Controlling the dewetting morphologies of thin liquid films by switchable substrates

Switchable and adaptive substrates emerged as valuable tools for controlling wetting and actuation of droplet motion. Here, we report a computational study of the dynamics of an unstable thin liquid film deposited on a switchable substrate, modeled with a space- and time-varying contact angle. For a sufficiently large rate of wettability variation, a topological transition appears. Instead of breaking up into droplets, as expected for a substrate with multiple wetting minima, a metastable rivulet state emerges. A criterion discriminating whether or not rivulets occur is identified in terms of a single dimensionless parameter. Finally, we show and derive theoretically how the film rupture times, droplet shape, and rivulet lifetime depend on the pattern wavelength and speed.

Figure 1

Stationary film thickness field ($t>t_0$) showing the formation of droplets. The color map indicates the contact angle pattern (Eq. (3) with $v_{\theta }=0$), with lower (higher) values in light blue (yellow).

Figure 2

Rupture times ${\tau }_r$ as a function of the pattern wavelength $\lambda$, for $v_{\theta }=0$ ($•$) and $v_{\theta }=20v_0$ ($\star$). The continuous and dashed lines indicate the linear, $\sim \lambda$, and quadratic, $\sim {\lambda }^2$, scaling laws, respectively.

Figure 3

Main panel: Time evolution of the height fluctuations $\mathrm{\Delta }h\left(t\right)$ during the dewetting process on the patterned substrate given by Eq. (3) with $v_{\theta }=0$ and $\lambda =512h_0$ ($•$), $\lambda =256h_0$ ($\blacksquare$), and $\lambda =170h_0$ ($\star$). Inset: Number of droplets $N\left(t\right)$ as a function of time. The three horizontal dashed lines indicate the number of minima of Eq. (3), which is $2{\left(\frac{L}{\lambda }\right)}^2$. The snapshots depict the stationary droplet states as grayscale images of the film thickness field $h(\mathbf{x},t)$.

Figure 4

Time evolution of the second-order Minkowski structure metric $q_2\left(t\right)$ for different $\mathrm{\Gamma }$ values, on a substrate with pattern wavelength $\lambda =256h_0$. The grayscale insets supply snapshots of the corresponding film thickness fields.

Figure 5

Main panel: Rivulet lifetimes ${\tau }_{\text{riv}}$ for various $\mathrm{\Gamma }$. The dashed line is a guide to the eye to highlight the logarithmic dependence, in agreement with the theoretical prediction, Eq. (6). Inset: Height fluctuations $\mathrm{\Delta }h\left(t\right)$ vs time, along the rivulet axis, for three different $\mathrm{\Gamma }$.