Abstract Liquid imbibition with dynamic contact angle is a ubiquitous phenomenon of fluid flow in porous media, but its analytical solution is challenging to derive. In this work, the analytical solution of liquid imbibition in an inclined capillary tube with velocity-dependent contact angle and gravity is first derived. The time required for the liquid-gas interface to reach a certain distance by spontaneous imbibition with static contact angle and dynamic contact angle are provided. Assuming that the porous medium consists of a bundle of tortuous capillary tubes with fractal distribution of pore size, a mathematical model of liquid imbibition in core-scale porous media with dynamic contact angle and gravity is developed. The studies show that the dynamic contact angle can significantly reduce the imbibition velocity at the initial stage of imbibition, especially in large pores, which forms a nonlinear correlation between imbibition velocity and imbibition time in a log-log plot.

中文翻译：

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具有动态接触角和重力的液体自吸进入气体饱和多孔介质的数学模型

摘要 具有动态接触角的液体自吸是多孔介质中流体流动的普遍现象，但其解析解很难推导出。在这项工作中，首先推导出具有速度依赖的接触角和重力的倾斜毛细管中液体吸收的解析解。提供了液-气界面通过静态接触角和动态接触角的自吸到达一定距离所需的时间。假设多孔介质由一束具有分形孔径分布的曲折毛细管组成，建立了具有动态接触角和重力的岩心多孔介质中液体渗吸的数学模型。