Analysis of mixed motion in deterministic ratchets via experiment and particle simulation

Deterministic lateral displacement (DLD) ratchets are microfluidic devices, which are used for size-based sorting of cells or DNA. Based on their size, particles are showing different kinds of motion, leading to their fractionation. In earlier studies, so-called zigzag and displacement motions are observed, and in recent study by our group (Kulrattanarak et al., Meas Sci Technol, 2010a; J Colloid Interface Sci, 2010b), we have shown that also mixed motion occurs, which is an irregular alternation of zigzag and displacement motion. We have shown that the mixed motion is due to asymmetry of the flow lane distribution, induced by the symmetry breaking of the oblique primitive lattice cell (Kulrattanarak et al. 2010b). In this study, we investigate mixed motion in depth by numerical and experimental analysis. Via 3D simulations, we have computed explicit particle trajectories in DLD, and are able to show that there are two critical length scales determining the type of motion. The first length scale d (f,1) is the first flow lane width, which determines the transition between zigzag motion and mixed motion. The other length scale, d (f,c) , determines the transition between mixed motion and displacement motion. Based on our experimental and numerical results we have been able to correlate the migration angle of particles showing mixed motion to the particle size, relative to the two critical length scales d (f,1) and d (f,c) .