Two-dimensional oscillatory motion of inertially focused particles in microfluidic flows

Inertially focused particles flowing in microchannels form an evenly spaced streamline on each channel face due to hydrodynamic interaction. Previous studies of this interaction have only reported the oscillatory pairwise dynamics of focused particles, which was limited to the one-dimensional (1D) streamwise direction. Thus, despite its practical and intellectual importance, there remains a lack of comprehensive research on the pairwise oscillation, due to the difficulty of high-resolution observation. Here, I explore the hydrodynamic interaction between inertially focused particles in microfluidic flows to determine the ordering mechanism. Direct numerical simulation (DNS) is applied to a pressure-driven flow of a pair of particles due to the lack of established formulas for the inertial focusing of finite-sized particles; in particular, only DNS allows the author to simulate the microscale flow structures. I describe the unique periodic oscillations of the pairwise particles as they flow downstream. Upon the formation of a train structure in the steady state, the following particle shows periodic oscillations on a two-dimensional (2D) limit cycle around its equilibrium position, whereas the leading particle exhibits 1D oscillation at a specific distance downstream. The 2D oscillatory motion of the following particle is produced by a combination of the lift forces and the disturbance flow induced by the leading particle, coupled with forward/backward transport by the main flow. Thus, the spacing of the particle train is a function of the particle size and flow conditions, leading to even spacing between inertially focused particles. The finding of the asymmetric oscillatory dynamics of the pairwise system provides direct evidence for the self-assembly mechanism of inertially focused particles. I highlight a mostly overlooked aspect of the lift forces: that they stabilize focused streamlines that might otherwise break apart due to finite-particle-induced disturbance flows.