Molecular configurations in the droplet detachment process of a complex liquid

We studied the microscopic polymer conformations in the droplet detachment process of an elastic semidilute polyelectrolytic xanthan solution by measuring the instantaneous birefringence. As in earlier studies, we observe the suppression of the finite time singularity of the pinch-off process and the occurrence of an elastic filament. Our microscopic measurements reveal that the relatively stiff xanthan molecules are already significantly prestretched to about 90% of their final extension at the moment the filament appears. At later stages of the detachment process, we find evidence of a concentration enhancement due to the elongational flow.

Figure 1

Stationary viscosities from shear rate and stress controlled measurements. Not all experiments and data points are shown. The lines are approximations by the Carreau model.

Figure 2

Experimental setup. See text for further explanation.

Figure 3

Photographs of the droplet detachment process of a $0.2\mathrm{wt}\%$ xanthan solution $({\eta }_{solv}=60\mathrm{mPa}\mathrm{s})$ taken every $0.1\mathrm{s}$, indicating, schematically, the laser beam positioned close to the neck and in a region as cylindrical as possible throughout the measurement.

Figure 4

Filament diameter $h\left(t\right)$ for different polymer concentrations and solvent viscosities. The parameters refer to Eq. (1). Not all data points are shown.

Figure 5

Apparent elongational viscosity for the same set of data as in Fig. 4.

Figure 6

Elongational viscosity for different solvent viscosities (squares) and polymer concentrations (circles). The data are taken at large Henky strain (compare Fig. 5). The continuous and the dashed lines show the theoretical values according to a fit with Bachelor’s formula for semidiluted rigid rods.

Figure 7

(a) Instantaneous birefringence versus the elapsed time. The arrows indicate a Henky strain of $\zeta =1.5$. (b) Instantaneous birefringence versus the Henky strain. The vertical line indicates the $\zeta =1.5$ position; the dashed lines are linear fits with slopes indicated by the numbers. Symbols are as in Fig. 1.