Two-way interactions of a rigid sphere and the vortical flow in an X-shaped microchannel

The X-shaped microchannel is an effective microfluidic device for particle processing, where a particle's residence time and oscillation frequency in the junction are key factors. This study quantitatively examines their dependence on the flow Reynolds number (Re), channel aspect ratio (AR), and particle blockage ratio (β) using direct numerical simulations via an immersed boundary–lattice Boltzmann method. Our simulations cover the ranges 60≤Re≤160, 0.5≤AR≤1, and 0.2≤β≤0.5. The particle's lateral entry position is fixed near the channel centerline, ensuring interaction with the vortical flow. It is known that a steady spiral vortex forms for 48<Re<300, with vortex breakdown (VB) occurring at Re>100. The results at AR=1 reveal two competing effects: (1) vortical flow weakening due to particle blockage, which reduces residence time; and (2) vortical flow augmentation due to VB shrinkage caused by the particle, which increases residence time. For Re<100, VB does not occur, and only the first effect is present, leading to a decrease in residence time as β increases. At Re>130 with β=0.2, the second effect dominates, increasing residence time relative to a massless point particle, with this increase further amplified at higher Re. A larger β favors the first effect. Frequency decreases with higher β (all Re, AR) and lower AR (for Re<100 only). At Re>100, lower AR shrinks VB simultaneously, fixing frequency approximately.