In immiscible liquid–liquid Newtonian flow through a porous medium, one phase often becomes trapped in corners or narrow regions by capillary forces as blobs (e.g. oil ganglia) deep within the matrix, whilst the second flow exhibits a steady and laminar flow (e.g. of water) that has negligible influence on the trapped liquid–liquid interfaces. However, recent microfluidic experiments have shown the situation radically changes when using a viscoelastic liquid, which is capable of exhibiting pore-scale unsteady flow that can deform such interfaces. Here, a computational model is developed which allows us to capture the forces that cause this behaviour and provide a framework for future investigations of this system. In this paper, the forces on trapped interfaces are investigated for the first time. Notably, when the viscoelastic flow becomes unsteady the forces on the trapped interfaces not only fluctuate but also become amplified, thus supporting experimental findings showing they can be used to free such interfaces. At Weissenberg values of 1.5 and above the fluctuations become important and the mean values of the forces on the interfaces decrease as the fluctuations grow.

在通过多孔介质的不混溶的液-液牛顿流中，当基质深处的斑点（例如油性神经节）时，一相通常会被毛细作用力困在角落或狭窄区域，而第二相则表现出稳定的层流（例如水）对捕获的液-液界面的影响可忽略不计。但是，最近的微流体实验表明，当使用粘弹性液体时，情况发生了根本性的变化，这种粘弹性液体能够表现出会导致这种界面变形的孔尺度不稳定流动。在这里，开发了一个计算模型，该模型使我们能够捕获导致这种行为的力，并为以后对该系统的研究提供框架。在本文中，首次研究了受困界面上的力。值得注意的是 当粘弹性流变得不稳定时，被困界面上的力不仅会波动，而且会放大，因此支持了实验发现，表明它们可用于释放此类界面。在Weissenberg值为1.5或更高时，波动变得很重要，并且界面上的力的平均值随波动的增加而减小。