We analyze the magnetization relaxation effects of a ferrofluid film flow governed by the ferrohydrodynamics encompassing the Fokker–Planck magnetization equation in a Couette–Poiseuille configuration subject to an applied uniform stationary magnetic field perpendicular to the boundaries. A solver based on OpenFOAM is programmed to find solutions numerically for the velocity, spin velocity, and magnetization in ferrofluid films under the combined pressure gradient, boundary flow, and magnetic field forcing. The solver is validated by comparison with the classical Couette–Poiseuille flows and the analytic solutions of the magnetization relaxation problem when the product of flow vorticity and relaxation time is much smaller than unit, $\Omega {\tau }_B\ll 1$. We compare the effects of magnetization relaxation obtained from the phenomenological magnetization equation with those from the equation derived microscopically. The results obtained from the former equation are not suitable for the description of ferrofluid film flows. Due to the magnetization relaxation effects, a misalignment between the local magnetization and the local magnetic field is observed. The net effects are that the flow is hampered by magnetic fields and it manifests as diminished slopes of vorticity profiles and reduced volumetric flow rates. The magnetization relaxation effects also slow down the spin velocity of particles or change their direction, which leads to an enhanced effective viscosity. The total tangential stress exerted on the moving boundary is higher than that of the classical Couette–Poiseuille flow owing to the addition of a magnetic stress. The magnetization relaxation effect is more significant in cases of ferrofluids with higher relaxation times.

中文翻译：

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均匀磁场下铁磁薄膜流中磁化弛豫的影响

我们分析了铁流体膜流的磁化弛豫效应，该流受铁磁流体动力学的支配，其中包括在垂直于边界的均匀固定磁场作用下，库特-泊厄构造中的福克-普朗克磁化方程式。对基于OpenFOAM的求解器进行编程，以找到在压力梯度，边界流和磁场强迫共同作用下铁磁流体膜中速度，自旋速度和磁化强度的数值解。当流动涡度和弛豫时间的乘积远小于单位乘积时，通过与经典Couette-Poiseuille流动以及磁化弛豫问题的解析解进行比较来验证该求解器，$\Omega {\tau }_{乙}\ll \mathrm{1个}$。我们比较了从现象学磁化方程获得的磁化弛豫效应和从微观推导的方程获得的磁化弛豫效应。从前一个方程式获得的结果不适用于描述铁磁薄膜流动。由于磁化弛豫效应，观察到局部磁化与局部磁场之间的未对准。最终的结果是，气流受到磁场的阻碍，表现为涡度曲线斜率减小和体积流量减小。磁化弛豫效应还会减慢颗粒的自旋速度或改变其方向，从而导致有效粘度提高。由于增加了磁应力，施加在运动边界上的总切向应力要高于经典的库埃特-泊瓦伊流。在具有更长弛豫时间的铁磁流体的情况下，磁化弛豫效果更为显着。