Abstract
Separation of enantiomers by flows is a promising chiral resolution method using cost-effective microfluidics. Notwithstanding a number of experimental and numerical studies, a fundamental understanding still remains elusive, and an important question as to whether it is possible to specify common physical properties of flows that induce separation has not been addressed. Here, we study the separation of rigid chiral objects of an arbitrary shape induced by a linear flow field at low Reynolds numbers. Based on a symmetry property under parity inversion, we show that the rate-of-strain field is essential to drift the objects in opposite directions according to chirality. From eigenmode analysis, we also derive an analytic expression for the separation conditions which shows that the flow field should be quasi-two-dimensional for the precise and efficient resolutions of microscopic enantiomers. We demonstrate this prediction by Langevin dynamics simulations with hydrodynamic interactions fully implemented. Finally, we discuss the practical feasibility of the linear flow analysis, considering separations by a vortex flow or an extensional flow under a confining potential.
Highlights
Among alternative physical separation methods that do not rely on a chiral selector4–6, chiral resolution by flows has recently received considerable attention with rapid developments in microfluidics7–19
We propose to quantify the degree of the separation by the Jensen-Shannon divergence (JSD):
According to our theoretic formulations, the chiral separation occurs when both of the following conditions have to be satisfied: First, one of the eigenvalues of velocity gradient tensor should be much smaller than the inverse of the separation time scale
Summary
Considering the measurement and control accuracy of current microfluidic devices (to our knowledge, of the order of 0.1% at best), one might view this range of ε to be synonymous for a singular flow It implies that the chiral separation is possible only by quasi-two-dimensional flows described by a velocity gradient tensor J with a vanishingly small eigenvalue. The previous criterion of Eq [21] predicts that for separation to occur, the upper bound of |ε| is given as ε ⪅ O(10−3) even when a very narrow initial distribution of molecular size is assumed (δ ~ 1) We test this prediction through numerical simulations, as varying the value of ε of the flows considered above. According to our theoretic formulations, the chiral separation occurs when both of the following conditions have to be satisfied: First, one of the eigenvalues of velocity gradient tensor should be much smaller than the inverse of the separation time scale (the eigenmode analysis).
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