Sharp-Interface Nematic–Isotropic Phase Transitions without Flow

We derive a supplemental evolution equation for an interface between the nematic and isotropic phases of a liquid crystal when flow is neglected. Our approach is based on the notion of configurational force. As an application, we study the behavior of a spherical isotropic drop surrounded by a radially oriented nematic phase: our supplemental evolution equation then reduces to a simple ordinary differential equation admitting a closed-form solution. In addition to describing many features of isotropic-to-nematic phase transitions, this simplified model yields insight concerning the occurrence and stability of isotropic cores for hedgehog defects in liquid crystals.