Nematic ordering of rigid rods in a gravitational field

The isotropic-to-nematic transition in an athermal solution of long rigid rods subject to a gravitational (or centrifugal) field is theoretically considered in the Onsager approximation. The new feature emerging in the presence of gravity is a concentration gradient that coupled with the nematic ordering. For rodlike molecules this effect becomes noticeable at centrifugal acceleration $g\sim {10}^3–{10}^4$ ${\mathrm{m}/\mathrm{s}}^2,$ while for biological rodlike objects, such as tobacco mosaic virus, the effect is important even for normal gravitational acceleration conditions. Rods are concentrated near the bottom of the vessel, which sometimes leads to gravity induced nematic ordering. The concentration range corresponding to phase separation increases with increasing g. In the region of phase separation the local rod concentration, as well as the order parameter, follow a step function with height.