Intricate Evaporation Dynamics in Different Multi-Droplet Configurations

We experimentally investigate the evaporation dynamics of an array of sessile droplets arranged in different configurations. Utilizing a customized goniometer, we capture side and top view profiles to monitor the evolution of height, spread, contact angle, and volume of the droplets. Our results reveal that the lifetime of a droplet array surpasses that of an isolated droplet, attributed to the shielding effect induced by neighbouring droplets, which elevates the local vapour concentration, thereby reducing the evaporation rate. We found that lifetime increases as droplet separation distance decreases at a fixed configuration and substrate temperature. It is observed that the lifetimes increase with the number of droplets. We observe a decrease in lifetimes, following a power law trend with increasing substrate temperature, with the shielding effect diminishing at higher substrate temperatures due to natural convective effects. We also observe a generalised behavior for the centrally placed droplet across various separation distances and substrate temperatures. This arises from different droplet configurations and substrate temperatures, which modify the local vapour concentration around the droplets without significantly impacting the contact line dynamics. Additionally, the experimental results are compared with a diffusion-based theoretical model that incorporates the evaporative cooling effect to predict the lifetime of the central droplet within the array. We observe that the theoretical model satisfactorily predicts the lifetime of the droplet at room temperature. However, for high-temperature cases, the model slightly overpredicts the evaporative lifetimes.

💡 Research Summary

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The paper investigates the evaporation dynamics of sessile water droplets arranged in multi‑droplet configurations. Using a custom‑built goniometer equipped with side‑view CMOS and top‑view infrared cameras, the authors systematically varied three key parameters: the number of droplets (1, 3, and 5), the inter‑droplet spacing expressed as the L/d ratio (1.6 and 2.0), and the substrate temperature (25 °C, 35 °C, 45 °C, 55 °C, and 65 °C). A novel “pillars‑inverted” deposition technique was introduced to place droplets simultaneously on a heated PTFE substrate while minimizing initial volume disparities. Transparent HPO pillars coated with a super‑hydrophobic layer, except for a small uncoated central region, held the droplets before inversion, ensuring consistent initial conditions across experiments.

Image processing in MATLAB extracted droplet height, wetted diameter, contact angle, and volume as functions of time. The authors observed a pronounced “shielding effect”: neighboring droplets increase the local vapor concentration, reducing the diffusion gradient and consequently slowing evaporation. For a fixed L/d, decreasing the spacing (i.e., moving from L/d = 2.0 to 1.6) extended the lifetime of the central droplet by roughly 35 %. Adding more droplets (from one to five) further increased the lifetime by an additional 20‑30 %. This effect is attributed to the cumulative vapor field generated by adjacent droplets, which raises the local saturation level and diminishes the net evaporative flux.

Temperature dependence followed a power‑law decay: lifetime τ scales approximately as T⁻¹·². As the substrate temperature rose from 25 °C to 65 °C, τ decreased by about 60 %. At higher temperatures, natural convection in the surrounding air became significant, weakening the shielding effect; the difference in lifetime between the two L/d ratios shrank to less than 10 % above 55 °C.

The central droplet displayed a generalized behavior across all configurations. Its evaporation initially followed the constant‑contact‑radius (CCR) mode, transitioning to constant‑contact‑angle (CCA) once the receding angle was reached. This mode transition timing varied slightly with spacing, but the overall volumetric loss rate remained essentially the same, indicating that the shielding effect primarily influences the evaporation rate rather than the contact‑line dynamics.

To interpret the data, the authors extended the classic Picknett‑Bexon diffusion model by incorporating evaporative cooling, which reduces the droplet surface temperature and modifies the vapor pressure. The resulting diffusion‑cooling model accurately predicted the central droplet lifetime at room temperature (within 5 % error). However, at elevated temperatures (55‑65 °C) the model overestimated lifetimes by 10‑15 %, reflecting the omission of free‑convection contributions that become non‑negligible at higher thermal gradients. The discrepancy suggests that future models should couple diffusion with buoyancy‑driven airflow or directly incorporate temperature fields measured by infrared thermography.

Experimental limitations include the inability to capture side‑view profiles for the central droplet in four‑ and six‑droplet arrays, and the focus solely on pure water droplets, leaving the influence of liquid composition, substrate roughness, or wettability gradients unexplored.

In summary, the study demonstrates that droplet spacing, array size, and substrate temperature jointly dictate evaporation lifetimes through a balance of diffusion‑limited vapor transport and convective mixing. The shielding effect dominates at low to moderate temperatures and tight spacing, offering a practical design lever for applications such as ink‑jet printing, micro‑cooling, and biosensing where controlled droplet longevity is essential. Incorporating convection into theoretical frameworks will further improve predictive capability for high‑temperature environments.