Homogenization of Nondilute Suspension of Viscous Fluid with Magnetic Particles
Homogenization of Nondilute Suspension of Viscous Fluid with Magnetic Particles
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DOI：
10.1137/21m1413833
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发表时间：
2021-01
期刊：
影响因子：
--
通讯作者：
T. Dang;Y. Gorb;Silvia Jiménez Bolanos
中科院分区：
文献类型：
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作者：
T. Dang;Y. Gorb;Silvia Jiménez Bolanos
本文旨在进行严格的均匀化的颗粒流组成的非稀悬浮液的粘性牛顿流体与可磁化颗粒。假设流体由斯托克斯流描述，而颗粒是顺磁性的或反磁性的，其中磁化场是磁场的线性函数。相应的偏微分方程的系数是局部周期的。还假设流体域和颗粒之间的单向耦合。这种悬浮液的均匀化或有效的响应，推导出所获得的渐近进行数学证明。后者采用双尺度收敛方法。因此，所提出的结果提供了一个合理的正式渐近分析L\'{e}vy和Sanchez-Palestine颗粒稳态Stokes流。
This paper seeks to carry out the rigorous homogenization of a particulate flow consisting of a non-dilute suspension of a viscous Newtonian fluid with magnetizable particles. The fluid is assumed to be described by the Stokes flow, while the particles are either paramagnetic or diamagnetic, for which the magnetization field is a linear function of the magnetic field. The coefficients of the corresponding partial differential equations are locally periodic. A one-way coupling between the fluid domain and the particles is also assumed. The homogenized or effective response of such a suspension is derived, and the mathematical justification of the obtained asymptotics is carried out. The two-scale convergence method is adopted for the latter. As a consequence, the presented result provides a justification for the formal asymptotic analysis of L\'{e}vy and Sanchez-Palencia for particulate steady-state Stokes flows.