Extensional flow of a free film of nematic liquid crystal with moderate elasticity

Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets nematic liquid crystal. The rod-like molecules these substances impart an elastic contribution to its response. We rescale weakly due Cummings et al. [European Journal Applied Mathematics 25 (2014): 397-423] describe case moderate elasticity. resulting system two nonlinear partial differential equations sheet thickness and axial velocity is fourth order space, but still represents significant reduction full system. analyze solutions from several different boundary conditions, motivated underlying application, with particular focus on dynamics mechanisms under stretching. solve numerically, via collocation either finite difference or Chebyshev spectral discretization together implicit time stepping. At early times, depending initial shape, pressure aids opposes flow, which changes shape may result loss minimum maximum at moving end. contrast this finding cases weak elasticity Newtonian where retains all extrema condition throughout time.