Janus gate: A unique topology blocks the flow of water in one direction but makes it run fast in the opposite direction.

Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.

Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. To investigate the effect of wettability heterogeneity on relative permeability of two‐phase flow in porous media, a multi‐relaxation‐time color‐gradient lattice Boltzmann model is adopted to simulate oil/water two‐phase flow in porous media with different oil‐wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil‐wet solid fraction under a constant water saturation. However, as the water saturation decreases to an intermediate value (about 0.4–0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water‐wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability‐related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two‐phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. The relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.