Numerical Simulation of Surface Acoustic Wave Actuated Separation of Rigid Enantiomers by the Fictitious Domain Lagrange Multiplier Method

Enantiomers are chiral objects which di er by their orientation and are thus referred to as lefthanded and right-handed enantiomers. In applications they mostly occur as so-called racemic compounds consisting of approximately the same amount of leftand right-handed species which may have completely di erent properties. Hence, the separation of leftfrom right-handed enantiomers is an important issue. Conventional technologies are based on gas or high pressure liquid chromatography, capillary electrophoresis, or nuclear magnetic resonance, but typically they are slow and require costly chiral media. A new idea for separation of chiral objects is based on introducing them in certain vorticity patterns, which has been shown towork in theory for an extremely simpli ed setting by Kostur et al. [14]. In this paper, we investigatewhether these ideas can be successfully adapted to a more realistic setup which can be implemented experimentally. For this purpose, we simulate transport of rigid chiral particles in a uidic environment by an application of the ctitious domain Lagrange multiplier method due to Glowinski et al. [11] which has been designed to study the motion of rigid particles in carrier uids. Numerical results are presented which illustrate the feasibility of enantiomer separation in ow elds consisting of pairwise counter-rotating vortices. Moreover, a rst experimental setup based on surface acoustic wave generated vorticity patterns on the surface of a carrier uid is devised which re ects the idealized numerical model and gives promising results with respect to properties of particle propagation. These ndingsmay lead to a new technology for enantiomer separation which is both fast and cost-e ective.