Separation of Enantiomers through Local Vorticity: A Screw Model Mechanism

We present a model to explain the mechanism behind enantiomeric separation under either shear flow or local rotational motion in a fluid. Local vorticity of the fluid imparts molecular rotation that couples to translational motion, sending enantiomers in opposite directions. Translation-rotation coupling of enantiomers is explored using the molecular hydrodynamic resistance tensor, and a molecular equivalent of the pitch of a screw is introduced to describe the degree of translation-rotation coupling. Molecular pitch is a structural feature of the molecules and can be easily computed, allowing rapid estimation of the pitch of 85 drug-like molecules. Simulations of model enantiomers in a range of fluids such as $\Lambda$- and $\Delta$-Ru(bpy)_3]Cl_2 in water and (R,R)- and (S,S)-atorvastatin in methanol support predictions made using molecular pitch values.A competition model and continuum drift diffusion equations are developed to predict separation of realistic racemic mixtures. We find that enantiomeric separation on a centimeter length scale can be achieved in hours, using experimentally-achievable vorticities. Additionally, we find that certain achiral objects can also exhibit a non-zero molecular pitch.