Cilia, hair-like, organelles that are found in the respiratory tract (nasal cavity, pharynx, trachea, and bronchi) rhythmically beat to clear mucus from the airways. Here, we formulate a novel model of fluid flow due to the movement of cilia, and in the companion paper, Part II, the model is numerically solved under simplifying assumptions using physical data from lung bronchi. The model is based on a porous media model, modified so that instead of fluid moving through a solid porous structure, the solid moves the fluid. Two macroscale regions are considered: a porous medium and a free-fluid domain. We use hybrid mixture theory to derive the governing equations so that we have a broader understanding of the assumptions used to obtain the model. The resulting model is the classical Brinkman Stokes equations generalized to account for the movement of the cilia. The model can be used as a prototype to determine the movement of fluid due to the given movement of a solid component of a porous material.

中文翻译：

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纤毛运动对流体速度的影响：I 多孔介质框架中由移动固体引起的流体流动模型

在呼吸道（鼻腔、咽部、气管和支气管）中发现的纤毛、毛发状细胞器有节奏地搏动以清除气道中的粘液。在这里，我们建立了一种由于纤毛运动而引起的流体流动的新模型，在配套论文第二部分中，该模型在简化假设下使用肺支气管的物理数据进行了数值求解。该模型基于多孔介质模型，经过修改，使流体不是通过固体多孔结构移动，而是由固体移动流体。考虑了两个宏观区域：多孔介质和自由流体域。我们使用混合混合理论来推导控制方程，以便我们对用于获得模型的假设有更广泛的理解。由此产生的模型是经典的 Brinkman Stokes 方程，用于解释纤毛的运动。该模型可用作原型来确定由于多孔材料的固体成分的给定运动而导致的流体运动。