Rapid viscoelastic spreading

We investigate the rapid spreading dynamics of a viscoelastic drop on a solid. Upon contact, surface tension drives a fast motion of the contact line along the substrate. Here we resolve this motion for viscoelastic liquids by experiments on aqueous polymer solutions of varying concentration. It is found that while the contact line motion is only mildly affected by the polymers, the interface profile becomes much sharper owing to singular polymer stress. This behavior is reminiscent of that observed for viscoelastic drop coalescence; in this context we revisit the analogy between spreading and coalescence, which sheds light also on the spreading of Newtonian liquids.

Figure 1

(a) Side-view schematic of the experimental setup: a drop of PEO is slowly brought into contact with a smooth, transparent and clean glass plate. (b) Upon contact, a water drop rapidly spreads over the solid. The white dashed line indicates the position of the substrate; the lower half of the image is a reflection. The contact line motion is described by the rapid growth of the contact radius $r_0$. (c) Spreading of a 2.0 wt % PEO drop. The wetting dynamics is weakly slowed down and the interface profiles are much sharper, as compared to the case of water. The scale bar, common to both series of snapshots, indicates $500\mu \mathrm{m}$. (d) Series of snapshots taken from below of a water drop spreading on a (transparent) substrate. Prior to contact, the thin air gap separating the drop from the solid produces an interference pattern. After contact, the liquid quickly wets the solid: the dark area expands radially by typically $200\mu \mathrm{m}$ in $50\mu \mathrm{s}$, resulting in spreading velocities of about 5 m/s. The scale bar indicates $200\mu \mathrm{m}$.

Figure 2

Temporal spreading dynamics. (a) Contact radius $r_0$ (scaled by the drop radius $R$), as a function of time $t$ (scaled by the inertio-capillary time $\tau$) for water and PEO solutions of varying concentrations. (b) Same data on a logarithmic scale. (c) Fitted exponent $\alpha$ extracted from $r_0/R=K{(t/\tau )}^{\alpha }$ as a function of $c$, the PEO concentration; the dashed line indicates the exponent expected for Newtonian liquids, $\alpha =1/2$. (d) Prefactor $K$ as a function of a function of $c$; the dashed line indicates the value expected for Newtonian liquids, $K=1.2$ [7, 11]. The error bars on $\alpha$ and $K$ arise from the averaging different experiments with the same liquid.

Figure 3

Evolution of the bridge profiles (including the reflection in the substrate and the profile prior to contact in light blue) for spreading drops of (a) water, (b) PEO with 1 wt %, and (c) PEO with 2 wt %, shown at different times [with $t/\lambda =0.0007\to 0.02$ for panel (b) and $t/\lambda =0.0003\to 0.01$ for panel (c)]. Viscoelastic profiles exhibit a much sharper bridge than water.

Figure 4

Bridge curvature $\kappa$ (normalized by the curvature $1/R$) plotted as a function of time $t$. (a) Time is normalized by the inertio-capillary time $\tau$. The suggested exponents are indicated as guide for eyes. (b) Same data (excluding water for which the relaxation time $\lambda$ is not defined), but time is normalized by the polymer relaxation time $\lambda$.

Figure 5

Direct evidence for the spreading-coalescence analogy for the temporal evolution of the bridge. The three panels directly compare the dynamics of the bridge radius $r_0\left(t\right)$ for coalescence (triangles, taken from [39]) and spreading (circles). The data for spreading and coalescence are indistinguishable for (a) water, (b) PEO with 1 wt %, and (c) PEO with 2 wt %.

Figure 6

Evolution of the bridge for coalescing drops of water, PEO with 1 wt %, and PEO with 2 wt %. Bridge profiles (rotated by ${90}^{\circ }$) are shown at different times matching those in Fig. 3, with $t/\lambda =0.0007\to 0.02$ for 1 wt % PEO and $t/\lambda =0.0003\to 0.01$ for 2 wt % PEO. Viscoelastic solutions exhibit a much sharper bridge than water.

Figure 7

Coalescence bridge curvature $\kappa$ (normalized by the drop radius $R$) plotted as a function of time $t$. (a) Time is normalized by the inertio-capillary time $\tau$. (b) Same data, but time is normalized by the polymer relaxation time $\lambda$.

Figure 8

(a–c) Bridge profiles of coalescing drops of water, PEO with 1 wt % and with 2 wt %, shown at different times, coinciding with Fig. 6. Profiles are rescaled accordingly to the Newtonian self-similar scaling, that is, by normalizing the horizontal and vertical bridge extent $r$ by $r/r_0-1$ and $x$ by $xR/r_0^2$. (d–f) Bridge profiles of spreading drops of water, PEO with 1 wt % and with 2 wt %, shown at different times, coinciding with Fig. 3, obtained by the same rescaling as in the top row.