Chiral Separation by Flows: The Role of Flow Symmetry and Dimensionality

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 druglike molecules. Simulations of model enantiomers in a range of fluids such as Λ- and Δ-[Ru(bpy)₃]Cl₂ 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 nonzero molecular pitch.

Effective aspect ratio of helices in shear flow

We report the results of simulations of rigid colloidal helices suspended in a shear flow, using dissipative particle dynamics for a coarse-grained representation of the suspending fluid, as well as deterministic trajectories of non-Brownian helices calculated from the resistance tensor derived under the slender-body approximation. The shear flow produces nonuniform rotation of the helices, similarly to other high aspect ratio particles, such that more elongated helices spend more time aligned with the fluid velocity. We introduce a geometric effective aspect ratio calculated directly from the helix geometry and a dynamical effective aspect ratio derived from the trajectories of the particles and find that the two effective aspect ratios are approximately equal over the entire parameter range tested. We also describe observed transient deflections of the helical axis into the vorticity direction that can occur when the helix is rotating through the gradient direction and that depend on the rotation of the helix about its axis.