Dynamical solutions for migration of chiral DNA-type objects in shear flows

We present a dynamical analysis of chiral object motions to explain physical mechanisms and give quantitative predictions on the shear-induced drift motions of chiral objects and the chiral separation of enantiomers using shear flows. For objects well represented by the uniaxial approximation, such as DNA and chiral disk hexamers, dynamical motions in low-Reynolds-number shear flows are solved analytically, in terms of steady-state object-flow interacting parameters, which can be calculated numerically by well-established methods. The shear-induced drifting speed of long helices are evaluated. Good agreements are found between our results and those obtained from dynamical simulations [Makino and Doi, Phys. Fluids 17, 103605 (2005)]. We also compare our results with those obtained experimentally [Marcos, Fu, Powers, and Stocker, Phys. Rev. Lett. 102, 158103 (2009)]. The analysis may also be extended to study other important chiral-flow interactions in nature environments and microfluidic devices, such as the particle-wall and interparticle interactions.