On spider-man and film casting: the mathematics of free liquid fibers and films in elongation
Wednesday, November 4, 2009 - 11:15am - 12:15pm
In this lecture we give an overview of the mathematical theory of free liquid fibers and films of highly viscous liquids in fiber spinning and film casting. The governing equations to be discussed arise as the slender body approximation of the Navier-Stokes equations with moving boundary as 1D or 2D nonlinear coupled hyperbolic-elliptic systems of pdes. Topics of interest in this presentation include existence and uniqueness results, failure of fiber breakup in the purely viscous regime, and spectral determinacy/regularity of the linearized film equations. Some open questions will be motivated.