Direct numerical simulations are presented for a porous media model consisting of two immiscible fluids, an invading and defending phase, in a two-dimensional micro-geometry filled with randomly sized and randomly distributed cylinders. First, interface instability and penetration modes are studied when varying the wetting features of a single pore in the porous medium. It is found that the displacement patterns not only change with the capillary number, as previously observed, but also are a function of the contact angle, even for a viscosity ratio of unity. This is an important conclusion suggesting that capillary number and viscosity ratio alone cannot completely describe the pore-scale displacement. Second, rapid pore-scale displacement is considered, where the displacements are accompanied by sudden interface jumps from one site to another, known as Haines jumps. The characteristic time and length scales of a Haines jump are examined to better understand the transient dynamics of the jump. We then focus on analyzing the Haines jump in a simple pore configuration where cylinders of equal size are placed at the vertices of equilateral triangles. We use this geometry to provide more insight into the effect of the contact angle at which the Haines jump is predicted.

在包含随机大小和随机分布的圆柱的二维微观几何结构中，提出了由两种不混溶流体（侵入和防御阶段）组成的多孔介质模型的直接数值模拟。首先，研究了改变多孔介质中单个孔的润湿特征时的界面不稳定性和渗透模式。已经发现，位移模式不仅如先前观察到的那样随着毛细管数而变化，而且即使对于粘度比为1的情况，也是接触角的函数。这是一个重要的结论，表明仅凭毛细管数和粘度比不能完全描述孔尺度位移。其次，考虑了快速的孔尺度位移，其中位移伴随着界面突然从一个位置跳到另一个位置，被称为海恩斯跳。检查Haines跳跃的特征时间和长度标度，以更好地理解跳跃的瞬态动力学。然后，我们着重分析简单孔结构中的Haines跃迁，其中等大小的圆柱体放置在等边三角形的顶点处。我们使用这种几何形状可以更深入地了解预测海恩斯跳跃的接触角的影响。