Yoshikawa H N, Meyer A, Crumeyrolle O, Mutabazi I
Laboratoire Ondes et Milieux Complexes, UMR 6294 CNRS-Université du Havre, 53, rue de Prony-76058 Le Havre Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):033003. doi: 10.1103/PhysRevE.91.033003. Epub 2015 Mar 3.
The stability of the circular Couette flow of a dielectric fluid is analyzed by a linear perturbation theory. The fluid is confined between two concentric cylindrical electrodes of infinite length with only the inner one rotating. A temperature difference and an alternating electric tension are applied to the electrodes to produce a radial dielectrophoretic body force that can induce convection in the fluid. We examine the effects of superposition of this thermoelectric force with the centrifugal force including its thermal variation. The Earth's gravity is neglected to focus on the situations of a vanishing Grashof number such as microgravity conditions. Depending on the electric field strength and of the temperature difference, critical modes are either axisymmetric or nonaxisymmetric, occurring in either stationary or oscillatory states. An energetic analysis is performed to determine the dominant destabilizing mechanism. When the inner cylinder is hotter than the outer one, the circular Couette flow is destabilized by the centrifugal force for weak and moderate electric fields. The critical mode is steady axisymmetric, except for weak fields within a certain range of the Prandtl number and of the radius ratio of the cylinders, where the mode is oscillatory and axisymmetric. The frequency of this oscillatory mode is correlated with a Brunt-Väisälä frequency due to the stratification of both the density and the electric permittivity of the fluid. Under strong electric fields, the destabilization by the dielectrophoretic force is dominant, leading to oscillatory nonaxisymmetric critical modes with a frequency scaled by the frequency of the inner-cylinder rotation. When the outer cylinder is hotter than the inner one, the instability is again driven by the centrifugal force. The critical mode is axisymmetric and either steady under weak electric fields or oscillatory under strong electric fields. The frequency of the oscillatory mode is also correlated with the Brunt-Väisälä frequency.
采用线性微扰理论分析了介电流体圆库埃特流的稳定性。该流体被限制在两个无限长的同轴圆柱电极之间，只有内电极旋转。在电极上施加温度差和交变电压，以产生径向介电泳体力，从而在流体中诱发对流。我们研究了这种热电力与离心力叠加的影响，包括其热变化。忽略地球引力，专注于诸如微重力条件下格拉晓夫数为零的情况。根据电场强度和温度差，临界模式可以是轴对称或非轴对称的，出现在静止或振荡状态。进行了能量分析以确定主要的失稳机制。当内圆柱比外圆柱热时，对于弱电场和中等电场，圆库埃特流因离心力而失稳。临界模式是稳定轴对称的，但在普朗特数和圆柱半径比的一定范围内的弱电场除外，在该范围内模式是振荡且轴对称的。这种振荡模式的频率与由于流体密度和介电常数分层引起的布伦特 - 维萨拉频率相关。在强电场下，介电泳力导致的失稳占主导，产生振荡非轴对称临界模式，其频率与内圆柱旋转频率成比例。当外圆柱比内圆柱热时，不稳定性再次由离心力驱动。临界模式是轴对称的，在弱电场下是稳定的，在强电场下是振荡的。振荡模式的频率也与布伦特 - 维萨拉频率相关。
