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.

Details of flow field are highly relevant to understand the mechanism of turbulence, but obtaining high-resolution turbulence often requires enormous computing resources. Although the super-resolution reconstruction of turbulent flow fields is an efficient way to obtain the details, the traditional interpolation methods are difficult to reconstruct small-scale structures, and the results are too smooth. In this paper, based on the transformer backbone architecture, we present a super-resolution transformer for turbulence to reconstruct turbulent flow fields with high quality. It is supervised and has a broader perceptual field for better extraction of deep-level features. The model is applied to forced isotropic turbulence and turbulent channel flow dataset, and the reconstructed instantaneous flow fields are comprehensively compared and analyzed. The results show that SRTT can recover the turbulent flow fields with high spatial resolution and capture small-scale details. It can obtain either the isotropic or the anisotropic turbulent properties even in complex flow configurations.

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.

As a native scheme to evaluate hydrodynamic force in the lattice Boltzmann method, the momentum exchange method has some excellent features, such as simplicity, accuracy, high efficiency and easy parallelization. Especially, it is independent of boundary geometry, preventing from solving the Navier–Stokes equations on complex boundary geometries in the boundary-integral methods. We review the origination and main developments of the momentum exchange method in lattice Boltzmann simulations. Then several practical techniques to fill newborn fluid nodes are discussed for the simulations of fluid-structure interactions. Finally, some representative applications show the wide applicability of the momentum exchange method, such as movements of rigid particles, interactions of deformation particles, particle suspensions in turbulent flow and multiphase flow, etc.

In this paper, we propose a numerical model to simulate gas–liquid–solid interaction problems, coupling the lattice Boltzmann method and discrete element method (LBM–DEM). A cascaded LBM is used to simulate the liquid–gas flow field using a pseudopotential interaction model for describing the liquid–gas multiphase behaviour. A classical DEM resorting to fictitious overlaps between the particles is used to simulate the multiple-solid-particle system. A multiphase fluid–solid two-way coupling algorithm between LBM and DEM is constructed. The model is validated by four benchmarks: (i) single disc sedimentation, (ii) single floating particle on a liquid–gas interface, (iii) sinking of a horizontal cylinder and (iv) self-assembly of three particles on a liquid–gas interface. Our simulations agree well with the numerical results reported in the literature. Our proposed model is further applied to simulate droplet impact on deformable granular porous media at pore scale. The dynamic droplet spreading process, the deformation of the porous media (composed of up to 1277 solid particles) as well as the invasion of the liquid into the pores are well captured, within a wide range of impact Weber number. The droplet spreading dynamics on particles is analysed based on the energy budget, which reveals mechanisms at play, showing the evolution of particle energy, surface energy and viscous dissipation energy. A scaling relation based on the impact Weber number is proposed to describe the maximum spreading ratio.