Imbibition is an important process encountered in many porous media applications. At the pore scale, pore network models (PNM) are computationally efficient and can model drainage accurately. However, using PNM to model imbibition still remains a challenge due to the complexities encountered in understanding pore-scale flow phenomena related to pore body filling (PBF) and snap-off along with the relative competition between these events. In this work, we use direct numerical simulations (DNS) to revisit the basic principles of PBF in a two-dimensional synthetic pore geometry. We notice that PBF during spontaneous imbibition is dependent on several parameters such as shape of the transition zone, contact angle and the fluid properties like density. The interactions between these parameters are investigated in a quantitative manner. We demonstrate the existence of a critical contact angle 𝜃_c and a barrier contact angle 𝜃_b. 𝜃_c depends on the shape of the pore geometry, whereas 𝜃_b depends on the pore geometry, contact angle and fluid properties. For a system comprising of light fluids, 𝜃_b is only slightly larger than 𝜃_c; whereas for a system occupied by dense fluids, 𝜃_b is notably larger than 𝜃_c. The contact angle of the wetting phase 𝜃 in relation to 𝜃_c and 𝜃_b decides if the wetting phase can imbibe a pore body. Imbibition always occurs if 𝜃 < 𝜃_c. For 𝜃 > 𝜃_c, we observe capillary barrier zones in which capillary forces accompany viscous forces to resist spontaneous imbibition. For this case, we observe smooth transition of the meniscus curvature while the meniscus enters and exits capillary barrier zones. For 𝜃_c ≤ 𝜃 ≤ 𝜃_b, inertia assists the wetting phase to overcome resisting forces and imbibe the pore space. For 𝜃 > 𝜃_b, the resisting forces dominate over inertia so that the wetting phase cannot imbibe the pore space. For the synthetic pore geometries investigated, we provide analytical and semi-analytical expressions to determine 𝜃_c and the position of capillary barrier zones respectively. The barrier contact angle 𝜃_b is computed numerically for several inertial systems and for various shapes of the synthetic pore geometry. The results of this quantitative analysis can be utilised to improve the existing pore filling rules and predictive capabilities of PNM used for two-phase flows.

中文翻译：

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进行自发吸收的孔网建模：接触角相关的侵入模式和动态毛细屏障的发生

吸着是许多多孔介质应用中遇到的重要过程。在孔隙尺度上，孔隙网络模型（PNM）在计算上是有效的，并且可以准确地对排水进行建模。然而，由于在理解与孔隙体充填（PBF）和折断有关的孔隙尺度流动现象以及这些事件之间的相对竞争方面遇到的复杂性，使用PNM进行吸水建模仍然是一个挑战。在这项工作中，我们使用直接数值模拟（DNS）来重新研究二维合成孔几何学中PBF的基本原理。我们注意到自发吸收过程中的PBF取决于几个参数，例如过渡区的形状，接触角和流体性质（例如密度）。这些参数之间的相互作用以定量方式研究。𝜃 _c和势垒接触角𝜃 _b。𝜃 _c取决于孔隙几何形状，而𝜃 _b取决于孔隙几何形状，接触角和流体性质。对于包含光流体的系统中， θ _b是仅稍大θ _Ç ; 而对于由稠密流体占据的系统，𝜃 _b明显大于𝜃 _c。润湿相的接触角θ相对于θ _{c ^}和θ _b决定润湿阶段是否可以吸收孔体。如果𝜃 < 𝜃 _c，则总是发生吸入。对于𝜃 > 𝜃 _c，我们观察到毛细屏障区，其中毛细作用力与粘性力相伴以抵抗自发吸收。对于这种情况，我们观察到弯液面进入和离开毛细管屏障区时弯液面曲率的平滑过渡。对于θ _Ç ≤ θ ≤ θ _b，惯性有助于润湿相以克服抵抗的力和吸收孔隙空间。对于𝜃 > 𝜃 _b，抵抗力在惯性上占主导地位，因此润湿阶段无法吸收孔隙空间。对于所研究的合成孔的几何形状，我们提供了解析和半解析表达式来分别确定𝜃 _c和毛细管屏障区的位置。阻挡接触角θ _b是数值地计算若干惯性系统和用于合成孔几何形状的各种形状。定量分析的结果可用于改善现有的孔填充规则和用于两相流的PNM的预测能力。