Fundamentals of Differential Particle Inertial Focusing in Symmetric Sinusoidal Microchannels

Focusing and separation of particles such as cells at high throughput is extremely attractive for biomedical applications. Particle manipulation based on inertial effects requires a high flow speed and thus is well-suited to high-throughput applications. Recently, inertial focusing and separation using curvilinear microchannels has been attracting a great amount of interest because of the linear structure for parallelization, small device footprint, superior particle-focusing performance, and easy implementation of particle separation. However, the curvature directions of these microchannels alternate, leading to variations in both the magnitude and direction of the induced secondary flow. Accumulation of this variation along the channel causes unpredictable behaviors of particles. This paper systematically investigates the inertial-focusing phenomenon in low-aspect-ratio symmetric sinusoidal channels. First, we comprehensively studied the effects of parameters such as viscosity, flow conditions, particle size, and geometric dimensions of the microchannel on differential particle focusing. We found that particle inertial focusing is generally independent of fluid kinematic viscosity but highly dependent on particle size, flow conditions, and channel dimensions. Next, we derived an explicit scaling factor and included all four dimensionless parameters (particle-blockage ratio, curvature ratio, Dean number, and channel aspect ratio) in a single operational map to illustrate the particle-focusing patterns. Finally, we proposed a rational guideline to intuitively instruct the design of channel dimensions for separation of a given particle mixture.