Hydrodynamics of Liquids of Chiral Molecules and Suspensions Containing Chiral Particles

We obtain hydrodynamic equations describing a fluid consisting of chiral molecules or a suspension of chiral particles in a Newtonian fluid. The hydrodynamic velocity and stresses arising in a flowing chiral liquid have components that are forbidden by symmetry in a Newtonian liquid. For example, a chiral liquid in a Poiseuille flow between parallel plates exerts forces on the plates, which are perpendicular to the flow. A generic flow results in spatial separation of particles of different chirality. Thus even a racemic suspension will exhibit chiral properties in a generic flow. A suspension of particles of random shape in a Newtonian liquid is described by equations which are similar to those describing a racemic mixture of chiral particles in a liquid.

Figure 1

A chiral liquid in a Poiseuille flow between parallel plates exerts a pair of opposite forces on the plates ${\mathbf{F}}_{\uparrow }=-{\mathbf{F}}_{\downarrow }$, which are directed into ($\otimes$) and out of ($\odot$) the page. A flow of a chiral liquid in a converging or diverging channel develops a helicoidal component of velocity directed into and out of the page, as shown at right. The distance to the origin of the channel, point $O$, is denoted by $r$. For a Newtonian fluid the flow lines (dotted lines) lie in the plane of the figure.