The deformation, movement and breakup of a wall-attached droplet subject to Couette flow are systematically investigated using an enhanced lattice Boltzmann colour-gradient model, which accounts for not only the viscoelasticity (described by the Oldroyd-B constitutive equation) of either droplet (V/N) or matrix fluid (N/V) but also the surface wettability. We first focus on the steady-state deformation of a sliding droplet for varying values of capillary number ( $Ca$ ), Weissenberg number ( $Wi$ ) and solvent viscosity ratio ( $\beta$ ). Results show that the relative wetting area $A_r$ in the N/V system is increased by either increasing $Ca$ , or by increasing $Wi$ or decreasing $\beta$ , where the former is attributed to the increased viscous force and the latter to the enhanced elastic effects. In the V/N system, however, $A_r$ is restrained by the droplet elasticity, especially at higher $Wi$ or lower $\beta$ , and the inhibiting effect strengthens with an increase of $Ca$ . Decreasing $\beta$ always reduces droplet deformation when either fluid is viscoelastic. The steady-state droplet motion is quantified by the contact-line capillary number $Ca_{cl}$ , and a force balance is established to successfully predict the variations of $Ca_{cl}/Ca$ with $\beta$ for each two-phase viscosity ratio in both N/V and V/N systems. The droplet breakup is then studied for varying $Wi$ . The critical capillary number of droplet breakup monotonically increases with $Wi$ in the N/V system, while it first increases, then decreases and finally reaches a plateau in the V/N system.
We present a theoretical and numerical study of a compound droplet flowing through a single pore-throat structure. By quantifying the capillary pressures in the pore and throat under various geometrical conditions, we derive a theoretical model to predict whether the compound droplet is able to penetrate into the throat in a pore-throat structure. Meanwhile, the lattice Boltzmann simulations are conducted to assess the capability and accuracy of the theoretical model. Through a combination of theoretical analysis and lattice Boltzmann simulations, we then investigate the effect of inner droplet size, compound droplet size, and surface wettability on the invasion behavior of a compound droplet. The results show that with increasing the inner droplet size or the compound droplet size, the compound droplet undergoes the transition from the state where the entire compound droplet can pass through the throat to the state where only a part of outer droplet penetrates into and blocks the throat. Although the theoretical predictions show good agreement with the simulation results for most of the cases investigated, it is found that the proposed theoretical model is not applicable to the cases in which the droplets are intermediate-wetting or wetting to the solid surface. This is because the shape of newly formed interface in the pore significantly deviates from the initial circle, which violates the assumption made in the derivation of the theoretical model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.