Penetration efficiency of nanoparticles in a bend of circular cross-section

In order to quantify the losses of nanoparticles in a bend of circular cross-section, the penetration efficiency of nanoparticles of sizes ranging from 5.6 nm to 560 nm in diameter is determined as a function of the Dean number, the Schmidt number and the bend angle. It is shown that the effect of the Dean number on the penetration efficiency depends on the particle size. The Dean number has a stronger effect on the penetration efficiency for small particles than for large particles. There exists a critical value of the Dean number beyond which the penetration efficiency turns from increasing to decreasing with the increase of the Dean number, and this critical value is dependent on the particle size and the bend length. The penetration efficiency increases abruptly when the Schmidt number changes from 7 500 to 25 000. Finally, a theoretical relation between the penetration efficiency and the Dean number, the Schmidt number and the bend length is derived.