Ligament Mediated Fragmentation of Viscoelastic Liquids

The breakup and atomization of complex fluids can be markedly different than the analogous processes in a simple Newtonian fluid. Atomization of paint, combustion of fuels containing antimisting agents, as well as physiological processes such as sneezing are common examples in which the atomized liquid contains synthetic or biological macromolecules that result in viscoelastic fluid characteristics. Here, we investigate the ligament-mediated fragmentation dynamics of viscoelastic fluids in three different canonical flows. The size distributions measured in each viscoelastic fragmentation process show a systematic broadening from the Newtonian solvent. In each case, the droplet sizes are well described by Gamma distributions which correspond to a fragmentation-coalescence scenario. We use a prototypical axial step strain experiment together with high-speed video imaging to show that this broadening results from the pronounced change in the corrugated shape of viscoelastic ligaments as they separate from the liquid core. These corrugations saturate in amplitude and the measured distributions for viscoelastic liquids in each process are given by a universal probability density function, corresponding to a Gamma distribution with $n_{\min }=4$. The breadth of this size distribution for viscoelastic filaments is shown to be constrained by a geometrical limit which can not be exceeded in ligament-mediated fragmentation phenomena.

Figure 1

Snapshot of the liquid jet in the air-assisted atomization for (a) the Newtonian solvent and (b) the viscoelastic solution (PEO-300 K-0.01% wt. in the solvent).

Figure 2

(a) Images from the fragmentation process for a Newtonian ligament (with the index $n=8$). The coalescence of the neighboring blobs in the ligament at $t=0$ (magenta circles on the left image) results in the final distribution of droplet sizes at $t=25\mathrm{ms}$. (b) Droplet size distributions for all tested liquids in the air-assisted atomization process. For each fluid we specify the values of Ohnesorge and Deborah number, $\{\text{Oh},\text{De}\}$:(black squares)$\{\text{Oh}=0.04,\text{De}=0\}$, (cyan triangles)$\{0.04,0.2\}$, (blue triangles)$\{0.04,1.3\}$, (magenta circles)$\{0.04,3.6\}$, (red circles)$\{0.04,10.0\}$. Solid lines are Gamma distributions for $n=6$ (black) and $n=4$ (red).

Figure 3

(a) Sudden stretch experiment for a viscoelastic solution at high strain rates ($\overline{\dot{\epsilon }}\simeq 120{\mathrm{s}}^{-1}$). (b) Schematics of a cylindrical ligament with initial radius $r_0$ corrugated by perturbations with similar wavelengths but varying amplitude $\xi$. (c) Ligament profiles for the Newtonian solvent (blue curve) compared with the viscoelastic solution (red curve) at the breaking point from the liquid hemispherical reservoirs ($t=0$). The dashed circles indicate the local protoblobs inside each ligament.

Figure 4

(a) Fragmentation after drop impact on a small target. Montage of images for (i) the Newtonian solvent and (ii) a polymer solution (PEO 300 K). (b) Snapshots of the droplets captured after fragmentation by jet impact atomization (i) for (ii) the Newtonian solvent and (iii) viscoelastic solution. (c) Summary of the measured values of the dispersity $\mathrm{SMD}/⟨d⟩$ in three different fragmentation processes for both the Newtonian solvent (blue) and the viscoelastic (denoted V.E.) solutions (red) compared with the theoretical prediction (solid line).