Pinning-depinning of the contact line during drop evaporation on textured surfaces: A lattice Boltzmann study.

The evaporation of the liquid droplet on a structured surface is numerically investigated using the lattice Boltzmann method. Simulations are carried out for different contact angles and pillar widths. From the simulation for the Cassie state, it is found that the evaporation starts in a pinned contact line mode. Then, when the droplet reaches the receding state, the contact line jumps to the neighboring pillar. Also, the depinning force decreases with increasing the contact angle or the pillar width. In the Wenzel state, the droplet contact line remains on the initial pillar for all of its lifetime.

Numerical simulation of dissolved air flotation using a lattice Boltzmann method.

In this paper, the behavior of a bubble and droplet rising in a system, namely, a dissolved air flotation system, is investigated under different conditions. A lattice Boltzmann model which is based on the Cahn-Hilliard equations for ternary flows is implemented. This model can handle high density and viscosity ratios, remove parasitic currents, and capture partial and total spreading conditions. Two classical problems, such as spreading of a liquid lens and the Rayleigh-Taylor instability are used to determine the accuracy of the model. As a practical application, three-component flow in a tank is studied and the dynamics of bubble and droplet under different conditions is investigated. We then concentrate on the dimensionless average velocity and locations of bubble and droplet at different density ratios, viscosity ratios, and diameter ratios. Also, total spreading and partial spreading conditions are compared. The numerical results are justifiable physically and show the ability of this model to simulate three-component flows.

Numerical investigation of vibration-induced droplet shedding on smooth surfaces with large contact angles.

In this work, numerical simulations are performed to study the droplet response to the vertical vibration of the substrate, under various frequencies and amplitudes using the multiphase lattice Boltzmann method. First, the numerical results are validated against published experimental data. The effects of droplet size, surface wettability, amplitude, and frequency of the vibrating substrate on droplet detachment are studied. For high contact angles, regardless of the droplet size, when the vibration frequency matches the droplet resonance frequency the droplet is easily removed from the surface. For lower contact angles, the resonance frequency is higher and the detachment amplitude increases significantly. It was also found that viscous forces do not affect the resonance frequency, but have a noticeable impact on the detachment amplitude. The findings of this study can be useful in applications where droplet shedding is crucial, e.g., condensation heat transfer.

Coalescence-induced droplet detachment on low-adhesion surfaces: A three-phase system study.

Coalescing water droplets on superhydrophobic surfaces can detach from the surface without the aid of any external forces. This self-propelled droplet detachment mechanism is useful in many applications, such as phase change heat transfer enhancement, self-cleaning surfaces, and anti-icing and antidew coatings. In this article, the coalescence-induced droplet jumping in a three-phase system is numerically investigated. The gaps between the surface structures are filled with a liquid that is immiscible with water, e.g., lubricant. A mass-conserving lattice Boltzmann method is implemented to study the effects of several parameters, such as interfacial tensions, droplet size, and surface wettability on the jumping process. The numerical results show that for relatively high values of lubricant-water interfacial tensions and large surface-water contact angles (>150^{∘}) the water droplets are capable of detaching. The critical droplet size for jumping is also highly dependent on the lubricant-water interfacial properties. The results of this study provide insights into the fluid-fluid and fluid-solid interactions and shed light on the underlying mechanisms involved in the droplet coalescence process on such surfaces.

Numerical investigation of vibration-induced droplet shedding on microstructured superhydrophobic surfaces.

The vibration-induced droplet shedding mechanism on microstructured superhydrophobic surfaces was simulated using the lattice Boltzmann method. The numerical simulations of natural droplet oscillations for various surface structures show that the natural frequency of the droplet is strongly dependent on surface morphology. The results show good agreement with basic theoretical values. Furthermore, simulations of the motion of the droplet subjected to vertical surface vibration demonstrate that droplets in the Cassie wetting state are easily removed from the surface, whereas for Wenzel state droplets, pinch-off occurs and only partial removal is possible. Microstructure spacing was found to be a key factor in the shedding process. On a surface with small microstructure spacing, the increased surface adhesion leads to a decrease of droplet departure velocity. In contrast, for large roughness spacing, the droplet is impaled on the microstructures, which causes the departure velocity to decrease. Reperforming the simulations under different vibration intensities reveals that as the vibration amplitude is increased, the optimum frequency for droplet removal decreases. The findings of this study shed light on the underlying mechanisms involved in forced vibrations of droplets and can be helpful in engineering applications in which droplet shedding processes are critical.

Numerical simulation of three-component multiphase flows at high density and viscosity ratios using lattice Boltzmann methods.

In this paper, we propose a multiphase lattice Boltzmann model for numerical simulation of ternary flows at high density and viscosity ratios free from spurious velocities. The proposed scheme, which is based on the phase-field modeling, employs the Cahn-Hilliard theory to track the interfaces among three different fluid components. Several benchmarks, such as the spreading of a liquid lens, binary droplets, and head-on collision of two droplets in binary- and ternary-fluid systems, are conducted to assess the reliability and accuracy of the model. The proposed model can successfully simulate both partial and total spreadings while reducing the parasitic currents to the machine precision.

Extended lattice Boltzmann scheme for droplet combustion.

The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method.

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013)] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

Extended lattice Boltzmann method for numerical simulation of thermal phase change in two-phase fluid flow.

In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.