A two-dimensional (2-D) multi-phase cellular automaton (CA)-finite difference (FD)-lattice Boltzmann (LB) coupled model is developed to simulate the hydrogen pore formation during dendritic and eutectic solidification of hypoeutectic Al-Si alloys. In this model, the dendrite and eutectic structures are simulated using a CA technique. The solute diffusion is solved by the FD method. The nucleation, growth, and motion behavior of gas pore, and hydrogen transport are simulated by a LB Shen-Chen scheme. It is found that the pores can grow fully but compete in the primary dendrite growth stage. Conversely, pores newly nucleated in residual inter-dendrite liquid during the eutectic solidification stage grow restrictedly and independently. Pore shape severely deformed by the compression of the surrounding solid structures. Moreover, the effects of the initial Si composition, initial hydrogen concentration and cooling rate on the pore formation are qualitatively and quantitatively studied. It is found that the initial Si composition significantly impacts on the pore size and distribution, but little effect on the porosity percentage which decreases markedly with the decreasing initial hydrogen concentration and increasing cooling rate. Comparison reveals that the simulated microstructure morphological characteristics and the predicted porosity percentage agree well with the experimental observation reported in the literature.
Superhydrophobic surfaces resulting from nanoarrays have good performance in anti-condensation. However, the study of droplet nucleation during water vapor condensation is a challenge because of the limitation of observation on a nanoscale, and therefore the fundamental understanding of the influence of geometrical parameters of nanoarrays on the condensation behavior is still less clear. In this work a three-dimensional (3D) multiphase lattice Boltzmann (LB) model is employed to simulate the phenomenon of droplet condensation on the superhydrophobic nanostructured surface. The model validation is carried out through the comparison of the simulations with the results from the Laplace's law and the intrinsic contact angle theory. The LB simulations accord well with the results from Laplace's law. The relative deviation between the simulated intrinsic contact angle and the theoretical value is less than 0.14%, demonstrating the validity of the LB model. Then, the 3D LB model is used to simulate the different preferential nucleation positions and final wetting states of condensate droplets by changing the geometrical parameters, including interpost space, post height and post width, and local wettability of the nanoarrays on superhydrophobic surfaces. It is found that for the nanostructured surfaces patterned with tall posts, the droplets nucleate in the upside interpost space and at the bottom of nanostructures simultaneously. By designing wider and thinner interpost spaces at the downside and upside of the tall nanostructures, respectively, the phenomenon of droplet nucleation at the bottom can be avoided. The simulation results show that the condensate droplets nucleated in the upside interpost space of tall nanostructures migrate upwards during growth, producing a Wenzel-to-Cassie wetting state transition. On the other hand, the condensate droplets nucleated at the bottom of nanostructured surface patterned with short posts produce the Wenzel state. However, by setting non-uniform hydrophilic and hydrophobic regions on the top of the short nanostructures, the condensate droplets are found to nucleate on the hydrophilic top and generate a Cassie state. The simulated final wetting states of condensate droplets on the nanostructures, having various geometrical parameters, compare reasonably well with the experimental observations reported in the literature. It is demonstrated that the migration of condensate droplets is correlated with the evolution of the statistical average force. If the direction of the statistical average force acting on the droplet is upward, the condensate droplets nucleated in the upside interpost space move upward during growth. The 3D LB simulations provide an insight into the physical mechanism of droplet nucleation, growth and wetting state transitions on superhydrophobic nanostructured surfaces.
A phase field model is used to study the effect of atherosclerotic plaque on hemodynamics. The migration of cells in blood flows is described by a set of multiple phase field equations, which incorporate elastic energies and the interacting effects of cells. Several simulations are carried out to reveal the influences of initial velocities of blood cells, cellular elasticity and block rates of hemodynamic vessels. The results show that the cell deformation increases with the growth of the initial active velocity and block rate but with the decrease of the cellular elasticity. The atherosclerotic plaque not only affects the deformation and migration of cells but also can promote the variation in hemodynamic properties. The atherosclerotic plaque causes a burst in cell velocity, and the greater the block rate and cellular elasticity, the more dramatic the variation of instantaneous velocity. The present work demonstrates that the phase field method could be extended to reveal formation atherosclerosis at the microscopic level from the perspective of hemodynamics.
A coupled model of lattice Boltzmann (LB) and phase-field method is proposed to study cell migration and deformation patterns in Poiseuille flow. The cell phase-field model is used to simulate the cell evolution over time, while the lattice Bhatnagar-Gross-Krook (LBGK) model is used to simulate fluid flow. The model is validated by performing simulations of cells head-on collision and plane Poiseuille flow. The study investigates the effects of initial position, shape energy $\mu$, elasticity modulus $\gamma$, and cell radius R on cell migration and deformation behavior. The impact of fluid velocity in Poiseuille flow on cell migration and deformation is investigated. The results demonstrate the potential of the present model for simulating the dynamics of cell behavior, and providing guidance for hemodynamic studies considering cells in microcirculation.
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