caa a22 4500 606166653 CHVBK 20210128100659.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10665-014-9697-2 doi (NATIONALLICENCE)springer-10.1007/s10665-014-9697-2 Modeling flow of nematic liquid crystal down an incline [Elektronische Daten] [M. Lam, L. Cummings, T.-S. Lin, L. Kondic] The flow of nematic liquid crystals down an inclined substrate is studied. Under the usual long wave approximation, a fourth-order nonlinear parabolic partial differential equation of the diffusion type is derived for the free surface height. The model accounts for elastic distortions of the director field due to different anchoring conditions at the substrate and the free surface. The partial differential equation we derive admits 2D traveling-wave solutions, which may translate stably or exhibit instabilities in the flat film behind the traveling front. These instabilities, which are distinct from the usual transverse instability of downslope flow, may be analyzed and explained by linear stability analysis of a flat translating film. Intriguing parallels are found with the instabilities exhibited by Newtonian fluid flowing on an inverted substrate and Newtonian fluid flow outside a vertical cylinder. Springer Science+Business Media Dordrecht, 2014 Inclined plane nationallicence Liquid crystal nationallicence Nematic nationallicence Thin film nationallicence Lam M. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut Cummings L. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut Lin T.-S Department of Mathematical Sciences, Loughborough University, LE11 3TU, Leicestershire, UK aut Kondic L. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut Journal of Engineering Mathematics Springer Netherlands 94/1(2015-10-01), 97-113 0022-0833 94:1<97 2015 94 10665 https://doi.org/10.1007/s10665-014-9697-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9697-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lam M. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut NATIONALLICENCE 700 1- Cummings L. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut NATIONALLICENCE 700 1- Lin T.-S Department of Mathematical Sciences, Loughborough University, LE11 3TU, Leicestershire, UK aut NATIONALLICENCE 700 1- Kondic L. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 94/1(2015-10-01), 97-113 0022-0833 94:1<97 2015 94 10665