Density-Driven Flows in Evaporating Binary Liquid Droplets

In the evaporation of microlitre liquid droplets, the accepted view is that surface tension dominates and the effect of gravity is negligible. We report, through the first use of rotating optical coherence tomography, that a change in the flow pattern and speed occurs when evaporating binary liquid droplets are tilted, conclusively showing that gravitational effects dominate the flow. We use gas chromatography to show that these flows are solutal in nature, and we establish a flow phase diagram demonstrating the conditions under which different flow mechanisms occur.

Figure 1

Time-averaged OCT cross-section images of sessile and pendant $2\mu \mathrm{L}$ droplets over 30 seconds of stage II evaporation: (a,b) ethanol-water; (c,d) water-$n$-butanol (see Video 1 in Supplemental Material [28]). Plus and minus signs indicate the expected difference in surface tension ($\gamma$) or density ($\rho$) with respect to the bulk. White arrows indicate observed flow direction. Colored arrows indicate expected flow direction from solutal Marangoni-Rayleigh driven effects. The scale bar shows distance in air.

Figure 2

OCT cross-section images, time averaged over 7 seconds, of $1\mu \mathrm{L}$ 2% ethanol-water droplets at various substrate tilt angles (see Video 2 in Supplemental Material [28]). Maximum vertical velocity, $U_{\max }$ ($\mu \mathrm{m}/\mathrm{s}$), at $t^{*}=0.05$ is given in each image. The clockwise (anticlockwise) flow rotation is indicated by brown (blue) shading.

Figure 3

(a) GC-determined ethanol concentration $c(t^{*})$ and maximum vertical velocity ($U_{\max }$) vs $t^{*}$ for $c_0=10\%$. The solid line is an exponential fit to the data. (b) Variation of total droplet volume ($V_T$) and $U_{\max }$ with $t^{*}$ for $c_0=20\%$. The inset shows an exponential decrease of ethanol volume with $t^{*}$. (c) Phase diagram showing the three stages characterized by ethanol flux $(J_E)$ and contact angle $\theta (t^{*})$ at $t^{*}$.