Inertial microfluidics: A method for fast prediction of focusing pattern of particles in the cross section of the channel.

Inertial microfluidics is utilized as a powerful passive method for particle and cell manipulation, which uses the hydrodynamic forces of the fluid in the channel to focus particles in specific equilibrium positions in the cross section of the channel. To achieve high performance manipulation, knowledge of focusing pattern of particles in the cross section of channel is essential. In this paper, we propose a method to address this important issue. To this end, firstly inertial microfluidics is analyzed in rectangular cross section channels. The results indicate that fluid flow velocity and channel's cross-sectional profiles have great impacts on the forces exerted on particles. Next, these results are utilized to propose a method to predict equilibrium positions in non-rectangular cross section channels through some simple calculations. This method is based on approximating the velocity profile of a non-rectangular cross section channel by utilizing portions of velocity profiles of different rectangular cross section channels. To analyze the method's performance, results obtained from the proposed method are compared with Direct Numerical Simulation (DNS) and experimental studies of seven non-rectangular channels. It is observed that the proposed approach accurately predicts particles trajectories and their equilibrium positions in the cross section of channels.