At the pore scale, capillary force plays an important role in the fluid displacement. For example, in the EOR applications, a dominant mechanism for residual oil left in reservoirs is the “snap-off” phenomenon, which has been extensively studied. For oil droplets in water-wet pores, Roof [
18] first proposed a structural criterion to determine the snap-off occurrence in circular pores. According to this classical model, snap-off occurs when
, where
Rb and
Rt are the effective radii of the pore body and pore throat respectively, and
Rc is the transverse radius of the throat curvature. The dependence of the snap-off on local geometry has been experimentally confirmed by Kiss et al. [
19] and Yu and Wardlaw [
20]. Extending from Roof’s criterion for circular pores, Ransohoff et al. [
21,
22] proposed a quasi-static criterion for non-circular pores by using a dimensionless interfacial curvature, which varied for capillaries with different cross-sectional shapes. Later, Al-Gharbi et al. [
23,
24] presented a dynamic pore-scale network model that could predict the meniscus oscillations and snap-off phenomena observed in micromodel experiments. Beresnev and Deng [
25] proposed a nonlinear dimensionless equation as a purely geometric criterion to describe the dynamics of snap-off and calculated the snap-off time, which was verified by the results of CFD simulations [
26,
27]. Deng et al. [
28,
29] further extended Roof and Ransohoff criteria by considering the imbalance between the pore body and the pore throat, considering a wetting film existing between a non-wetting fluid and wall. Roman and Abu-Al-Sand et al. [
30,
31] developed a multiscale sharp-interface level-set method to investigate the snap-off coalescence phenomenon for immiscible two-phase flow with a pre-existing thin film on solid surfaces, whose results were validated by comparison with both theory and experiments. Recently, Deng et al. [
32] analysed the dynamics of the wetting/non-wetting interface instability in sinusoidal constricted capillary tubes by using a theoretical model to couple the wetting film thickness to the local capillary number (
Ca) at the pore throat. Although the pore-scale snap-off process has been extensively investigated , there are still three main limitations: (i) most of previous research was based on core-scale study with a main focus on the flow displacement in a crossing pore network , and detailed study at a single pore scale is still insufficient; (ii) previous pore-scale studies are mainly focused on super-critical carbon dioxide as the non-wetting fluids, which cannot represent water/oil displacement suitable for EOR and oil remediation applications; (iii) no study has been investigated on potential ways to suppress the snap-off process at the pore scale to decrease the amount of trapped oil.