Gravitational Effect on the Formation of Surface Nanodroplets

Nanoscale droplets at a solid-liquid interface are of high relevance for many fundamental phenomena and applied processes. The solvent exchange process is a simple approach to produce, e.g., oil nanodroplets over a large surface area on a substrate, by exchange oil-saturated ethanol by oil-saturated water, which has a lower oil solubility than ethanol. In this process, the size of the nanodroplets is closely related to the flow conditions. To achieve control of the droplet size, it is essential to fully understand the nucleation and growth of nanodroplets under different flow conditions. In this work, we investigate the gravitational effect on the droplet formation by the solvent exchange. We compared the droplet size as the substrate was placed on the upper or lower wall in a horizontal fluid channel or on the sides of a vertical channel with an upward or downward flow. We found significant difference in the droplet size for the three substrate positions in a wide channel with height h = 0.21 mm. The difference of droplet size was eliminated in a narrow channel with height h = 0.07 mm. The relevant dimensional control parameter for the occurrence of the gravitational effects is the Archimedes number Ar and these two heights correspond to Ar = 10 and Ar = 0.35, respectively. The gravitational effects lead to a nonsymmetric parabolic profile of the mixing front, with the velocity maximum being off-center and thus with different distances α(Ar)h and (1 - α(Ar))h to the lower and upper wall, respectively. The ratio of the total droplet volume on the lower and upper wall is theoretically found to be (α(Ar)/(1 - α(Ar)))(3). This study thus improves our understanding of the mechanism of the solvent exchange process, providing guidelines for tailoring the volume of surface nanodroplets.