eng Extensional flow of nematic liquid crystal under electric field gradient Cummings, L. J. Myers, T.G. Low, J. Centre de Recerca Matemàtica info:eu-repo/semantics/preprint Centre de Recerca Matemàtica 2011 Cristalls líquids Desenvolupaments asimptòtics http://ddd.uab.cat/record/85591 oai:www.recercat.cat:2072/179280 oai:ddd.uab.cat:85591 info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 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 fi bers), albeit with a modi fied "Trouton ratio". However, with a symmetry-breaking electric field gradient applied, behavior deviates from the Newtonian case, and the sheet can undergo fi nite-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.