Open Access Article
Elham
Mirzahossein
a,
Marion
Grzelka
b and
Daniel
Bonn
*a
aVan der Waals–Zeeman Institute, Institute of Physics, University of Amsterdam, 1098XH Amsterdam, The Netherlands. E-mail: d.bonn@uva.nl
bLaboratoire Léon Brillouin, Université Paris-Saclay, CEA, CNRS, 91191 Gif-sur-Yvette, France
First published on 22nd September 2025
The drying of polymer solution droplets produces a fascinating array of morphologies, driven by the formation of a gel-like 'skin' at the vapor/liquid interface. While this skin plays a crucial role in shaping the final droplet form, its precise influence has remained elusive. We present a study that combines innovative fluorescence techniques with classical fluid dynamics to provide insights into the effect of skin formation on the macroscopic final structure of the droplet. Using viscosity-sensitive molecular rotors, we achieve unprecedented real-time, spatially-resolved measurements of local viscosity during the drying process. This novel approach allows us to directly observe and quantify skin formation and growth with micrometer-scale precision. Our experiments reveal that the average thickness and spatial non-uniformity of the skin are the key determinants of the final droplet shape. Droplets were investigated under identical ambient conditions and pinned contact lines, varying only the initial contact angle. This approach yields three distinct morphologies: coffee-rings, ‘Mexican hats’, and snap-through buckled shapes. For initial contact angle around 30°, skin formation initiates at the contact line rather than the apex, explaining the classic coffee-ring effect. For initial contact angle around 55°, a thicker skin forms near the contact line compared to the apex, resulting in a weaker central region. As evaporation proceeds, this non-uniform skin deforms into the characteristic Mexican hat shape. In contrast, surfaces with initial contact angle around 110° produce a thin, uniform skin that undergoes a dramatic snap-through buckling instability. Crucially, we demonstrate that the timing of morphological changes is directly linked to abrupt variations in skin thickness. Our results not only provide a comprehensive understanding of these complex phenomena but also align with and extend recent theoretical predictions by Head. This work bridges the gap between microscopic skin dynamics and macroscopic droplet behavior, offering a new paradigm for controlling deposition patterns in applications ranging from inkjet printing to biomedical assays.
Despite extensive research, fundamental questions persist regarding the onset of skin formation, its temporal evolution, and its impact on drying kinetics.13–16 The dynamics of skin formation in sessile droplets are particularly complex due to the presence of a contact line. While rapid evaporation in spherical droplets tends to produce a uniform skin, the fixed contact line in sessile droplets generates a strong radial flow towards the edge, resulting in the well-known ‘coffee stain effect’.17 However, the coffee stain is not the only possible deposition pattern. The initial contact angle of a droplet significantly influences the global evaporation rate and the spatial distribution of deposited solute, leading to a wide range of morphologies in polymer-containing sessile droplets, even under identical solute concentrations and ambient conditions.2,18–22 Mexican hat shapes and snap-through buckling instabilities are among the most frequently observed morphologies. While several experimental studies have investigated this phenomenon, numerical simulations of this complex 3D evaporation problem remain scarce. To our knowledge, Head is the only one to have explored the deformation of elastic shells with identical initial contact angles, demonstrating the crucial role of skin thickness distribution in determining final droplet morphologies.23 However, these simulations neglected the viscoelastic nature of the droplet and the dynamics of shell formation.
The lack of micrometer-scale rheological measurements throughout the drying process has hindered our understanding of how skin formation directly affects final droplet morphology. In particular, there is a scarcity of experimental data detailing the spatial and temporal initiation of skin formation and its thickness distribution around the droplet. In this study, we address these knowledge gaps by employing fluorescent molecular rotors to monitor local viscosity during the drying process of aqueous dextran solution droplets. These molecular rotors are fluorescent molecules whose intensity and lifetime are highly sensitive to their immediate environment, with both parameters increasing as local viscosity rises.24,25 By leveraging this property, we provide unprecedented insights into the drying process of sessile polymer solution droplets at both macroscopic and microscopic scales. Our approach allows us to capture skin thickness variations across the droplet over time, revealing heterogeneities in skin thickness and viscosity. Moreover, we observe two distinct mechanical instabilities for droplets on and surfaces with initial contact angle 55° and 110°, characterized by abrupt changes in skin thickness around the time of deformation. This comprehensive analysis bridges the gap between microscopic skin dynamics and macroscopic droplet behavior, offering a new paradigm for understanding and controlling deposition patterns in a wide range of applications.
All measurements were conducted using #1.5H coverslips (Deckgäser) with a thickness of 170 ± 5 μm. To prepare surfaces with an initial contact angle of approximately 30 ± 5°, the coverslips were washed with 99% ethanol, thoroughly rinsed with ultrapure water, dried with nitrogen, and then treated in a plasma cleaner for 30 seconds. For surfaces with an initial contact angle of about 55 ± 5°, the coverslips were simply rinsed with water and dried with nitrogen. Surfaces exhibiting an initial contact angle of around 110° were created by soaking the coverslips in a 1% (v/v) toluene/trichlorooctylsilane mixture for 15 minutes, followed by rinsing with isopropanol and drying under nitrogen. The glass coverslips were used immediately after preparation.
To examine the macroscopic deformation of the droplet, side-view images of droplets are captured as a function of time using a CCD camera (Stingray).
To measure fluorescence and rheological properties simultaneously, a rheometer head (Anton Paar DSR 502) is mounted on a Zeiss Axiovert 200 M confocal microscope (see Fig. S1). The rheometer is operated in oscillation mode at a small strain of 0.2% and a frequency ω = 10 rad s−1 using a 25 mm parallel plate geometry with a gap of 1 mm. The initial polymer solution, identical to that used in the drying droplet experiments, is placed under the rheometer geometry. Both rheological and fluorescence properties are recorded simultaneously during evaporation and gelation at a relative humidity of 50% (see SI for details). The fluorescence lifetime imaging microscopy (FLIM) was conducted using the time-correlated single photon counting (TCSPC) method on a Leica TCS SP8 inverted confocal microscope equipped with a 20× dry objective (NA = 0.75). The nominal z-resolution, based on the selected wavelength, pinhole size, and objective, is estimated to be 2 μm. The 4-DASPI dye was excited at a repetition rate of 40 MHz using the instrument's pulsed 470 nm laser, and emission was collected between 500 and 700 nm. 4-DASPI inside the dextran polymer solution exhibits a multi-exponential decay. Therefore, all fluorescence lifetime measurements of 4-DASPI are amplitude-averaged lifetimes (see SI for details).
Depending on the surface used for drying experiments, different time-lapse and z-stack imaging protocols were employed. We previously demonstrated that 4-DASPI adsorbs onto hydrophobic surfaces (corresponding to an initial contact angle θini ∼ 110°), resulting in an increased fluorescence lifetime within the first 10 μm from the surface.27 However, the lifetime reaches a plateau when measured deeper into the liquid. Therefore, z-stack measurements were performed for 20 < z < 180 μm on surfaces with θini ∼ 55° and for 20 < z < 300 μm on surfaces with θini ∼ 110°. For surfaces with θini ∼ 30°, z-stack measurements closer to the surface were feasible, as the dye shows negligible sensitivity to these more hydrophilic surfaces. Therefore, z-stack measurements were performed for 5 < z < 60 μm.
The results presented in Fig. 2a enable us to link rheological properties to fluorescence intensity. By using the relationship between fluorescence intensity and a lifetime of 4-DASPI in dextran polymer solutions obtained using FLIM setup (shown in the inset of Fig. 2b), we can also correlate the storage and loss moduli with the fluorescence lifetime (〈τ〉) shown in Fig. 2b. A detailed explanation of the direct correlation between fluorescence intensity and lifetime can be found in SI (see Fig. S3).
During the process of drying, as the solvent within the dextran solution begins to evaporate, both the storage (G′) and the loss (G′′) moduli increase up to a point where G′ ≈ G′′. This point is commonly taken as the sol–gel transition point. Beyond this point, both parameters consistently rise together over time. The confocal measurements show that the increase in normalized fluorescence intensity,
matches the increase of both G′ and G′′. After approximately 30
000 s, G′ exceeds G′′, after which elasticity dominates in the system. At this point, the formation of the elastic skin begins and the system switches to a predominantly elastic regime which corresponds to an average fluorescence lifetime 〈τ〉 = 1.3 ± 0.1 ns. This point is defined as the threshold at which skin formation begins in our system. Moreover, as usually done for viscoelastic materials,29,30 we can correlate the fluorescence lifetime with the complex viscosity
(see Fig. S3 and S4).
For a droplet on a surface with an initial contact angle θini ∼ 30° (Fig. 3a), the fluorescence lifetime increases rapidly within the initial few layers. Therefore, the droplet rapidly gelates at lower z positions (z = 5, 15, 25 μm) near the contact line, while the upper layers do not gelate. Instead, these upper layers recede in the z direction due to ongoing evaporation until all the liquid evaporates. Note that the droplet reaches its maximum height between z = 25 μm and 45 μm, making it impossible to measure the fluorescence lifetime in higher layers (z = 45 μm and z = 60 μm) after 800 seconds. Ultimately, only the coffee stain undergoes complete gelation and no shell forms around the droplet. The white dashed line in Fig. 3 right-hand side represents the elastic-dominant regime (skin formation) defined through rheological measurements, which corresponds to a fluorescence lifetime of 1.3 ns.
For droplets on surfaces with an initial contact angle θini ∼ 55° (Fig. 3b), at the first layer (z = 20 μm), 〈τ〉 experiences a rapid increase, reaching a saturation point at around 2.0 ± 0.1 ns. Near the top of the droplet, at z = 180 μm, the increase occurs more gradually: Initially, at t = 84 s after drop-casting, G′ remains relatively constant over the z-positions, with G′ roughly between 10 and 70 Pa. However, with time, a significant elasticity gradient emerges across different z-positions due to the substantial accumulation of polymers closer to the contact line. This gradient intensifies until a point, where the lowest layer gelates and forms a skin, followed by successive gelation of the other layers from bottom to top as time goes on. Around t ∼ 670 s, all layers become interconnected due to the formation of a continuous skin around the droplet. However, the bulk of the droplet remains fully liquid over this timeframe (see Fig. S7 for t < 700 s).
In contrast, the dynamics are completely different for the droplets drying on surfaces with an initial contact angle θini ∼ 110° (Fig. 3c). Across all z-positions near the vapor/liquid interface, 〈τ〉 exhibits a remarkably smaller variance compared to droplets on surfaces with θini ∼ 30° and 55°. Consequently, all layers form a skin within a relatively narrow time-frame.
For a droplet on a surface with θini ∼ 30° (Fig. 4a) the skin thickness Hs(z) smoothly increases in the initial few layers, while no skin forms at the upper layers (z = 45 and 60 μm) as explained above, (see Fig. 3a). For dextran droplets on a surface with θini ∼ 55°, the skin thickness Hs(z) at various z-positions within the droplet gradually increases over time. Notably, there is a substantial difference in skin thickness between the layer near the contact line (z1 = 20 μm), and the layer close to the apex of the droplet (z2 = 180 μm). At a certain point, there is an abrupt change in skin thickness Hs(z1 = 20 μm) and the radius of the cross-section of the droplet which can be seen in Fig. 4b (dark red data points) and Fig. S9, respectively. These changes likely correspond to the abrupt increase of the droplet height, giving birth to a final Mexican hat shape. The time at which this sharp transition occurs is called the deformation time, τD. At this point, the droplet undergoes a mechanical instability. This is ascribed to the deformation of the droplet, transitioning from a spherical cap shape to the distinctive “Mexican hat” shape, as shown in Fig. 1b. The drying process continues until full solvent evaporation, eventually resulting in further instabilities like wrinkling and, ultimately, the formation of a cavity within the droplet (see Fig. S6). As shown in Fig. 4c, the trend is significantly different for dextran droplets on surfaces with θini ∼ 110°. The skin thickness at different z-positions displays a growth pattern up to the point where the apex inverts, the phenomena known as snap-through instabilities. Following this inversion, the top layer experiences a relatively sharp increase in skin thickness, referred to as the deformation time τD, (Fig. 4c dark blue data points). After the inversion of the apex, the droplet has inner skin and outer skin. Therefore the total skin is plotted in Fig. 4c, which is the sum of the inner and outer skin. The growth patterns of the inner and outer skin are individually illustrated in Fig. S10. As the solvent continues to evaporate, a cavity also forms within the droplet (see Fig. S6).
where z1 corresponds to the point closer to the contact line and z2 corresponds to the point closer to the apex23 (Fig. 4b and c). When ρ = 0, the droplet exhibits uniform shell thickness, whereas for large ρ, the shell becomes thinner closer to the apex relative to the contact line. ρ = 1 indicates that Hs(z2) = 0, meaning no skin forms at higher z positions. For droplets on a surface with θini ∼ 30°, no skin forms at higher z positions, resulting in ρ = 1. Consequently, the droplet does not buckle and exhibits the well-known coffee stain effect. For polymer droplets on surfaces with initial contact angle around 55°, the calculated ρ value just before deformation time (τD) is approximately 0.91, with an average skin thickness 〈Hs〉 = 265 μm. This indicates a thick shell, thinner near the apex and thicker toward the contact line. Numerical simulations23 suggest that increasing ρ reduces the buckling pressure of the droplet. For ρ > 0.7, the shell is substantially “weaker” compared to an ideal thin elastic shell. Consequently, the shell deforms more significantly near the apex than at the contact line as pressure changes, leading to the formation of a Mexican hat shape. In contrast, polymer droplets on surfaces with θini ∼ 110° exhibit a ρ value close to zero (between −0.4 and 0.1 due to thickness measurement uncertainties) just before τD, with an average skin thickness 〈Hs〉 = 30 μm. This indicates a thin shell with uniform skin distribution. Numerical simulations23 predict that for a thin elastic shell with relatively uniform skin thickness (ρ close to zero), capillary pressure increases with further solvent evaporation until reaching a critical pressure. At this point, to minimize the total free energy, the shell discontinuously inverts its spherical surface at the apex, as observed for an ideal elastic shell.31,32 This results in snap-through buckling.
Supplementary information (SI): Description of the setup to simultaneously measure fluorescence and rheological properties, macroscopic droplet shape analysis, link between fluorescence lifetime and intensity, relation of complex viscosity with fluorescence properties, 3D reconstruction of drying droplets derived from confocal microscopy, fluorescence lifetime gradients within a droplet, evaluation of skin thickness, microscopic droplet shape analysis, inner and outer skin of snap-through buckling. See DOI: https://doi.org/10.1039/d5sm00279f.
| This journal is © The Royal Society of Chemistry 2025 |