Supplementary information
(1) Fig. S1
Fig. S1 (a) The counter-rotating vortex in the cross section of serpentine channel with different aspect ratios (APs), (i) AP=1/5 and (ii)
AP=3/5. (b) The fluid velocity along z (vertical) direction is responsible for the mixing effect. Its average magnitude is plotted under (i)
zigzag channel with different aspect ratios when input velocity is the same (1 ms-1), and (ii) different input velocities when AP is set as 1/5.
The average velocity along z axis is calculated as: ∯|𝑣𝑧 |𝑑𝑆⁄𝑆, where S is the area of channel cross section A-A, and vz is fluid velocity
along z direction. (c) Particle equilibrium positions by inertial migration in a straight channel with different aspect ratios (APs). (i) Four
equilibrium positions when AP=1 (Di Carlo 2009). (ii) Two equilibrium positions when AP=1/3~1/2 (Hansson et al. 2012). (iii ~ v) No
distinct equilibrium positions along the long face when AP=1/5, and the weak equilibrium positions varies under different channel Reynolds
numbers.
(2) Fig. S2
Fig. S2 Schematic illustration of geometry of the serpentine channel (a) and experimental setup (b).
(3) Fig. S3
Fig. S3 Focusing process between 1st and 5th periods.
(4) Equation (S4)


w

  f Dh

2 Lc min 1.8  10 4 U 0f .63 
 




100  10 3
Lc min 32 .779U 0f .63  1.111U f
1.63
Dh
2R






  p   f a 2U f / 18 R 




(S3)

It should be noted here that as a zigzag serpentine channel is not curved rigorously, so the value of the channel curvature R here is applying
an equivalent inscribed circle radius.
(5) Fig. S5
Fig. S5 Particles become defocused when Channel Reynolds number exceeds 200, due to strong enough mixing effects of secondary
counter-rotating streams.
Di Carlo D (2009) Inertial microfluidics. Lab Chip 9:3038-3046.
Hansson J, Karlsson JM, Haraldsson T, Brismar H, van der Wijngaart W, Russom A (2012) Inertial
microfluidics in parallel channels for high-throughput applications. Lab Chip 12:4644-4650.