Research On The Particles Sedimentation And Brownian Motion

The present work is mainly involving numerical inverstigations on the particle sedimentation and Brownian motion via lattice Boltzmann method.First, a direct-forcing fictitious domain (DF/FD) scheme is introduced into lattice Boltzmann method for the construction of a LB-DF/FD method, which can be used for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD method by using two unrelated meshes, an Eulerian mesh for the fluid and a Lagrangian mesh for the solid particle, which avoids the re-meshing procedure and do not need to calculate the hydrodynamic forces at each time step. Furthermore, in comparison with "bounce-back" scheme, the present LB-DF/FD is more powerful in dealing with fluid-particle interaction.Second, the present LB-DF/FD method has been validated by comparing its results with previous numerical results for a single circular particle, two circular particles,128 circular particles and a single elliptical particle settling under gravity. Moreover, the present method is used to numerically investigate the dynamics and interaction of two elliptical particles in side-by-side arrangement settling in an infinitely long channel. One particle (EPO) is initially kept horizontal (major axis perpendicular to sedimentation) for all simulations while the other's (EP1) orientation is varied. The results show that if EP1 strays away from horizontality the particles undergo transitions from a steady state to reach a peiriodic-like state with varing amplitude. Furthermore, there are two distinct peiriodic-like states for the particle motion when EP1 orientation is varied, in which a critical orientation of EP1, depending on the fluid-particle density ratio, is observed to distinguish the two states.Third, a single-relaxation-time fluctuating lattice Boltzmann model for direct numerical simulation (DNS) of particle Brownian motion is established. The fluctuating distribution functions in lattice Boltzmann equations are presented for the D2Q9 and D3Q15 lattice model. Besides, the present model is used to simulate cirucular, elliptical and rectangular particle (two-dimensional) Brownian motion and spherical particle (three-dimensional) Brownian motion. Numerical results include the mean-square displacements, mean-square velocitys, velocity autocorrelation functions and self-diffusion coefficients of particles. The equipartition theorem, fluctuation-dissipation theorem and isolated-sphere result have been investigated for these numerical results to validate the present model.Finally, a LB-DF/FD model used for the simulation of particle Brownian motion is developed by adopting the technique of Langevin-type equation based DNS scheme. In the model the thermal fluctuations are introduced as random forces and torques acting on the Brownian particle. The hydrodynamic interaction is introduced by directly resolving the fluid motions. In comparison with fluctuating hydrodynamics, this model needs much less computational resources and can provide a high-efficient approach for simulating particle Brownian motion. A sphere fluctuating in a still fluid and trapped in a harmonic potential have been simulated. The results are inverstigated to check the accuracy and effectiveness of the LB-DF/FD model.