Scaling transitions during rupture of thin liquid sheets of power-law fluids

Rupture of thin liquid sheets is critical in applications as diverse as crop spraying, foam stability, coating flows, and polymer processing. Here, the van der Waals-driven thinning and rupture of sheets of power-law fluids are analyzed for fluids with a range of Ohnesorge numbers Oh ≡ µ₀/√(ρh₀σ), where µ₀, ρ, h₀ and σ represent the zero-deformation-rate viscosity, density, initial sheet thickness and surface tension, and power-law exponent n. The variation with time remaining until rupture of the film thickness, lateral length scale, and lateral velocity is determined analytically through asymptotic analysis of the governing spatially one-dimensional partial differential equations obtained by taking advantage of the long wavelength approximation. This analysis is confirmed and extended by numerical solution of the multi-dimensional continuity and Cauchy momentum equations. A plethora of scaling regimes that arise for different dominant balances between inertial, viscous, van der Waals, and capillary forces are identified, and transitions between these regimes are determined and delineated in the parameter space of (Oh, n).