Controlling droplet deposition with surfactants

Droplets impacting on a surface are key to a wide range of applications such as spray deposition and inkjet printing. Yet, a full understanding of how they spread and retract is still lacking. Surfactants are often added to improve spreading and coverage of aqueous solutions, resulting in variations of the surface tension at timescales beyond the reach of conventional dynamic surface tension measurement methods. Here we study the impact dynamics of aqueous surfactant solutions on hydrophobic surfaces at millisecond timescales. We find that the spreading and retraction of droplets cannot be adequately described by the equilibrium surface tension. We infer the dynamic surface tension in the first milliseconds after impact from the spreading dynamics of droplets. “Slow” surfactants that take a lot of time to reach newly created droplet surface, only slightly decrease or even increase the surface tension, while “fast” surfactants, on the other hand, allow efficient wetting of aqueous solutions on hydrophobic surfaces. Our findings allow us to tailor surfactants for efficient drop deposition or spray application.

Figure 1

Droplet rebound and coverage on plant leaves. (a) Snapshots of a water droplet bouncing off a hydrophobic cabbage leaf. (b) Relative improvement of the liquid coverage of broccoli leaves as a function of surfactant concentration. Coverage is determined from an added fluorescent, which lights up, thus indicating where the leaves are covered. The deposition improves with higher concentrations of surfactant. Even though the equilibrium surface tension of the “slow” surfactant (22 mN/m, red squares) is lower, the “fast” surfactant (32 mN/m, green diamonds) gives a better coverage.

Figure 2

(a) Image sequence of a water droplet impact showing the spreading (first row), retraction (second row), and relaxation (third row) of the droplet. Time stamps are in ms. (b) Normalized droplet diameter $D/D_0$ as determined using the maximum diameter (red squares) and the contact line diameter (blue circles) as a function of spreading time. The impact velocity of the droplet is 1.4 m/s.

Figure 3

Surface tension as determined from bubble pressure tensiometer measurements as a function of surface age (time that has passed since the creation of the surface) for 10 CMC concentrations of the fast (green diamonds) and slow (red squares) surfactants and water (blue circles, constant at 72 mN/m). The dashed lines are the best fits of Eq. (3) to the experimental data. These fits are used to extrapolate the dynamic surface tension of the liquids to the typical time of spreading of a droplet, which is 3 ms (gray dotted line). Fit parameters ${\sigma }_0\left(\text{mN/m}\right)$, ${\sigma }_{\infty }\left(\text{mN/m}\right)$, $\tau \left(\text{s}\right)$, $n$ are ${\sigma }_0=72$, ${\sigma }_{\infty }=19.4$, $\tau =62.1$, $n=7.51\times {10}^{-1}$ (slow), ${\sigma }_0=72$, ${\sigma }_{\infty }=18.3$, $\tau =9.83\times {10}^{-8}$, $n=5.13\times {10}^{-2}$ (fast).

Figure 4

Droplet spreading and retraction. (a) Snapshots of typical droplet spreading for water (in blue), slow surfactant solution (0.1 CMC; in red) and fast surfactant (0.1 CMC; in green) impacting at a speed of 1.9 m/s. Time stamps are in ms. Maximum spreading is reached at 3 ms, equilibrium around 21 ms. Conventional surface tension measurement techniques do not reach these timescales. (b) Normalized droplet diameter $D/D_0$ as a function of time for the same droplets as shown in panel (a). (c) Retraction rate $\dot{\epsilon }$ normalized by the retraction rate of water (${\dot{\epsilon }}_{\text{water}}=50{\text{s}}^{-1}$ at an impact speed of 1.9 m/s), as a function of surfactant concentration.

Figure 5

Effective dynamic surface tension at maximum spreading. Dynamic surface tension $\sigma$ calculated using the two methods described in the main text as a function of fast (green diamonds) and slow (red squares) surfactant concentration for (a) medium impact velocity $v=1.6\mathrm{m}/\mathrm{s}$. The dotted lines are extrapolations based on BPT measurements (see Supplemental Material [18]) and Eq. (3). (d) Dynamic surface tension at maximum spreading as a function of surfactant concentration for other surfactants (AOT, CTAB, glucamide, and polysorbate 20) as calculated using the two methods described in the text. Impact velocity $v=1.6\mathrm{m}/\mathrm{s}$. The dotted lines are extrapolations based on BPT measurements and Eq. (3).

Figure 6

Dynamic surface tension at maximum spreading as a function of droplet impact velocities for a solution of fast surfactant with a concentration of 1 CMC. The dotted line is the extrapolation of BPT measurements using Eq. (3).

Figure 7

(a) Retraction rate $\dot{\epsilon }$ of droplets for $1.7<v<2.1$ m/s plotted against surface tension calculated from $D_{\max }/D_0$. The dotted line is the prediction by Eq. (4). (b) Dimensionless retraction rate versus $1/\text{Oh}$. The dotted line is the best fit to the data $\propto 1/\text{Oh}$.