Two-phase porous media flow is important in many applications from drug delivery to groundwater diffusion and oil recovery and is of particular interest to biomedical diagnostic test developers using cellulose and nitrocellulose membranes with limited fluid sample volumes. This work presents a new two-phase porous media flow model based on the incompressible Navier–Stokes equation. The model aims to address the limitations of existing methods by incorporating a partial saturation distribution in porous media to account for limited fluid volumes. The basic parameters of the model are the pore size distribution and the contact angle. To validate the model, we solved five analytical solutions and compared them to corresponding experimental data. The experimentally measured penetration length data agreed with the model predictions, demonstrating model accuracy. Our findings suggest that this new two-phase porous media flow model can provide a valuable tool for researchers developing fluidic assays in paper and other porous media.

中文翻译：

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基于不可压缩纳维-斯托克斯方程的两相多孔介质流动模型

两相多孔介质流在从药物输送到地下水扩散和石油回收的许多应用中都很重要，并且对于使用纤维素和硝化纤维素膜和有限流体样本量的生物医学诊断测试开发人员特别感兴趣。这项工作提出了一种基于不可压缩纳维-斯托克斯方程的新两相多孔介质流模型。该模型旨在通过在多孔介质中结合部分饱和度分布来解决有限的流体体积，从而解决现有方法的局限性。模型的基本参数是孔径分布和接触角。为了验证模型，我们求解了五个解析解并将它们与相应的实验数据进行比较。实验测量的穿透长度数据与模型预测一致，证明了模型的准确性。我们的研究结果表明，这种新的两相多孔介质流动模型可以为研究人员在纸张和其他多孔介质中开发流体测定提供有价值的工具。