On the role of water activity on the formation of a protein-rich coffee ring in an evaporating multicomponent drop

Abstract

The coffee-ring effect is a universal feature of evaporating sessile droplets with pinned contact line, wherein solutes or particles are advected to the droplet's edge due to evaporation-driven flows. While existing models have successfully described this phenomenon in particle-laden droplets, they often assume that the evaporative flux, and thus hydrodynamics, are decoupled from solute transport. This assumption breaks down in complex fluids, such as protein or polymeric solutions, where the solute can influence evaporation through changes in water activity. Here, we investigate model respiratory droplets primarily composed of water, salt, and a type of the glycoprotein mucin. Using fluorescence microscopy, we observe the formation of a well-defined protein ring at the droplet edge as water evaporates. The growth and morphology of this ring exhibit a strong dependence on ambient relative humidity ($H_r$), revealing dynamics that existing models cannot capture. Specifically, we find that protein accumulation at the edge is governed by the feedback between local solute concentration and evaporation rate. To account for this, we develop a minimal theoretical model based on the lubrication approximation, incorporating the coupling between hydrodynamics and solute transport through the evaporation rate. Our framework reproduces key features of the experimental observations and suggests a physical basis for the $H_r$-dependent stability and infectivity of respiratory droplets containing viruses.

Figures (16)

• Figure 1: Schematic of the procedure used to obtain the radial intensity profile. a) Time-lapse images of the evaporating droplet are acquired using an epifluorescence microscope inside a humidity-controlled chamber. b) Example of a fluorescence image obtained during evaporation. c) The droplet is segmented into concentric annular regions, and the mean fluorescence intensity is computed for each region. For visualization purposes, fewer regions are shown than were used in the actual analysis. d) From this process, the radial intensity profile is extracted for each image.
• Figure 2: Calibration of fluorescence intensity as a function of droplet height and protein mass fraction. (a) Fluorescence intensity profiles at different relative heights $h^*$ for varying protein mass fraction $C_p = 0.003, 0.025, 0.1$, confirming the linear relationship between intensity and height. (b) Slopes of the fitted lines, $m$, from (a) demonstrating the linear dependence of fluorescence intensity on protein mass fraction. (c) Representative time evolution of the total fluorescence intensity, showing distinct regimes during evaporation. All quantitative analyses presented throughout this article are based on data from the constant-intensity regime.
• Figure 3: Fluorescence images showing a) the initial homogeneous distribution of protein, b) the formation of a peripheral protein ring, and c) final crystallization. Droplet evaporated at $H_r=30.4\%$ and $T=20.5^\circ$C.
• Figure 4: Experimental results. (a) Temporal evolution of the ring width, $\delta$. (b) Mass of protein, $m_p$, in the ring normalized by the total protein mass in the droplet, $M_p$, as a function of time. (c) Dependence of the maximum height-integrated protein fraction, normalized by the total protein mass in the droplet divided by the contact area $A_c$, with the relative humidity.
• Figure 5: Material and thermodynamical properties used in the model. (a) Water activity as a function of protein mass fraction for different salt mass fractions $w_s = 0, 0.09, 0.18, 0.26, 0.35$. Increasing salt concentration shifts the water activity curves downward. (b) Evolution of protein diffusivity as a function of protein concentration, display on a logarithmic scale.