面向斯托克斯流通过薄孔洞弹性层的纳米尺度弹性位移Navier滑移类型有效界面律

本文推导了描述流体通过厚度和周期为 $\varepsilon$（远小于体域规模）的薄弹性多孔膜的有效模型。微观模型涉及由固相和流体填充孔隙组成的周期结构薄膜， governed by a coupled fluid-structure interaction system: instationary Stokes equations for the fluid and linear elasticity for the solid, with two distinct scalings of the elastic stress tensor yielding different effective behaviors. 使用适用于薄域和振荡微结构的两尺度收敛技术，膜被简化为一个有效界面，并推导了跨界条件。 resulting macroscopic model couples the bulk fluid domains via effective interface laws of Navier-slip-type including the dynamic displacement. The character of this coupling depends critically on the choice of the scaling in the elastic stress tensor, leading to either a membrane equation or a Kirchhoff-Love plate equation for the effective displacement. The resulting interface conditions naturally admit mass exchange between the adjacent fluid regions. In the analytical framework, a new two-scale compactness theorem for the symmetric gradient is established, underpinning the passage to the limit in the coupled system. Moreover, cell problem techniques are employed systematically to construct admissible test functions and to rigorously extract the effective macroscopic coefficients.