Separation of chiral particles in a rotating electric field

When a particle having a permanent dipole is placed in a rotating electric field in a fluid, it will migrate along the direction of the angular vector of the field. The average velocity of the particle is calculated based on a Brownian motion framework that accounts for the translation-rotation coupling. An explicit expression is given for the average velocity of the particle as a function of the hydrodynamic mobility tensors and the frequency of the field. The expression indicates that the chiral particle and its mirror-image particle move in opposite direction (which accounts for the right/left molecular separation in racemic solutions), and that the migration velocity has a peak at a certain frequency determined by the geometry of the particle. Calculations are made for a twisted ribbon particle and the relation between the migration velocity and the structure of the twisted ribbon particle is discussed.