Asymmetric instability in thin-film flow down a fiber

Thin-film flow down a vertical fiber gives rise to a number of instabilities that define the bead-on-fiber morphology including Plateau-Rayleigh breakup, isolated bead formation, and convective instabilities. Experiments are performed that reveal an asymmetric instability which depends upon the liquid surface tension and fiber diameter and exhibits all the bead-on-fiber morphologies. The bead dynamics are described by the bead spacing and bead velocity, with the asymmetric morphology displaying more regular dynamics than the symmetric morphology. For the asymmetric morphology, the transition from the Plateau-Rayleigh to convective regime agrees well with predictions for a free viscous jet, indicating a minimal effect between the thin film and fiber. In addition, the dimensionless bead velocity is shown to scale with the capillary number for all experimental data. These observations for the asymmetric bead dynamics can be used as a design tool for heat and mass transfer applications.

Figure 1

(a) Experimental setup and (b) sketch of the bead properties showing the bead spacing $S_b$, bead velocity $V_b$, bead diameter $D_b$, and fiber diameter $D_f$.

Figure 2

(a) Phase diagram of the bead symmetry, as it depends upon the surface tension and fiber diameter for the observed (b) symmetric and (c) asymmetric morphology.

Figure 3

(a) Symmetric and (b) asymmetric bead morphology exhibit isolated (left), Plateau-Rayleigh (middle), and convective (right) regimes. The bead diameters shown in the middle image of (a) and (b) are 2.38 and 2.245 mm, respectively.

Figure 4

Bead velocity $V_b$ against flow rate $Q$, as it depends upon viscosity $\mu$ for the (a) symmetric and (b) asymmetric morphology for a fixed nozzle diameter $D_n=1.2$ mm and fiber diameter $D_f=0.2032$ mm.

Figure 5

Bead spacing $S_b$ against viscosity $\mu$ at the onset of the convective regime for nozzle diameter $D_n=1.2$ mm and fiber diameter $D_f=0.2032$ mm.

Figure 6

(a) Bead velocity against viscosity at the onset of the convective regime for nozzle diameter $D_n=1.2$ mm and fiber diameter $D_f=0.2032$ mm. (b) Bead velocity $V_b$ against fiber diameter $D_f$ at the onset of the convective regime contrasting the symmetric ($\mu =48m\mathrm{Pa}$ s) and asymmetric ($\mu =787m\mathrm{Pa}$ s) morphology for $D_n=1.2$ mm.

Figure 7

Transition velocity ratio $\tilde{V}$ against Reynolds number Re at the absolute-convective transition point contrasting the symmetric and asymmetric morphology for all data.

Figure 8

Bead velocity ratio $V^{*}$ against capillary number Ca for all data.

Figure 9

Frequency $f$ against flow rate $Q$ for all data.