Alkadiyne-Pyrene Conjugated Frameworks with Surface Exclusion Effect for Ultrafast Seawater Desalination.

Billions of populations are suffering from the supply-demand imbalance of clean water, resulting in a global sustainability crisis. Membrane desalination is a promising method to produce fresh water from saline waters. However, conventional membranes often encounter challenges related to low water permeation, negatively impacting energy efficiency and water productivity. Herein, we achieve ultrafast desalination over the newly developed alkadiyne-pyrene conjugated frameworks membrane supported on a porous copper hollow fiber. With membrane distillation, the membrane exhibits nearly complete NaCl rejection (>99.9%) and ultrahigh fluxes (∼500 L m-2 h-1) from the seawater salinity-level NaCl solutions, which surpass the commercial polymeric membranes with at least 1 order of magnitude higher permeability. Experimental and theoretical investigations suggest that the large aspect ratio of membrane pores and the high evaporation area contribute to the high flux, and the graphene-like hydrophobic surface of conjugated frameworks exhibits complete salt exclusion. The simulations also confirm that the intraplanar pores of frameworks are impermeable for water and ions.

Sliding Behavior of Droplets on a Tilted Substrate with a Chemical Step.

Controlling and predicting the motion of droplets on a heterogeneous substrate have received widespread attention. In this paper, we numerically simulate the droplet sliding through a "chemical step", that is, different wetting properties at two sides of the step, on a tilted substrate by the multiphase lattice Boltzmann method (LBM). Three kinds of equilibrium statuses are reproduced by observing the deformation of the droplet and the velocities of the front contact line. This study shows the droplet obtains a driving force to break through the step by deformation in the initial stage that the droplet is blocked. The droplet spreads to two sides along the step when the front end is blocked and is stretched after the front end is passed over the step. The lengths of the lateral spreading and the longitudinal stretching and the time required to pass over the step depend on the strength of the step. In the sliding process, the kinetic energy is converted into surface energy as the droplet is blocked, and the gravitational potential energy is converted into surface and kinetic energy following the droplet passes over the step. If the droplet can slide through the step, the more strength in the step, the more the gravitational potential energy is converted, and the more the surface energy increases. When the strength of the step is small, unbalanced Young's force hinders the contact line moving forward after the central part of the front end of the droplet breaks through the step. While the velocity of droplet sliding slows down with the increasing strength of the step, the unbalanced Young's force pushes the contact line forward against the resistance. These observations throw insight into the dynamics of the droplets sliding on a heterogeneous surface, which may facilitate potential applications like microfluidics and liquid transportation.

Electrowetting lattice Boltzmann method for micro- and nano-droplet manipulations.

Electrowetting has become a widely used tool for manipulating tiny amounts of liquids on surfaces. This paper proposes an electrowetting lattice Boltzmann method for manipulating micro-nano droplets. The hydrodynamics with the nonideal effect is modeled by the chemical-potential multiphase model, in which the phase transition and equilibrium are directly driven by chemical potential. For electrostatics, droplets in the micro-nano scale cannot be considered as equipotential as macroscopic droplets due to the Debye screening effect. Therefore, we linearly discretize the continuous Poisson-Boltzmann equation in a Cartesian coordinate system, and the electric potential distribution is stabilized by iterative computations. The electric potential distribution of droplets at different scales suggests that the electric field can still penetrate micro-nano droplets even with the screening effect. The accuracy of the numerical method is verified by simulating the static equilibrium of the droplet under the applied voltage, and the results show the apparent contact angles agree very well with the Lippmann-Young equation. The microscopic contact angles present some obvious deviations due to the sharp decrease of electric field strength near the three-phase contact point. These are consistent with previously reported experimental and theoretical analyses. Then, the droplet migrations on different electrode structures are simulated, and the results show that droplet speed can be stabilized more quickly due to the more uniform force on the droplet in the closed symmetric electrode structure. Finally, the electrowetting multiphase model is applied to study the lateral rebound of droplets impacting on the electrically heterogeneous surface. The electrostatic force prevents the droplets from contracting on the side which is applied voltage, resulting in the lateral rebound and transport toward the side.

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.

Movable and Focus-Tunable Lens Based on Electrically Controllable Liquid: A Lattice Boltzmann Study.

Adjusting the focal length by changing the liquid interface of the liquid lens has become a potential method. In this paper, the lattice-Boltzmann-electrodynamic (LB-ED) method is used to numerically investigate the zooming process of a movable and focus-tunable electrowetting-on-dielectrics (EWOD) liquid lens by combining the LBM chemical potential model and the electrodynamic model. The LB method is used to solve the Navier-Stokes equation, and the Poisson-Boltzmann (PB) equation is introduced to solve the electric field distribution. The experimental results are consistent with the theoretical results of the Lippmann-Young equation. Through the simulation of a liquid lens zoom driven by EWOD, it is found that the lens changes from a convex lens to a concave lens with the voltage increases. The focal length change rate in the convex lens stage gradually increases with voltage. In the concave lens stage, the focal length change rate is opposite to that in the convex lens stage. During the zooming process, the low-viscosity liquid exhibits oscillation, and the high-viscosity liquid appears as overdamping. Additionally, methods were proposed to accelerate lens stabilization at low and high viscosities, achieving speed improvements of about 30% and 50%, respectively. Simulations of lens motion at different viscosities demonstrate that higher-viscosity liquids require higher voltages to achieve the same movement speed.

Multiphase curved boundary condition in lattice Boltzmann method.

The boundary treatment is fundamental for modeling fluid flows especially in the lattice Boltzmann method; the curved boundary conditions effectively improve the accuracy of single-phase simulations with complex-geometry boundaries. However, the conventional curved boundary conditions usually cause dramatic mass leakage or increase when they are directly used for multiphase flow simulations. We find that the principal reason for this is the absence of a nonideal effect in the curved boundary conditions, followed by a calculation error. In this paper, incorporating the nonideal effect into the linear interpolation scheme and compensating for the interpolating error, we propose a multiphase curved boundary condition to treat the wetting boundaries with complex geometries. A series of static and dynamic multiphase simulations with large density ratio verify that the present scheme is accurate and ensures mass conservation.

Geometric Model and Numerical Study of Aqueous Humor Hydrodynamics in the Human Eye.

The flow of aqueous humor (AH) in the human eye plays a key role in the process of transporting nutrients to the intraocular tissues and maintaining normal intraocular pressure. The pathogenesis of many ophthalmic diseases is also closely related to the flow of AH. Therefore, it is of great significance to study the mechanism of AH dynamics in the human eye. In this paper, we used image processing technology to denoise and segment the anterior segment optical coherence tomography (AS-OCT) images and established a geometric model based on the human eye. At the same time, a model of AH dynamics in the human eye based on the lattice Boltzmann (LB) method was proposed. Then, we simulated the AH flow in the human eye with different morphological structures and different physical properties and analyzed the factors that affect the AH flow, including the shape of anterior chamber (AC), the crypts of iris, the indentation of cornea, the permeability of trabecular meshwork (TM), the secretion rate of AH, and the viscosity of AH. The results showed that the changes in eye tissue morphological structures and physical properties would affect the flow of AH. For example, the maximum velocity of AH flow decreases with the increases in cornea deformation. When the distance of cornea indentation changes from 0.3 mm to 0.5 mm, the maximum velocity of AH reduces by 17%. In the asymmetrical AC, the AH will form two different vortices. In the crypts of the iris, we found that the AH flow forms small vortices, a phenomenon that has not been reported in other papers. In addition, we found that the intraocular pressure (IOP) decreases with the increase of the TM permeability and increases with the increase of the AH secretion rate, and it is not sensitive to changes in the viscosity of AH.

Aqueous humor dynamics in human eye: A lattice Boltzmann study.

This paper presents a lattice Boltzmann model to simulate the aqueous humor (AH) dynamics in the human eye by involving incompressible Navier-Stokes flow, heat convection and diffusion, and Darcy seepage flow. Verifying simulations indicate that the model is stable, convergent and robust. Further investigations were carried out, including the effects of heat convection and buoyancy, AH production rate, permeability of trabecular meshwork, viscosity of AH and anterior chamber angle on intraocular pressure (IOP). The heat convection and diffusion can significantly affect the flow patterns in the healthy eye, and the IOP can be controlled by increasing the anterior chamber angle or decreasing the secretion rate, the drainage resistance and viscosity of AH. However, the IOP is insensitive to the viscosity of AH, which may be one of the causes that the viscosity would not have been considered as a factor for controlling the IOP. It's interesting that all these factors have more significant influences on the IOP in pathologic eye than healthy one. The temperature difference and the eye-orientation have obvious influence on the cornea and iris wall shear stresses. The present model and simulation results are expected to provide an alternative tool and theoretical reference for the study of AH dynamics.

Lateral Drop Rebound on a Hydrophobic and Chemically Heterogeneous Surface.

In this paper, the process of a drop rebounding from a hydrophobic and chemically heterogeneous surface is investigated using the multiphase lattice Boltzmann method. The bounce behavior of drops is dependent on the degree of hydrophobicity and heterogeneity of the surface. When the surface is homogeneous, the drop rebounds vertically and the height increases with the enhancement of the surface hydrophobicity. For the heterogeneous surface with two different hydrophobic parts, the drop rebounds laterally toward the lower hydrophobic side. Because the high hydrophobic side exerts the stronger unbalanced Young's force on the contact line compared with the low hydrophobic side, the difference of the forces results in the asymmetrical rebound. A phase diagram displays the rebound numbers of a drop impacting on the various chemically homogeneous and heterogeneous surfaces. A simply quantitative estimation is made to predict the rebound heights and flying times through the contact angles of the surface. This work promotes the understanding of the rebound mechanism of a drop impacting on a chemically heterogeneous surface and provides a guiding strategy for the precise control of the lateral behavior of rebounding drops by hydrophobic and heterogeneous surfaces.

Chemical-potential multiphase lattice Boltzmann method with superlarge density ratios.

The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations show that the method reaches very low temperatures, at which the liquid-gas density ratio is more than 10^{14}, while the thermodynamic consistency is still preserved. Decoupling the mesh space from the momentum space through a proportional coefficient, a smaller mesh step provides denser lattice nodes to exactly describe the transition region and the resulting dimensional transformation has no loss of accuracy. A compact finite-difference method is applied to calculate the discrete derivatives in the mesh space with high-order accuracy. These enhance the computational accuracy of the nonideal force and suppress the spurious currents to a very low level, even if the density ratio is up to tens of thousands. The simulation of drop splashing verifies that the present model is Galilean invariant for the dynamic flow field. An upper limit of the chemical potential is used to reduce the influence of nonphysical factors and improve the stability.

The roles of wettability and surface tension in droplet formation during inkjet printing.

This paper describes a lattice Boltzmann-based binary fluid model for inkjet printing. In this model, a time-dependent driving force is applied to actuate the droplet ejection. As a result, the actuation can be accurately controlled by adjusting the intensity and duration of the positive and negative forces, as well as the idle time. The present model was verified by reproducing the actual single droplet ejection process captured by fast imaging. This model was subsequently used to investigate droplet formation in piezoelectric inkjet printing. It was determined that the wettability of the nozzle inner wall and the surface tension of the ink are vital factors controlling the print quality and speed. Increasing the contact angle of the nozzle inner delays the droplet breakup time and reduces the droplet velocity. In contrast, higher surface tension values promote earlier droplet breakup and faster drop velocity. These results indicate that the hydrophilic modification of the nozzle inner wall and the choice of inks with high surface tensions will improve printing quality.

Chemical-potential-based lattice Boltzmann method for nonideal fluids.

Chemical potential, as an important thermodynamic quantity, has been popularly used in thermodynamic modeling for complex systems, especially for those involving the phase transitions and chemical reactions. Here we present a chemical-potential-based multiphase lattice Boltzmann model, in which the nonideal force is directly evaluated by a chemical potential. The numerical computation is more efficient than the pressure-tensor-based model [Wen et al. Europhys. Lett. 112, 44002 (2015)10.1209/0295-5075/112/44002] because the calculations of the pressure tensor and its divergence are avoided. We have derived several chemical potentials of the popular equations of state from the free-energy density function. The theoretical analyses and numerical results support that the present model satisfies thermodynamics and Galilean invariance. An effective chemical-potential boundary condition is also implemented to investigate the wettability of a solid surface, and the contact angle can be linearly tuned by the surface chemical potential.

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.

Reversible state transition in nanoconfined aqueous solutions.

Using molecular dynamics simulations, we find a reversible transition between the dispersion and aggregation states of solute molecules in aqueous solutions confined in nanoscale geometry, which is not observed in macroscopic systems. The nanoscale confinement also leads to a significant increase of the critical aggregation concentration (CAC). A theoretical model based on Gibbs free energy calculation is developed to describe the simulation results. It indicates that the reversible state transition is attributed to the low free energy barrier (of order kBT) in between two energy minima corresponding to the dispersion and aggregation states, and the enhancement of the CAC results from the fact that at lower concentrations the number of solute molecules is not large enough to allow the formation of a stable cluster in the confined systems.

Lattice-type-dependent momentum-exchange method for moving boundaries.

The conventional momentum-exchange method (CME) is verified to be accurate for the stationary boundary by Mei et al. [Phys. Rev. E 65, 041203 (2002)], but it might be inaccurate when the boundary is moving in the lattice Boltzmann simulations. A lattice-type-dependent momentum-exchange method (LME) is presented to evaluate the hydrodynamic force on moving boundaries, in which the additional momenta induced by the type-changing lattices are well considered. LME preserves the superior features of CME, such as reliability, simplicity, and parallelism. Without any interpolation and integration, the algorithm is independent of boundary geometries, and therefore, efficient in computation and easy to be implemented in both two and three dimensions. A series of cylinder sedimentations are simulated to illustrate the accuracy and robustness of LME, and the results are in excellent agreement with those by the arbitrary Lagrangian-Eulerian technique (ALE). The lateral migrations of a particle are also investigated in the simulations of a neutrally buoyant cylinder in a Poiseuille flow, and consistent with the Segré-Silberberg effect.