Effect of Polymer Additives on the Wetting of Impacting Droplets

When a droplet of water impacts a hydrophobic surface, the drop is often observed to bounce. However, for about 10 years it has been known that the addition of very small quantities ($\sim 100\mathrm{ppm}$) of a flexible polymer such as poly-(ethylene oxide) can completely prevent rebound. This effect has for some time been explained in terms of the stretching of polymer chains by a velocity gradient in the fluid, resulting in a transient increase in the so-called “extensional viscosity.” Here we show, by measuring the fluid velocity inside the impacting drop, that the extensional viscosity plays no role in the antirebound phenomenon. Using fluorescently labeled $\lambda$ DNA we demonstrate that the observed effect is due to the stretching of polymer molecules as the droplet edge sweeps the substrate, retarding the movement of the receding contact line.

Figure 1

Particle image velocimetry. Example data sets showing the fluid velocity as a function of time for (a) pure water [at radii (mm) 0.7 ▴, 1.3 ▵, 1.6 ▪, 2.8 □] (b) 200 ppm PEO (at radii 1.2 ▴, 2.0 ▵, 2.1 ▪, 2.7 □). The radius of the contact line at maximum spread for $\mathrm{water}=4.1$, $\mathrm{PEO}=3.9\mathrm{mm}$. Inset (a) shows a spreading droplet. The arrow indicates the view obtained by the microscope objective. Inset (b) shows a typical image obtained of fluorescent colloids in a spreading drop. Using particle image velocimetry the initial retraction velocity of the fluid as a function of radius can be estimated. Images are collected at 2000 fps but the laser produces $8000\mathrm{\text{pulses}}/\mathrm{s}$. This results in each particle being exposed 4 times. By measuring the distance traveled by each particle between pulses the velocity of the fluid can be estimated ($V_{\mathrm{Colloid}}\sim \Delta x{f}_{\mathrm{Laser}}$). The direction of fluid motion in the PIV inset is from left to right.

Figure 2

Initial retraction velocities in a droplet. Initial retraction velocities as a function of radial position inside pure water (▴) and 200 ppm PEO drops (▵) as compared with the drop edge for water (▪) and 200 ppm PEO drop (□). The retraction velocity for the drop edge in a PEO drop is an order of magnitude slower than in the bulk of the drop. Since the initial retraction velocities of the bulk fluid are similar for both water and PEO the extensional viscosities must also be similar. The antirebound effect cannot therefore be due to an increase in extensional viscosity, rather it appears to be the drop edge which slows retraction.

Figure 3

Slip distance of the droplet edge. Inset: The position of the drop edge (closed symbols) and corresponding contact angle (open symbols) for an impacting drop of water (○) and 200 ppm PEO (□), drop height 20 mm. Main Panel: Distance travelled by the contact line during the first oscillation of the retracting drop for different concentrations of PEO. For PEO drops it is observed that the majority of the fluid oscillates towards and away from the drop edge resisted by a force at the contact line. The inertia of the moving fluid causes the contact line to move with every oscillation, a distance which depends on polymer concentration. The distance moved during the first oscillation is indicated by the value $X_{\mathrm{slip}}$. A higher concentration of polymer results in a stronger resistance to movement at the contact line, providing additional evidence that the antirebound phenomenon is a contact line effect.

Figure 4

Stretching of DNA by retracting droplets. (Top) Close-up of receding drop edge showing “DNA fingers” protruding beyond the contact line. (Bottom) Fluorescent microscope image of DNA, which is left behind on the surface after the droplet has retracted. The molecules are aligned radially (see inset). The arrow indicates the direction of the retreating contact line. The scale bar in both images is $20\mu \mathrm{m}$ which is comparable to the length of a single stretched molecule. The image shows multiple DNA molecules lying end to end.