Extensional flow of nematic liquid crystal with an applied electric field

Systematic asymptotic methods are used to formulate a model for the extensional flow of a thin sheet of nematic liquid crystal. With no external body forces applied, the model is found to be equivalent to the so-called Trouton model for Newtonian sheets (and fibres), albeit with a modified 'Trouton ratio'. However, with a symmetry-breaking electric field gradient applied, behaviour deviates from the Newtonian case, and the sheet can undergo finite-time breakup if a suitable destabilizing field is applied. Some simple exact solutions are presented to illustrate the results in certain idealized limits, as well as sample numerical results to the full model equations.