Steady Particle Distribution in Microchannel Flows with Entrance-Injected Particles

Predicting particle distribution in particulate flows commonly requests numerical simulations. The present work aims to develop analytical expressions for steady particle volume fraction in particulate microchannel plane flows based on an adopted shear-induced lift force model. The initially uniformly distributed particles are injected to the pressure-driven channel flow at an inlet velocity slower or faster than the fluid inlet velocity. The lift-force-driven lateral particle migration develops before the particles match the fluid velocity, which leads the non-uniform particle distribution over the channel cross-section. When the increasing particle Stokes number reaches a critical value, the particle volume fraction reduces to zero at the channel wall or the midline, depending on the sign of lift force coefficient and whether the particle-to-fluid inlet velocity ratio is smaller or larger than the unity. The role of the lift force coefficient in the steady particle distribution is discussed for heavy particles, nanoparticles and gas bubbles, respectively. When the particle-to-fluid inlet velocity ratio is at least one order of magnitude smaller than the unity, two specific locations (symmetric about the midline at a distance about 0.45 the half-channel height from the midline) are identified at which the steady particle volume fraction remains nearly equal to the migration-free value, independent on specific values of the lift force coefficient, the particle Stokes number and the particle-to-fluid density ratio. Comparison of the predicted results with known data available in the literature is made with some qualitative agreement.