Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models

Enhanced permeation of a hydrophobic fluid through particles with hydrophobic and hydrophilic patterned surfaces

The wetting properties of solid surfaces are significant in oil/gas and liquid displacement processes. It is difficult for hydrophobic fluids to permeate channels filled with hydrophilic particles and an aqueous phase, and this is thought to be the primary cause of low yields in low permeability reservoir operations. Using three-dimensional lattice Boltzmann simulations, we show that particles with hydrophobic and hydrophilic patterned surfaces can greatly improve hydrophobic fluid permeation. Specifically, a hydrophobic fluid can easily access micro-channels in the hydrophobic regions, which extend rapidly even to the hydrophilic regions and accelerate hydrophobic fluid escape. This work enriches understanding of multiphase flow in porous media at the pore scale and fracture conductivity and is expected to have great significance in the exploitation of low permeability reservoirs and shale gas.

Lattice Boltzmann modeling of directional wetting: comparing simulations to experiments

Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting.

Effects of the hierarchical structure of rough solid surfaces on the wetting of microdroplets

We used the lattice Boltzmann method to investigate how the hierarchical structure of a rough solid surface, which in this work is modeled as the microstructure (micropillars) covered with nanostructures (nanopillars), affects the contact angle of microdroplets atop of the solid surface and the wetting transition between the Wenzel and Cassie states. Our simulation results show that the Wenzel-to-Cassie state transition can be achieved by decreasing the fluid-solid attraction, increasing the micropillar spacing, or coating the microstructures with nanostructures. For the effect of the hierarchical structure on the contact angle, we find that the micropillars show a negligible effect on the contact angle, but they may affect the sliding angle. In contrast, it is the nanostructure that determines the contact angle. The contact angle increases with the nanopillar length until reaching a maximal value, but its dependence on the nanopillar spacing becomes more complicated. The contact angle may first increase with the nanopillar spacing and then decreases, or decreases monotonously, depending on whether the liquid enters the nanostructure or not. In this work, we also demonstrate in the presence of contact line pinning, that the pinning effect affects the apparent contact angle.

Flow past superhydrophobic surfaces with cosine variation in local slip length

Anisotropic superhydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of superhydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length. We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Boltzmann simulations. Compared to the case of superhydrophobic stripes, the cosine texture can provide a very large effective slip. However, the difference between eigenvalues of the slip-length tensor is smaller, indicating that the flow is less anisotropic.

Combined effects of surface roughness and wetting characteristics on the moving contact line in microchannel flows

The present study investigates moving contact lines in microfluidic confinements with rough topographies modeled with random generating functions. Using matched asymptotic expansion, the description of the whole contact line is obtained and the dynamic contact angle is extracted by extrapolating the bulk meniscus to the channel wall. Significant variations are observed in the contact angle because of the heterogeneities of the confining walls of the microfluidic channel. The effects of the surface wetting condition also play a crucial role in altering the description of the contact line bearing particular nontrivial interactions with the topological features of the solid boundaries. In an effort to assess the underlying consequences, two different surface wetting conditions are studied; namely, complete wetting substrate and partial wetting substrate. Our studies reveal that the consequent wetting characteristics are strongly influenced by action of intermolecular forces in presence of surface roughness. The effect of slip, correlation length, and roughness parameters on the dynamic contact angle have been also investigated.

Tensorial slip of superhydrophobic channels

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.

Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization

We investigate thermal and isothermal symmetric liquid-vapor separations via a fast Fourier transform thermal lattice Boltzmann (FFT-TLB) model. Structure factor, domain size, and Minkowski functionals are employed to characterize the density and velocity fields, as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the spinodal decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth, while the exponent for thermal system is lower than that for isothermal system. With respect to the density field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction, and lower interfacial stresses are the main reasons for the differences in thermal system. Different from the isothermal case, the release of latent heat causes the changing of local temperature, which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium much more quickly. The increasing of mean temperature makes the interfacial stress lower in the following way: σ=σ(0)[(T(c)-T)/(T(c)-T(0))](3/2), where T(c) is the critical temperature and σ(0) is the interfacial stress at a reference temperature T(0), which is the main reason for the prolonged SD stage and the lower growth exponent in the thermal case. Besides thermodynamics, we probe how the local viscosities influence the morphology of the phase separating system. We find that, for both the isothermal and thermal cases, the growth exponents and local flow velocities are inversely proportional to the corresponding viscosities. Compared with the isothermal case, the local flow velocity depends not only on viscosity but also on temperature.

Simulations of slip flow on nanobubble-laden surfaces

On microstructured hydrophobic surfaces, geometrical patterns may lead to the appearance of a superhydrophobic state, where gas bubbles at the surface can have a strong impact on the fluid flow along such surfaces. In particular, they can strongly influence a detected slip at the surface. We present two-phase lattice Boltzmann simulations of a flow over structured surfaces with attached gas bubbles and demonstrate how the detected slip depends on the pattern geometry, the bulk pressure, or the shear rate. Since a large slip leads to reduced friction, our results give assistance in the optimization of microchannel flows for large throughput.

Multiphase lattice Boltzmann method for particle suspensions

A two-dimensional mass conserving lattice Boltzmann method (LBM) has been developed for multiphase (liquid and vapor) flows with solid particles suspended within the liquid and/or vapor phases. The main modification to previous single-phase particle suspension models is the addition of surface (adhesive) forces between the suspended particle and the surrounding fluid. The multiphase dynamics between fluid phases is simulated via the single-component multiphase model of Shan and Chen [Phys. Rev. E 47, 1815 (1993)]. The combined multiphase particle suspension model is first validated and then used to simulate the dynamics of a single-suspended particle on a planar liquid-vapor interface and the interaction between a single particle and a free-standing liquid drop. It is observed that the dynamics of suspended particles near free-standing liquid droplets is affected by spurious velocity currents although the liquid-vapor interface itself is a local energy minimum for particles. Finally, results are presented for capillary interactions between two suspended particles on a liquid-vapor interface subjected to different external forces and for spinodal decomposition of a liquid-vapor mixture in the presence of suspended particles. Qualitative agreements are reached when compared with results of suspended particles in a binary mixture based on multicomponent LBM models.

Capillary filling with pseudo-potential binary Lattice-Boltzmann model

We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The phenomenological way to impose a given contact angle is analysed. Particular attention is given to the case of complete wetting, that is contact angle equal to zero. Numerical results yield quantitative agreement with the theoretical Washburn's law, provided that the correct ratio of the dynamic viscosities between the two fluids is used. Finally, the presence of precursor films is experienced and it is shown that these films advance in time with a square-root law but with a different prefactor with respect to the bulk interface.

Wall boundary conditions in the lattice Boltzmann equation method for nonideal gases

Wall boundary conditions for the lattice Boltzmann equation (LBE) method for nonideal gases proposed by Lee and Fischer [Phys. Rev. E 74, 046709 (2006)] are examined. The LBE simulations of the contact line are typically contaminated by small but strong counter-rotating parasitic currents near solid surfaces. We find that these currents can be eliminated to round-off if the potential form of the intermolecular force is used with the boundary conditions based on the wall energy approach and the bounce-back rule. Numerical tests confirm the elimination of the parasitic currents in the vicinity of the contact line and the agreement of the calculated density, excess mass, and contact angle at the solid surfaces with theory.

Distribution of multiphase fluids in porous media: comparison between lattice Boltzmann modeling and micro-x-ray tomography

A parallel implementation of the three-dimensional Shan-and-Chen multicomponent, multiphase lattice Boltzmann method (LBM) was used to simulate the equilibrium distributions of two immiscible fluids in porous media. The simulations were successfully validated against cone-beam x-ray microtomographic data on the distribution of oil (decane), water, and air phases in a 5-mm cube of porous medium composed of packed quartz sand grains. The results confirm that LBM models allow for the straightforward incorporation of complex pore space geometry determined from x-ray microtomography measurements and that simulated wetting and nonwetting phase distributions are consistent with x-ray observations on both macroscopic and microscopic scales.