Confined drying of a binary liquid mixture droplet: A quantitative interferometric study under humidity control

TL;DR

This study introduces a precise interferometric method to analyze the drying process of binary liquid droplets under controlled humidity, enabling detailed measurement of internal concentration and transport properties with high accuracy.

Contribution

The paper presents a novel combined interferometric and humidity-controlled approach for quantitatively studying drying dynamics and transport mechanisms in complex fluid droplets.

Findings

Accurate measurement of drying kinetics and concentration fields.

Extraction of concentration-dependent diffusion coefficient and water activity.

Validation of the methodology with experimental and theoretical agreement.

Abstract

We present a methodology that combines Mach-Zehnder interferometry, a custom relative humidity (RH) controlled chamber, and a confined two-dimensional droplet geometry to enable precise investigations of drying of complex fluids and the associated transport mechanisms. This approach is applied to a model binary mixture, water-glycerol, the concentration-dependent thermodynamic and transport properties of which are relatively well documented. High-resolution interferometric imaging (6 $\mu$m pixel$^{-1}$, 1 frame s$^{-1}$) allows simultaneous measurement of drying kinetics and internal concentration fields with $\pm 0.5\%$ accuracy, characterized here over a wide range of RH (25-95%), and thus P\'eclet numbers. The experimental results closely match a quasisteady, isothermal model of vapor-diffusion-controlled evaporation coupled to diffusion within the droplet. These data enable extraction of both the concentration-dependent mutual diffusion coefficient $D(\varphi)$ and the water chemical activity $a_w(\varphi)$ over almost the entire range of glycerol volume fraction $\varphi$, even from a single low-RH experiment. While $a_w(\varphi)$ agrees well with literature values, our measurements yield a consistent fit for $D(\varphi)$. Complementary experiments with fluorescence microscopy confirm that buoyancy-driven convection, although present, remains negligible, so that mass diffusion dominates solute transport in this confined geometry. The overall agreement validates the methodology, demonstrating its robustness as a quantitative framework for probing drying dynamics and transport in complex fluids, with broad applicability to controlled evaporation studies.