This paper suggests a fractal two-phase fluid model for the polymer melt filling process to deal effectively with the unsmooth front interface. An infinitesimal fluid element model in a fractal space is proposed to establish the governing equations according to the conservation laws in fluid mechanics, the fractal divergence and fractal Laplace operator are defined. The unsmooth interface is solved numerically, and fibers’ motion properties on the interface are also elucidated. Moreover, the distribution of fibers on the interface at different stages shows the fractal property of the fibers’ motion. However, the motion of fibers is affected by the flow of macroscopic polymer melt, and the fiber orientation in the interface shows a certain statistical regularity. Based on the characters of fiber orientation, the fractal interface can be used for the optimal design of the polymer melt filling process.

中文翻译：

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聚合物填充过程中纤维运动的分形两相流动模型

本文提出了聚合物熔体填充过程的分形两相流体模型，以有效处理不光滑的前界面。根据流体力学的守恒定律，提出了分形空间中的极小流体元模型，建立了控制方程，定义了分形散度和分形拉普拉斯算子。对非光滑界面进行了数值求解，并阐明了界面上纤维的运动特性。此外，不同阶段纤维在界面上的分布表现出纤维运动的分形特性。但纤维的运动受宏观聚合物熔体流动的影响，界面中的纤维取向表现出一定的统计规律。根据纤维取向的特点，