Injection of anthropogenic carbon dioxide (CO₂) into geological formations is a promising approach to reduce greenhouse gas emissions into the atmosphere. Predicting the amount of CO₂ that can be captured and its long-term storage stability in subsurface requires a fundamental understanding of multiphase displacement phenomena at the pore scale. In this paper, the lattice Boltzmann method is employed to simulate the immiscible displacement of a wetting fluid by a non-wetting one in two microfluidic flow cells, one with a homogeneous pore network and the other with a randomly heterogeneous pore network. We have identified three different displacement patterns, namely, stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number (Ca), viscosity ratio (M), and the media heterogeneity. The non-wetting fluid saturation (S_nw) is found to increase nearly linearly with logCa for each constant M. Increasing M (viscosity ratio of non-wetting fluid to wetting fluid) or decreasing the media heterogeneity can enhance the stability of the displacement process, resulting in an increase in S_nw. In either pore networks, the specific interfacial length is linearly proportional to S_nw during drainage with equal proportionality constant for all cases excluding those revealing considerable viscous fingering. Our numerical results confirm the previous experimental finding that the steady state specific interfacial length exhibits a linear dependence on S_nw for either favorable (M ≥ 1) or unfavorable (M < 1) displacement, and the slope is slightly higher for the unfavorable displacement.

Using a lattice Boltzmann multiphase model, three-dimensional numerical simulations have been performed to understand droplet formation in microfluidic cross-junctions at low capillary numbers. Flow regimes, consequence of interaction between two immiscible fluids, are found to be dependent on the capillary number and flow rates of the continuous and dispersed phases. A regime map is created to describe the transition from droplets formation at a cross-junction (DCJ), downstream of cross-junction to stable parallel flows. The influence of flow rate ratio, capillary number, and channel geometry is then systematically studied in the squeezing-pressure-dominated DCJ regime. The plug length is found to exhibit a linear dependence on the flow rate ratio and obey power-law behavior on the capillary number. The channel geometry plays an important role in droplet breakup process. A scaling model is proposed to predict the plug length in the DCJ regime with the fitting constants depending on the geometrical parameters.

Using a phase-field model to describe fluid/fluid interfacial dynamics and a lattice Boltzmann model to address hydrodynamics, two dimensional (2D) numerical simulations have been performed to understand the mechanisms of droplet formation in microfluidic T-junction. Although 2D simulations may not capture underlying physics quantitatively, our findings will help to clarify controversial experimental observations and identify new physical mechanisms. We have systematically examined the influence of capillary number, flow rate ratio, viscosity ratio, and contact angle in the droplet generation process. We clearly observe that the transition from the squeezing regime to the dripping regime occurs at a critical capillary number of 0.018, which is independent of flow rate ratio, viscosity ratio, and contact angle. In the squeezing regime, the squeezing pressure plays a dominant role in the droplet breakup process, which arises when the emerging interface obstructs the main channel. The droplet size depends on both the capillary number and the flow rate ratio, but is independent of the viscosity ratio under completely hydrophobic wetting conditions. In the dripping regime, the droplet size will be significantly influenced by the viscosity ratio as well as the built-up squeezing pressure. When the capillary number increases, the droplet size becomes less dependent on the flow rate ratio. The contact angle also affects the droplet shape, size, and detachment point, especially at small capillary numbers. More hydrophobic wetting properties are expected to produce smaller droplets. Interestingly, the droplet size is dependent on the viscosity ratio in the squeezing regime for less hydrophobic wetting conditions.