# Gravitational effect in evaporating binary microdroplets

## TL;DR

This study investigates how gravity influences flow patterns in evaporating glycerol-water microdroplets, revealing that density gradients caused by differential evaporation drive convective flows, with experimental and numerical validation.

## Contribution

It demonstrates that gravitational effects, governed by the Archimedes number, significantly affect flow fields in small evaporating droplets, a novel insight for microfluidic applications.

## Key findings

- Gravity-driven flow depends on droplet height and Archimedes number.
- Opposite flow directions observed in sessile and pendant droplets.
- Numerical simulations agree with experimental flow patterns.

## Abstract

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.