Lattice Boltzmann simulation of three-phase flows with moving contact lines on curved surfaces

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Pore-Scale Study on Shale Oil-CO2-Water Miscibility, Competitive Adsorption, and Multiphase Flow Behaviors

Due to the fracturing fluid imbibition and primary water, oil-water two-phase fluids generally exist in shale nanoporous media. The effects of water phase on shale oil recovery and geological carbon sequestration via CO2 huff-n-puff is non-negligible. Meanwhile, oil-CO2 miscibility after CO2 huff-n-puff also has an important effect on oil-water two-phase flow behaviors. In this work, by considering the oil-CO2 competitive adsorption behaviors and the effects of oil-CO2 miscibility on water wettability, an improved multicomponent and multiphase lattice Boltzmann method is proposed to study the effects of water phase on CO2 huff-n-puff. Additionally, the effects of oil-CO2 miscibility on oil-water flow behaviors and relative permeability are also discussed. The results show that due to Jamin's effect of water droplets in oil-wetting pores and the capillary resistance of bridge-like water phase in water-wetting pores, CO2 can hardly diffuse into the oil phase, causing a large amount of remaining oil. As water saturation increases, Jamin's effect and the capillary resistance become more pronounced, and the CO2 storage mass gradually decreases. Then, based on the results from molecular dynamics simulations, the influences of oil-CO2 miscibility on oil-water relative permeability in calcite nanoporous media are studied, and as the oil mass percentage in the oil-CO2 miscible system decreases, the oil/water relative permeability decreases/increases. The improved lattice Boltzmann model can be readily extended to quantitatively calculate geological CO2 storage mass considering water saturation and calculate the accurate oil-water relative permeability based on the real 3D digital core.

Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method

Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.

Kelvin-Helmholtz Instability Augmented by von Kármán Vortex Shedding during an Oil Droplet Impact on a Water Pool

The impact of an oil droplet on a water surface has been explored with the aid of computational fluid dynamics simulations. The study reveals the details of the spatiotemporal evolution of such a ternary system with a triplet of interfaces, e.g., air-water, oil-water, and oil-air, when the impact velocity of the oil droplet with the water surface is high. The oil droplet is found to flatten, spread, stretch, and eventually dewet on the water surface of the deep crater to show a host of interesting post-impact flow morphologies. Furthermore, at higher impact velocities, the formation of a biphasic oil-water crown is observed followed by the ejection of secondary water droplets from the crown tip due to capillary instability. The rapidly spreading oil film on the "crater" of the water surface is found to undergo Kelvin-Helmholtz instability before dewetting the same due to cohesion failure. Subsequently, the formation of an array of secondary oil droplets is observed during the process of dewetting. The dominant wavelength evaluated from the linear stability analysis of a representative flow system could faithfully predict the simulated spacing of dewetted oil droplets floating on the crater. Importantly, the variations in Laplace pressure around the curvatures of the undulatory interfaces along with sharp viscosity gradients across the three-phase contact line is found to engender interesting recirculation patterns, which eventually shed to form a coherent wake region in air near the crater. We also uncover the conditions under which the counter-rotating vortices shed along the oil-water interface resembling a von Kármán vortex street.

Influence of the pre-impact shape of an oil droplet on the post-impact flow dynamics at air-water interface

We computationally explore the effects of pre-impact shape of an oil droplet on the spatiotemporal dynamics after the droplet impacts an air-water interface. Simulations reveal that the initial shape of the impacting oil-droplet alters the post-impact transient flow structures during the evolution. The spherical and oblate drop spreads over the crater to manifest interesting flow morphologies including the formation of oil-toroids and compound oil-droplets. However, the prolate drop impinges much deeper into the water pool after impact to create a few more exclusive flow features, such as, interface overturning, vortex shedding and formation of secondary droplets. The temporal variation of the crater depth shows distinct three stage dynamics, which can be explained by the generic energy analysis of the entire system. The combined theoretical and numerical energy analyses reveal the influences of the pre-impact drop shape and their effects on the subsequent energy conversion after the impact takes place. The analysis also reveals that the initial surface and kinetic energies are different for non-spherical droplets than for the spherical ones. The conversion of such excess surface energy due to the non-spherical curvature into kinetic energy dictates the impact and subsequently the crater dynamics of such systems. Such influences largely lead to the exclusive flow patterns demonstrated here. Concisely, this study presents a tri-phasic computational model, which is capable of analyzing the salient features of the impact and splash dynamics of the non-spherical droplets into a water continuum.