Buoyancy-induced on-the-spot mixing in droplets evaporating on nonwetting surfaces

We investigate hitherto-unexplored flow characteristics inside a sessile droplet evaporating on heated hydrophobic and superhydrophobic surfaces and propose the use of evaporation-induced flow as a means to promote efficient “on-the-spot” mixing in microliter-sized droplets. Evaporative cooling at the droplet interface establishes a temperature gradient that induces buoyancy-driven convection inside the droplet. An asymmetric single-roll flow pattern is observed on the superhydrophobic substrate, in stark contrast with the axisymmetric toroidal flow pattern that develops on the hydrophobic substrate. The difference in flow patterns is attributed to the larger height-to-diameter aspect ratio of the droplet (of the same volume) on the superhydrophobic substrate, which dictates a single asymmetric vortex as the stable buoyancy-induced convection mode. A scaling analysis relates the observed velocities inside the droplet to the Rayleigh number. On account of the difference in flow patterns, Rayleigh numbers, and the reduced solid-liquid contact area, the flow velocity is an order of magnitude higher in droplets evaporating on a superhydrophobic substrate as compared to hydrophobic substrates. Flow velocities in all cases are shown to increase with substrate temperature and droplet size: The characteristic time required for mixing of a dye in an evaporating sessile droplet is reduced by ∼8 times on a superhydrophobic surface when the substrate temperature is increased from 40 to 60 °C. The mixing rate is ∼15 times faster on the superhydrophobic substrate compared to the hydrophobic surface maintained at the same temperature of 60 °C.

Figure 1

Experimental setup for flow visualization.

Figure 2

Flow field inside a droplet evaporating on a hydrophobic surface maintained at 50 °C at an instantaneous volume of $2\mu \mathrm{l}$. Streaklines are visualized by superimposing multiple sequential (a) side-view images and (b) top-view images. Velocity vector maps of the (c) central vertical plane and (d) horizontal plane are shown.

Figure 3

Variation of flow velocity on the hydrophobic substrate with changing volume of the evaporating droplet along its vertical axis of symmetry, corresponding to substrate temperatures of (a) 40 °C, (b) 50 °C, and (c) 60 °C.

Figure 4

(a) Velocity magnitude along the vertical axis of symmetry of the droplet at a volume of $2\mu \mathrm{l}$ on the hydrophobic surface. (b) Variation of the maximum velocity inside the droplet at different substrate temperatures and volume, with respect to Rayleigh number.

Figure 5

(a) Schematic sketch of the flow pattern observed inside a droplet evaporating on a superhydrophobic substrate maintained at 50 °C. The inset shows an SEM image of the superhydrophobic surface used in the experiments. Streaklines are visualized by superposing multiple sequential (b) side-view images and (c) top-view images. Velocity vector maps of the central (d) vertical plane and (e) horizontal plane.

Figure 6

Velocity vectors in the central vertical plane of the droplet corresponding to superhydrophobic substrate temperatures of (a) 40 °C, (b) 50 °C, and (c) 60 °C.

Figure 7

Time series images demonstrating dye mixing in an evaporating droplet on a superhydrophobic substrate maintained at (a) 40 °C, (b) 50 °C, (c) 60 °C, and on (d) hydrophobic substrate maintained at 60 °C.

Figure 8

Velocity vectors in a droplet of volume $2\mu \mathrm{l}$ evaporating on a hydrophobic surface (a) before and (b) after velocity correction and on a superhydrophobic surface (c) before and (d) after velocity correction; the substrates are maintained at 50 °C.

Figure 9

Peclet number at different instantaneous droplet volumes corresponding to different surface temperatures for a hydrophobic substrate.