Scaling analysis of the Plateau–Rayleigh instability in thin film flow down a fiber

thin viscous film flowing down a fiber is subject to Plateau–Rayleigh instability leading to temporal beading patterns, characterized by the bead spacing S_b , bead velocity V_b , and bead diameter D_b . In this study, experiments are performed to document the beading pattern as it depends upon the flow rate Q , nozzle diameter D_n , fiber diameter D_f and liquid viscosity μ . The large experimental data set collapses upon scaling with the Nusselt solution for gravity-driven thin film flow with viscous time scale showing the dimensionless bead diameter scales with the capillary number. The dimensionless bead frequency and bead spacing are similarly related and characterize the dispersion relationship. Graphic abstract