Conroy Devin, Matar Omar K
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ UK.
J Eng Math. 2017;107(1):253-268. doi: 10.1007/s10665-017-9938-2. Epub 2017 Sep 15.
We consider the interfacial dynamics of a thin, ferrofluid film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly conducting, and its dynamics are governed by a coupled system of the steady Maxwell, Navier-Stokes, and continuity equations. The magnetization of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved by means of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We study the three-dimensional evolution of the film to spanwise perturbations by solving the nonlinear equations numerically. The constant-volume configuration is considered, which corresponds to a slender drop flowing down an incline. A parametric study is then performed to understand the effect of the magnetic field on the stability and structure of the interface.
我们考虑在磁场作用下，沿倾斜基底流下的薄铁磁流体薄膜的界面动力学，该薄膜上方由无粘性气体界定。假设流体具有弱导电性，其动力学由稳态麦克斯韦方程、纳维 - 斯托克斯方程和连续性方程的耦合系统控制。薄膜的磁化强度是磁场的函数，并由朗之万函数规定。我们利用长波简化来求解薄膜内部压力、速度和磁场的动力学。气相中的势通过傅里叶变换求解。通过使用运动学条件和磁场，施加适当的界面条件可构建界面形状的演化方程。我们通过数值求解非线性方程来研究薄膜对展向扰动的三维演化。考虑了等容构型，这对应于沿斜坡流下的细长液滴。然后进行参数研究以了解磁场对界面稳定性和结构的影响。
