Snap‐off is a phenomenon that occurs when a non‐wetting fluid is displaced by wetting fluid in pore‐throat channels, leading to the breakup of droplets at the throat. Snap‐off plays a key role in many industrial processes involving immiscible multiphase flows, such as aquifer remediation, carbon capture and geological storage, recovery of hydrocarbons. Here we derive geometric criteria for the capillary snap‐off at the pore‐throat junctions in 2D microchannels with rectangular cross‐sections. The criteria are theoretically presented in three categories according to the range of the throat depth, h. We find that if h is smaller than the throat width, snap‐off will be inhibited, if h is larger than the pore width, snap‐off may occur but it is independent of h, and if h is in between the throat width and the pore width, a critical depth exists for the occurrence of snap‐off. These criteria are verified using numerical CFD simulations and validated using microfluidic experiments. These results indicate the conditions for snap‐off in the pore‐throat channel with rectangular cross‐sections, which clarify previous debates in the literature. One application of this work is for micromodels, which are porous microfluidic chips used as tools to observe multiphase flow in porous media at the pore‐scale. Most micromodels are two‐dimensional (2D), which have rectangular cross‐sections with uniform depth. The geometric criteria derived here provide guidelines for the design of micromodels used in the study of multiphase flow processes in porous media.

Summary: Accurate characterization of shale pore structures is of paramount importance in elucidating the distribution and migration mechanisms of fluids within shale rocks. However, the acquisition of high-resolution (HR) images of shale rocks is limited by the precision of the scanning equipment. Even with higher-precision devices, compromising the image field of view becomes inevitable, making it challenging to faithfully represent the actual conditions of shale. We propose a stepwise 3D super-resolution (SR) reconstruction method for shale digital rocks based on the widely used focused-ion-beam scanning electron microscope (FIB-SEM) technique. This method effectively addresses the issues of inconsistent horizontal and vertical resolutions as well as low 3D image resolution in FIB-SEM images. By adopting this approach, we significantly enhance image details and clarity, enabling successful observations of pores smaller than 10 nm within shale and laying a foundation for further pore-scale flow simulations. Furthermore, we extract the pore network model (PNM) from the SR reconstructed digital rock to analyze the pore size distribution, coordination number, and pore-throat ratio of shale samples from the Jiyang Depression. The results demonstrate a pore radius distribution in the range of 0 nm to 40 nm, which aligns with the results from nitrogen adsorption experiments. Notably, pores with radii smaller than 10 nm account for 50% of the total connected pores. The proportion of isolated pores in the SR reconstructed shale PNM is significantly reduced, with the coordination number mainly distributed between 1 and 4. The pore-throat ratio of shale ranges from 1 to 3, indicating a relatively uniform development of pores and throats. This study introduces a novel method for accurately characterizing the shale pore structure, which aids researchers in evaluating the pore size distribution and connectivity of shales.