A new basic single-corner capillary model is presented. In this model, the distribution of immiscible fluids is determined by a particular threshold pressure. Additionally, we derive and analyze the interface curvature and profile of the fluid menisci in different tubes. Various polygonal cross sections are obtained by repeatedly superposing the basic single-corner capillary model. We study the relationship between the number of polygon edges and the distribution of fluids as well as the saturation of the wetting phase in equilateral polygon tubes. Furthermore, for the first time, we discuss the interaction of the corners to reveal the five stages of the fluid interfaces with various corner geometries. The dimensionless interface curvature and the radius of the circle are considered to extend our conclusions to similar cross-sectional capillary tubes of different sizes.

To clarify the initiation and migration mechanisms of a discontinuous oil phase in pores, a numerical study was performed to interpret the starting phenomenon and flowing rules of oil trapped in capillaries that have noncircular cross sections. In this study, capillaries with three different cross sections were used to investigate the deformation law of oil and the pressure drop across these microchannels at different displacement velocities by computational fluid dynamics (CFD). The geometrical structure of the microchannels was precisely controlled, and the migration process of the oil, which is too small to be observed by direct experimentation, was assessed and quantitatively analyzed. By analyzing the shape of the trapped oil after reaching a steady state at different velocities, the nonstart and start conditions could be distinguished and the accuracy of the numerical method was verified by a comparison with an analytical method (the MS-P method). Two aspects of oil migration in noncircular microchannels were observed in combination with previous studies: there is a driving force on the cross section of the oil drop and a viscous force at the oil-water interface in the corners, and the more irregular the pore section is, the more easily the trapped oil will migrate. Additionally, the influence of the microchannel cross-sectional shape on the non-Darcy flow of a discontinuous oil phase was clarified. It can be concluded that the presence of the non-Darcy flow in pores arises because trapped oil, as a discontinuous phase, cannot be separated from the capillary wall without reaching critical velocity.

The transport of discontinuous oil phases in constricted microchannels is a significant issue within the domains of the petroleum industry, bioengineering, and other industrial processes. During the transport, there is a pressure obstructing the drop flow through the narrow throat, which is named the Jamin effect. In this study, computational fluid dynamics technique is employed to observe and analyze the pressure drop of the discontinuous oil phase during its passage through a constricted microchannel and provides a quantitative analysis for the Jamin effect. The results show that the discontinuous oil phase undergoes five stages during its migration in the constricted microchannel, namely, the preparatory stage, the development stage of the forward meniscus, the quasi-stable stage, the regression stage of the rear meniscus, and the stable stage. Moreover, the composition of resistance in the Jamin effect is not solely due to capillary pressure, as traditional scholars believe. The analysis indicates that the equivalent viscosity of the discontinuous oil phase remains consistent during both the preparatory stage and the stable stage, demonstrating that the magnitude of the equivalent viscosity is unaffected by the profile of the oil phase. Additionally, the effects of oil phase saturation, viscosity, and capillary number on the Jamin effect also have been discussed.