  The flow in an evaporating glycerol-water binary sub-millimeter droplet with
Bond number Bo $\ll$ 1 is studied both experimentally and numerically. First,
we measure the flow fields near the substrate by micro-PIV for both sessile and
pendant droplets during the evaporation process, which surprisingly show
opposite radial flow directions -- inward and outward, respectively. This
observation clearly reveals that in spite of the small droplet size,
gravitational effects play a crucial role in controlling the flow fields in the
evaporating droplets. We theoretically analyze that this gravity-driven effect
is triggered by the lower volatility of glycerol which leads to a preferential
evaporation of water then the local concentration difference of the two
components leads to a density gradient that drives the convective flow. We show
that the Archimedes number Ar is the nondimensional control parameter for the
occurrence of the gravitational effects. We confirm our hypothesis by
experimentally comparing two evaporating microdroplet systems, namely a
glycerol-water droplet and a 1,2-propanediol-water droplet. We obtain different
Ar, larger or smaller than a unit by varying a series of droplet heights, which
corresponds to cases with or without gravitational effects, respectively.
Finally, we simulate the process numerically, finding good agreement with the
experimental results and again confirming our interpretation.
