Stability condition of self-organizing staggered particle trains in channel flow

The inertial focusing of particles in channel flow of a Newtonian fluid is studied using the lattice Boltzmann method. The effects of Reynolds number (Re) and blockage ratio (k) on the stability condition of self-organizing staggered particle trains are explored. The results show that, for staggered particle pairs, the particles will move close to each other with a damped oscillatory trajectory and form a steady horizontal spacing eventually. For single-line particle pairs, the inter-particle spacing increases continuously to a larger value for further downstream. Two lines of 12 particles will self-organize the staggered particle trains. The formation of stable staggered particle trains is dependent on Re and k. Particles with low k in the staggered particle trains are more likely to be unstable or fluctuate within a certain range when Re is larger than a critical value. As k increases, the critical values of Re corresponding to the inter-particle spacing with a stable value or a certain range of fluctuation are also increased. The mean particle spacing decreases with increasing k and decreasing Re, and the blockage ratio k has a greater effect on the particle spacing than Reynolds number Re.