Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants

Abstract

Surfactants are widely used in many industrial processes, where the presence of surfactants not only reduces the interfacial tension between fluids but also alters the wetting properties of solid surfaces. To understand how the surfactants influence the droplet motion on a solid surface, a hybrid method for interfacial flows with insoluble surfactants and contact-line dynamics is developed. This method solves immiscible two-phase flows through a lattice Boltzmann colorgradient model and simultaneously solves the convection− diffusion equation for surfactant concentration through a finite difference method. In addition, a dynamic contact angle formulation that describes the dependence of the local contact angle on the surfactant concentration is derived, and the resulting contact angle is enforced by a geometrical wetting condition. Our method is first used to simulate static contact angles for a droplet resting on a solid surface, and the results show that the presence of surfactants can significantly modify surface wettability, especially when the surface is more hydrophilic or more hydrophobic. This is then applied to simulate a surfactantladen droplet moving on a substrate subject to a linear shear flow for varying effective capillary number (Ca e ), Reynolds number (Re), and surface wettability, where the results are often compared with those of a clean droplet. For varying Ca e , the simulations are conducted by considering a neutral surface. At low values of Ca e , the droplet eventually reaches a steady deformation and moves at a constant velocity. In either a clean or surfactant-laden case, the moving velocity of the droplet linearly increases with the moving wall velocity, but the slope is always higher (i.e., the droplet moves faster) in the surfactantladen case where the droplet exhibits a bigger deformation. When Ca e is increased beyond a critical value (Ca e,c ), the droplet breakup would happen. The presence of surfactants is found to decrease the value of Ca e,c , but it shows a non-monotonic effect on the droplet breakup. An increase in Re is able to increase not only droplet deformation but also surfactant dilution. The role of surfactants in the droplet behavior is found to greatly depend upon the surface wettability. For a hydrophilic surface, the presence of surfactants can decrease the wetting length and enables the droplet to reach a steady state faster; while for a hydrophobic surface, it increases the wetting length and delays the departure of the droplet from the solid surface.

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

“…Non-Newtonian fluids and plastic solids were simulated in Jackson and Nikiforakis (2019). Droplet dynamics on a solid surface with insoluble surfactants was numerically studied in Zhang, Liu and Ba (2019b). The bipolar charge transport model was simulated in Ren et al (2019).…”

Pore-Scale Modeling of Two-Phase Flows with Soluble Surfactants in Porous Media

“…With the obtained interfacial force F s , the forcing term can be expressed as , where I is a 9 × 9 unit matrix. Accordingly, the fluid velocity could be calculated by in order to recover the macroscopic governing eqs and up to the second-order accuracy.…”

“…This is mainly due to the lack of a solver that is competent to simulate two-phase flows with surfactants in complicated porous media. Although a number of numerical methods to model two-phase flows with surfactants have been developed, they are limited to either a surfactant-contaminated interface away from the solid wall − or a surfactant-laden droplet on a flat wall. − The numerical modeling of two-phase flows with surfactants in complex porous media is a challenging task. Surfactants can not only diffuse and convect along the interface but also be desorbed from or absorbed into the interface.…”

Simplified Formula for the Critical Entry Pressure and a Comprehensive Insight into the Critical Velocity of Dislodgment of a Droplet in Crossflow Filtration

“…Chemical methods − involve the use of chemicals to mobilize the accumulated droplets at the surface of the membrane by changing their affinity characteristics with the membrane or by dissolving accumulated materials. , Physical methods, , on the other hand, involve the use of different techniques including acoustic waves or mechanical vibrations to destabilize accumulated droplets. Other methods have also been considered including crossflow or pulsatile flow methodologies to intensify the shear stress at the membrane surface and make easy the dislodgment of pinned droplets. − One method that has gained popularity in minimizing the problem of fouling has been the use of back flushing technique . In this technique, the pressures in both the feed and permeate sides of the filtration cell are exchanged and permeation flow is reversed.…”