A numerical study on a macroscopic Stokes number based on shear-induced interparticle collisions in a micro-separator/classifier

Characterization of microseparator/classifier with a simple arc microchannel

“…The representative shear rate is determined based on experimental results as where U and D h is mean axial velocity and equivalent diameter in the arc section. The discussions on those representative values were given in previous studies 39, 41. A typical shear rate of 10 5 s −1 in the device, for instance, causes a velocity variation of 1 m/s even around a 10 μm particle.…”

“…In this case, the slurry can be regarded as dilute. As a threshold, the previous numerical studies proposed a Stk s value of 0.1 from both microscopic and macroscopic viewpoints 39, 41. In the present study, therefore, the threshold value is examined based on the recovery of acrylic particles.…”

“…It is of practical interest to predict a maximum feed concentration with a highest separation efficiency, which would be obtained at a lowest feed concentration due to no or negligible interaction between particles. For the prediction, in the previous numerical studies,39, 41 a novel Stokes number Stk s is proposed as a ratio of particle relaxation time τ p (including “added mass force”) to an estimated interparticle collision interval τ s due to a shear flow as where ρ p and ρ f is particle and fluid density, d p is particle diameter, μ is fluid viscosity, α p is particle volume fraction, and S is shear rate, respectively. The τ s is an inverse of collision frequency between spherical particles in a Couette flow.…”

“…In the practical operations, the maximum feed concentration without the decline would become a crucial interest. Therefore, a novel Stokes number definition was proposed based on the numerical results to predict the limit 39, 41…”