Numerical Simulation Study On Electrowetting Of Micro-nano Droplets Based On Lattice Boltzmann Method

Controlling fluid motion based on surface wettability is a promising and highly soughtafter technology.As fluid manipulation continuously evolves to the micro-and nano-scale,related experimental and theoretical studies are becoming increasingly complex and difficult.Numerical simulation based on high performance computing is gradually developed as an effective research tool.The lattice Boltzmann method is a new approach to computational fluid dynamics that originated from mesoscopic kinetic theory,whose main calculations use only local data and the algorithm has a natural parallel character.Based on the verification of the model validity and computational efficiency,the flexible manipulation of micro-nano droplets via the applied electric field is achieved by numerical simulation.The main content includes the following sections.（1）A model for solving the electrowetting behavior of micro-nano droplets is constructed based on the lattice Boltzmann method.The electrowetting behavior includes hydrodynamics and electrostatics,where hydrodynamics is modeled by a chemical potential multiphase flow model.In electrostatics,the effect of the Debye shielding effect on the internal potential distribution of microscale droplets is different from that of macroscale droplets due to the Debye shielding effect.Therefore,the nonlinear continuous PoissonBoltzmann equation is linearly discretized in a Cartesian coordinate system to iteratively calculate the potential distribution of the droplets and thus the role of the electrostatic force.Due to the high computational cost,the CUDA programming technique is used to parallelize the algorithmic process of the electrowetting model and speed up the computation.For the question about single instruction multiple data such as flow field evolution and potential iterative computation,GPUs are used to accelerate the computation.The thread structure is a one-dimensional Grid with one-dimensional Block.The one-dimensional array is used to store the data in a two-dimensional grid in the order of Y first and then X.It makes array elements conveniently correspond to thread indexes.The SOA memory layout is used for merged access and acceleration.The acceleration ratio is about 80 times.（2）The potential distribution of droplets at different scales is simulated and analyzed.The results show that the double electric layer is not sufficient to shield the electric field inside a microscale droplet and that the shielding effect increases with increasing droplet radius.At large size,the electric field cannot penetrate the droplet and the droplet interior can be regarded as an equipotential body.The grid independence of the numerical calculation method is further demonstrated using different grid densities.The accuracy of the numerical method is verified by simulating the static equilibrium structure of the droplet under the applied voltage and quantitatively analyzing the relationship between the contact angle and voltage.The results show that the apparent contact angle agrees well with the LippmannYoung equation,but the microscopic contact angle deviates from the equation.To explain this phenomenon,a computational analysis of the electric field strength along the droplet profile shows that the cause is the sharp decrease in electric field strength near the three-phase contact point,which is consistent with the results of previous experimental and theoretical analyses.In this paper,the lattice Boltzmann method and CUDA-based GPU acceleration are used to construct electrowetting models at the micro-nano scale.（3）Droplet migration driven by an electric field,which is widely used in practical research and industry,is simulated.Numerical calculations are performed for droplet migration in an open electrode structure and a closed symmetric electrode structure,and the potential distribution,electric field strength,and migration velocity of the two structures are compared and analyzed.Then,the lateral bouncing of droplets hitting the potential heterogeneous surface is simulated.The relationship between the momentum distribution and the electric potential distribution is calculated and analyzed to reveal the law of motion.The electrowetting simulation method proposed in this paper can reveal the effect of the electric field on the wettability of micro-nano droplets.It is able to computationally analyze some physical quantities that are difficult to obtain in practical experiments and promotes the understanding of the mechanism of droplet motion driven by electrowetting.It is expected that the simulation method will find further applications in numerical simulations in areas such as digital microfluidics and varifocal microlenses.