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Highlights • Three kind of equilibrium status are observed for trapped droplets. • Droplets can be trapped by the wetting defect with a weak strength. • The upper limit of defect strength is independent of the capillary number. Abstract With the development of techniques to control the wettability on solid surface, directional control of droplets on such surfaces exhibit promising applications in the design of microfluidic devices. The sliding droplet can even be trapped by the heterogeneous surface that is equipped with wetting defects. However, its detailed mechanism and general physical conditions required for trapping droplets displaced by another fluid have never been fully described. In this work, we present numerical simulations based on front-tracking method to investigate the trapping of droplets on a hydrophilic surface with a stripe-like chemical wetting defect displaced by another immiscible liquid. Three kind of equilibrium status are observed for trapped droplets based on the analysis on the dynamic of the contact line. We determine the transition conditions between trapping and escaping by mapping droplet dynamics as a function of nondimensional defect strength and capillary number. To reveal the underlying mechanism of droplets escaping, the deformation and motion including the dynamics of triple-phase contact line are explored as the droplet passing through the defect. It is found that the unbalanced Young's force acting the contact line could be a driving or resistance force, which is the key factor to dominate the critical condition of the trapping-to-escaping transition. [ABSTRACT FROM AUTHOR]

Highlights • A model was developed for compound droplet involving moving contact line problem. • We observed several interesting events of droplet sliding, detachment and pinch-off. • Capillary numbers of inner and outer droplet significantly affect droplet dynamics. • Effects of surface tension and inner droplet radius on droplet were studied. Abstract The dynamic behavior of compound droplets on the wall of a rectangle channel by the action of an imposed shear flow is simulated using our developed three-dimensional front-tracking method combined with generalized Navier boundary condition. The validity of the present method was confirmed by comparing results of the compound droplet spreading under gravity force with analytical solutions. To determine the physical condition required for detaching/pinching-off the compound droplet, we have performed a large number of simulations with varying capillary numbers of two interfaces and obtained a phase diagram of compound droplets on solid surface in shear flow. The deformation and motion of the compound droplet including its contact line motion are investigated. It is found that the behavior of the compound droplet is controlled by two dimensionless parameters, the capillary numbers of the outer interface and the inner interface. Moreover, we also analyze the deformation and migration of the inner droplet and discuss its effect on the compound droplet. The simulation demonstrate that the lateral migration of the small inner droplet could accelerates the pinch-off process and the large inner droplet could promote the detachment for a moderate capillary number of the outer interface. [ABSTRACT FROM AUTHOR]

In polymer flooding, the primary attentions focused on the influence of polymer concentration and the elasticity on fluid breakup. However, the shear-thinning characteristic can also significantly affect the apparent viscosity of the fluid. We simulated the breakup process of the dispersed phase in both shear-thinning and Newtonian fluids by using volume of fluid method, encompassing various viscosity ratios, capillary numbers, and rheological parameters. The critical conditions of capillary number and viscosity ratio for breakup of the dispersed phase were obtained, indicating that the dispersed phase was more prone to breakup in shear-thinning fluids. The mechanism of fluid breakup induced by shear-thinning was examined through the analysis of viscosity, pressure, and the magnitude of vorticity. Attributed to heightened destabilization in the radial direction and diminished viscous forces, fluid breakup processes were enhanced by lower zero-shear viscosity and reduced power-law index. The fluid breakup caused by the radial instability of shear-thinning fluids is distinguishing from the classical Roof snap-off theory. Inspiring by these results, enhancing rheological parameters such as power-law index and zero-shear viscosity in designing polymer flooding technique can accelerate the occurrence of the breakup process, thereby achieving control over the oil recovery process. [Display omitted] • Volume of fluid method is utilized to simulate fluid breakup in pore-throat. • The fluid breakup is more susceptible to occur in surrounding shear-thinning fluids. • Breakup processes are enhanced in lower zero-shear-viscosity and power-law index. • Delaying effect of rheological parameters on breakup follows: power-law index > zero-shear-viscosity > relaxation time. [ABSTRACT FROM AUTHOR]