Study on Spontaneous Capillary Imbibition in Irregular Geometries Using the Lattice Boltzmann Approach

Spontaneous liquid–liquid capillary imbibition in axially varying capillaries is central to petroleum engineering applications such as water-driven enhanced oil recovery, where the dynamic contact angle (DCA) governs interfacial motion. We extend the classical Lucas–Washburn (LW) formulation to account for axial variations in the hydraulic radius, early-time inertia, and viscous dissipation in the displaced non-wetting phase. In parallel, we develop a cascaded multicomponent Shan–Chen lattice Boltzmann model (LBM) that resolves the in situ evolution of the DCA and simulate imbibition in three area-matched geometries: convergent conical, divergent conical, and parabolic. The axial profile is shown to control both the imbibition rate and the DCA. For a viscosity-matched binary fluid, the temporal variation in the DCA is set by the local contraction rate: the DCA decreases as the capillary widens and increases as it narrows. Stronger intrinsic wettability enlarges the discrepancy between the DCA and the static contact angle (SCA). Moreover, at fixed non-wetting-phase viscosity, decreasing the wetting/non-wetting viscosity ratio reduces the imbibition rate and drives the DCA toward the SCA. Predictions from the extended LW equation that neglect DCA exhibit systematic deviations from LBM results, whereas supplying the time-resolved DCA yields close quantitative agreement across all geometries. These findings identify the DCA as a critical state variable for reduced-order prediction of imbibition in axially varying capillaries and inform the design of enhanced-oil-recovery and microfluidic systems.