Lattice Boltzmann Simulations of Particle-Particle Interaction in Steady Poiseuille Flow

The moving behaviour of two- and three-particles in a pressure-driven flow is studied by the lattice Boltzmann simulation in two dimensions. The time-dependent values, including particles＇ radial positions, translational velocities, angular velocities, and the x-directional distance between the particles are analysed extensively. The effect of flow Reynolds number on particle motion is also investigated numerically. The simulation results show that the leading particle equilibrium position is closer to the channel centre while the trailing particle equilibrium position is closer to the channel wall. If Reynolds number Re is less than 85.30, the larger flow Reynolds number results in the smaller x-directional equilibrium distance, otherwise the x-directional distance increases almost linearly with the increase of time and the particles separate finally. The simulation results are helpful to understand the particle-particle interaction in suspensions with swarms of particles.     

基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解

Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程, 再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组, 求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法, 得到了该方程的精确行波解.同时也得到了该方程的一个Backlund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法.     

Lattice Boltzmann simulation of behaviour of particles moving in blood vessels under the rolling massage

The rolling massage is one of the most important manipulations in Chinese massage, which is expected to eliminate many diseases. Here, the effect of the rolling massage on a pair of particles moving in blood vessels under rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulated results show that the motion of each particle is considerably modified by the rolling massage, and it depends on the relative rolling velocity, the rolling depth, and the distance between particle position and rolling position. Both particles' translational average velocities increase almost linearly as the rolling velocity increases, and obey the same law. The increment of the average relative angular velocity for the leading particle is smaller than that of the trailing one. The result is helpful for understanding the mechanism of the massage and to further develop the rolling techniques.