Electrified viscous thin film flow over topography
Electrified viscous thin film flow over topography
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DOI：
10.1017/s002211200700986x
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发表时间：
2007-11
影响因子：
3.7
通讯作者：
D. Tseluiko;M. Blyth;D. Papageorgiou;J. Vanden-Broeck
中科院分区：
文献类型：
--
作者：
D. Tseluiko;M. Blyth;D. Papageorgiou;J. Vanden-Broeck
本文研究了在垂直电场作用下，沿具有周期性凹坑的倾斜壁面向下的重力驱动液膜流动。薄膜被假定为理想导体，薄膜上方的空气边界区域被视为理想电介质。特别是，电场和地形之间的相互作用进行检查，通过预测稳定条件下的膜表面的形状。一个非线性的，非局部的演化方程的液体膜的厚度，使用长波渐近分析。定常解计算流入一个矩形沟槽和一个矩形丘，其形状近似与光滑的功能。膜轮廓的壁的几何形状的陡度增加的限制行为进行了讨论。使用大量的数值证据，它是建立在地形陡度增加对矩形步骤，沟槽，或土堆，界面斜率保持有界，和膜不接触的墙壁。在没有电场的情况下，薄膜在向下的台阶上方形成毛细脊，在向上的台阶前方形成轻微的凹陷。它演示了如何电场可用于完全消除毛细脊在向下的步骤。相反，施加电场导致在向上的台阶处产生自由表面脊。还考虑了电场对膜流进入相对窄的沟槽、在相对窄的丘上和向下略微倾斜的基板的影响。
The gravity-driven flow of a liquid film down an inclined wall with periodic indentations in the presence of a normal electric field is investigated. The film is assumed to be a perfect conductor, and the bounding region of air above the film is taken to be a perfect dielectric. In particular, the interaction between the electric field and the topography is examined by predicting the shape of the film surface under steady conditions. A nonlinear, non-local evolution equation for the thickness of the liquid film is derived using a long-wave asymptotic analysis. Steady solutions are computed for flow into a rectangular trench and over a rectangular mound, whose shapes are approximated with smooth functions. The limiting behaviour of the film profile as the steepness of the wall geometry is increased is discussed. Using substantial numerical evidence, it is established that as the topography steepness increases towards rectangular steps, trenches, or mounds, the interfacial slope remains bounded, and the film does not touch the wall. In the absence of an electric field, the film develops a capillary ridge above a downward step and a slight depression in front of an upward step. It is demonstrated how an electric field may be used to completely eliminate the capillary ridge at a downward step. In contrast, imposing an electric field leads to the creation of a free-surface ridge at an upward step. The effect of the electric field on film flow into relatively narrow trenches, over relatively narrow mounds, and down slightly inclined substrates is also considered.