In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

The drift behavior of spiral waves under the influence of a polarized electric field is investigated in the light that both the polarized electric field and the spiral waves possess rotation symmetry. Numerical simulations of a reaction-diffusion model show that the drift velocity of the spiral tip can be controlled by changing the polarization mode of the polarized electric field and some interesting drift phenomena are observed. When the electric field is circularly polarized and its rotation follows that of the spiral, the drift speed of the spiral tip reaches its maximal value. On the contrary, opposite rotation between the spiral and electric field locks the drift of the spiral tip. Analytical results based on the weak deformation approximation are consistent with the numerical results. We hope that our theoretical results will be observed in experiments, such as the Belousov-Zhabotinsky reaction.

Very small synthetic motors that use chemical reactions to drive their motion are being studied widely because of their potential applications, which often involve active transport and dynamics on nanoscales. Like biological molecular machines, they must be able to perform their tasks in complex, highly fluctuating environments that can form chemical patterns with diverse structures. Motors in such systems can actively assemble into dynamic clusters and other unique nonequilibrium states. It is shown how chemical patterns with small characteristic dimensions may be utilized to suppress rotational Brownian motions of motors and guide them to move along prescribed paths, properties that can be exploited in applications. In systems with larger pattern length scales, domains can serve as catch basins for motors through chemotactic effects. The resulting collective motor dynamics in such confining domains can be used to explore new aspects of active particle collective dynamics or promote specific types of active self‐assembly. More generally, when chemically self‐propelled motors operate in far‐from‐equilibrium active chemical media the variety of possible phenomena and the scope of their potential applications are substantially increased.