are found to be self-similar. In contrast, in the absence of electrostatic effects, the film does not rupture in finite time but instead evolves to very long-lived quasi-static structures that are interrupted by an abrupt re-distribution of these very slowly evolving drops and lobes. The present study shows that electrokinetic effects can be tuned to rupture the film in finite time and the time to rupture can be controlled by varying the system parameters. Some intriguing and novel behaviour is also discovered in the limit of large scaled inverse Debye lengths, namely stable and smooth non-uniform steady state film shapes emerge as a result of a balance between destabilizing capillary forces and stabilizing electrokinetic forces.