The droplet perched on a surface is more than a pretty drop of water in a science fair. Its edge, the contact line where liquid meets solid and air, encodes a negotiation between molecules: a quiet vote about how much a surface wants to be kissed or ignored by a liquid. In industry, that tiny decision matters for condensing steam, coating delicate membranes, or harvesting water from a humid night sky. The static contact angle—the angle a droplet makes with the surface at equilibrium—summarizes all those interactions in a single, stubborn number. If we could predict that number quickly and accurately for real-world mixtures of liquids, we’d have a powerful lever for designing surfaces and processes. A team at the University of Stuttgart has taken a big step toward that goal by marrying a microscopic theory with real-world measurements—and it works surprisingly well for a broad class of liquids and mixtures, with a caveat that invites future refinement.
Led by Benjamin Bursik and Joachim Gross at the University of Stuttgart, with coauthors Nikolaos Karadimitriou and Holger Steeb, the study tests a classical density functional theory (DFT) model to predict static contact angles of both pure substances and mixtures on a solid PTFE (Teflon) surface. The core idea is to pull a macroscopic property—the contact angle—out of a microscopic description of how fluid molecules talk to each other and to a solid. The researchers lean on a Helmholtz energy functional grounded in PC-SAFT, a statistical-mechanical model that treats molecules as chains of tangentially bonded spheres. The solid surface is represented not by a real atomic map of PTFE but by an effective, one-dimensional external potential characterized by a single adjustable energy parameter. The ambition is audacious: can this framework, with minimal tweaking, predict contact angles across a wide range of substances and their mixtures? The answer, in broad strokes, is yes—and the deviations teach us where the model still has to grow.
That claim matters because it promises a bridge from molecular physics to engineering practice. If a physicist can predict how a droplet wets a surface from the properties of the fluids alone, you can feed those predictions into continuum-flow models, optimize coatings, or tailor surfaces for energy or water-harvesting challenges—without banging through hours of expensive atomistic simulations or a battery of experiments for every new liquid. The study does not claim to replace detailed surface chemistry; PTFE is a relatively non-polar, smooth substrate in this work. But it does suggest a practical route to predict wetting for many real-world liquids and their mixtures, governed by the same physics that shapes a glass of oil and water sitting on a plastic plate. And in the long run, it hints at how to design surfaces so droplets behave the way we want, whether that means shedding rain from a sensor or guiding fuel vapors in a microfluidic device.
A theory that watches droplets from the inside
Classical density functional theory is a way to answer: what does the fluid look like, density by density, around any region in space? In this study, the density is described for each fluid component, and the theory seeks densities 𝜌i(r) that minimize the grand potential Ω, a quantity that encodes both the fluid’s internal interactions and its interactions with the surrounding environment. In formula sublime, Ω[{𝜌i(r)}] = F[{𝜌i(r)}] − ∑i ∫ (𝜌i(r) μi − 𝑉ext,i(r)) di. The fluid-fluid interactions are assembled in a Helmholtz energy functional F composed of several contributions: ideal gas behavior, hard-sphere repulsions, chain connectivity, dispersion, and, for some substances, hydrogen bonding (association) and dipolar forces. The model is not a single equation but a tapestry built from components tuned to bulk phase data for real substances, then extended to inhomogeneous situations like a droplet near a solid interface. The key here is that you do not need discrete atomistic configurations to predict how a surface will wet a liquid; you compute average densities and their variations, and from those, you extract interfacial tensions and, via Young’s equation, the contact angle Θ.
To connect the liquid to the solid, the researchers use an effective external potential Vext,i(z) that depends only on the distance z from the surface. The solid is treated as a planar, uniform plane, with a single adjustable parameter 𝜀ss that tunes the strength of solid-fluid interactions. They calibrate 𝜀ss by matching the measured contact angle of n-octane on PTFE, a non-polar fluid on a non-polar surface, and then treat all other predictions as genuine tests of the model’s predictive power. The fluids themselves are described by PC-SAFT, a framework that models molecules as chains of segments; for mixtures, cross-interactions are handled with Lorentz–Berthelot combining rules, possibly refined by a small set of binary parameters drawn from literature. In short: one solid parameter fit, many fluid parameters drawn from bulk data, and then the theory spins out interfacial tensions for the three phase boundaries—vapor-liquid, solid-liquid, and solid-vapor. Put into Young’s equation, these tensions yield the contact angle for a macroscopic droplet. It’s physics from the inside out, not trial-and-error at the edge of a droplet.
The team also explored a more granular variant of the theory, called PC-iSAFT, which keeps track of individual segments within a molecule rather than averaging over the whole molecule. That finer-grained approach is designed to capture orientation effects—how a polar or hydrogen-bonding molecule preferentially positions itself at the interface. While not a magic fix, it helps explain why alcohols—monohydric ones in particular—systematically deviated when the orientation of polar groups at the surface wasn’t explicitly accounted for. The result is a nuanced picture: for many non-polar, polar, and hydrogen-bonding fluids, the PC-SAFT–DFT framework predicts contact angles with striking accuracy; when orientation matters more, a more detailed segment-level model improves the match but does not always erase the gap entirely.
From equations to the lab bench
The experimental side of the study is meticulous and deliberate, designed to test predictions against clean, controlled data. The PTFE substrate is chosen for its well-characterized non-polar, dispersive interactions. The researchers perform sessile droplet measurements under near-ambient conditions, using a dry nitrogen purge to limit external contaminants. Droplets of 6 microliters are dispensed with precision, and the resulting droplets are imaged to extract the contact angle where the liquid, solid, and vapor meet. The setup records multiple experimental runs to gauge reproducibility, and the authors report a standard deviation of about 1.7 degrees within a run and around 3 degrees when comparing across runs. That latter figure underscores how sensitively the contact angle can depend on subtle surface states—whether the surface is perfectly clean, whether residues from previous liquids linger, or how the surface’s microscopic roughness has changed after cleaning. It’s a reminder that a single macroscopic angle encodes a lot of microscopic history.
One of the paper’s practical moves is transparent: the atmosphere surrounding the droplet is nearly a background actor. The authors show that neglecting trace nitrogen and oxygen in the DFT calculations—a simplifying assumption—does not meaningfully alter the predicted contact angles for most substances. For the purposes of early validation and broad screening, that’s a helpful simplification, because it keeps the model tractable and fast. In a world of complex fluids and real surfaces, speed matters; if a model can give you a good first-pass angle quickly, you can narrow down which systems merit more expensive, atomically resolved simulations or targeted experiments.
And there’s a human dimension to the lab work as well. The team repeats measurements across several experimental runs, each time re-fitting the solid–fluid energy parameter to the octane reference. That approach reflects a practical engineering mindset: you acknowledge that the real world isn’t perfectly uniform, so you encapsulate that variability in a single, transferable parameter. The result is a method that feels both principled and useful: you ground a broad predictive model in a single, robust calibration point, then “trust” its predictions across a spectrum of liquids and their mixtures.
Wetting in mixtures and what it means for real life
The study’s most exciting punchline isn’t just about predicting the angle for pure liquids, but about predicting the angles for mixtures. Real-world liquids are rarely pure; they’re blends of non-pond-polar solvents, polar solvents, alcohols, water, and sometimes donors and acceptors in hydrogen-bonding networks. The researchers test binary mixtures, exploring how the mix of two liquids shifts the contact angle on PTFE as the composition changes. Once again, the DFT predictions track the experimental trends: as you tilt the composition from one end to the other, the contact angle can swing up or down in non-linear ways, and the model captures those changes. In particular, the results show that an octane-rich mixture of certain hydrocarbons tends to wet the surface more readily than octane alone, while mixing in water or strongly hydrogen-bonding components tends to increase the angle. The model even captures the nuanced behavior when one mixture component is water and the other is a polar partner like NMP, where cross-association between the molecules matters for the resulting surface tension balance.
In their more complex sets of mixtures, the authors examine cases where the pure components are well described by the model and cases where orientational effects become important. For many non-polar or moderately polar mixtures, the angle predictions stay within about 5 to 10 degrees of experimental values, which the authors deem satisfactory given the simplifications. When pure components show larger discrepancies—especially monohydric alcohols, which carry a polar OH group that tends to orient toward the solid in a way the simple external potential doesn’t fully capture—the predictions drift. Here the PC-iSAFT variant, with its segment-level accounting for molecular orientation, helps narrow the gap but doesn’t always close it. The takeaway is crisp: if you nail the pure-fluid interface well, you can predicting the angles of many mixtures with reasonable confidence. If the pure-fluid picture is off, the mixture predictions will be off with it.
Why does this matter outside the lab? Because wetting governs how droplets move, spread, coalesce, or evaporate in real devices. In condensers, for example, drop-wise condensation (as opposed to film-wise condensation) can dramatically improve heat transfer efficiency. Coatings that make surfaces either repel water or invite droplets to roll off can control how moisture interacts with sensors, membranes, or energy devices. Multiphase flows in microfluidic circuits—the kind of thing used in chemical synthesis or biomedical devices—depend delicately on contact angles to guide droplets along channels without sticking or pinning. If you can predict how a given liquid or a mixture will wet a surface, you can size and shape devices, choose materials, and design control strategies with fewer blind spots. That is the practical arc of this research: a principled theory that translates molecular detail into a user-friendly macroscopic handle.
Of course, the results come with humility baked in. The authors are clear that their PTFE tests reflect a fairly smooth, non-polar solid. Extending the approach to chemically rough, heterogeneous, or highly polar surfaces will require additional calibration and perhaps new physics to capture, for example, how local surface chemistry couples with orientational distributions or how line tensions at the droplet edge shift in curved geometries. The authors also point out that while the surrounding atmosphere seems negligible for their current comparisons, real devices sometimes operate in gases with reactive or strongly solvating species. These are not show-stoppers, but they are the kinds of caveats that signal where future work will push the model from a robust predictor into a more complete, general-purpose tool.
So what did we learn from this collaboration at the University of Stuttgart? We learned that a density-functional framework, anchored in PC-SAFT and tuned by a single solid–fluid energy parameter, can accurately predict the static contact angle for a wide set of real liquids and their mixtures on a model non-polar surface. The approach links the microscopic world of molecular interactions to the macroscopic world of droplets and coatings, offering a computationally efficient middle ground between fully atomistic simulations and coarse, empirical correlations. The strongest successes come when the pure liquids themselves are well described by the model; the most interesting gaps point to where molecular orientation or surface heterogeneity matters most—precisely where the field has been craving a more nuanced description. In short: the theory works, and the deviations map out the physics we still need to capture to make the predictions even more trustworthy across the full spectrum of real-world fluids.
As a closing thought, the work is a reminder that “fundamental” science doesn’t live in a vacuum. The same equations that describe a tiny capillary bridge inside a nanopore can, with the right packaging, guide engineers designing heat exchangers or humidity harvesters. The authors’ transparent methods and openly reported data—plus the ability to run the PC-SAFT–DFT framework on a modern software stack—mean this is a tool that other researchers and industry teams can pick up, test, and adapt. It’s a small but meaningful step toward a world where the way a droplet kisses or avoids kissing a surface is not a mystery but a parameter you can tune with confidence.
In the end, what we learn from the University of Stuttgart team is not a single equation that explains every droplet’s whim. It is a principled, scalable approach that makes the complex interplay of fluids at interfaces feel a bit more manageable. The study turns the dream of predictive wetting into something tangible: a method that, for many real mixtures, can tell you how a droplet will flirt with a surface before you even place it there. And that, in turn, could help us design surfaces that better manage heat, moisture, and flow—whether the goal is to squeeze more efficiency from a power plant condenser or to master the tiny droplets that carry medicines through microfluidic channels.
Lead researchers and institutional home: This work was carried out at the University of Stuttgart, with the Institute of Thermodynamics and Thermal Process Engineering and the Institute of Applied Mechanics playing central roles. The study is led by Benjamin Bursik and Joachim Gross, with significant contributions from Nikolaos Karadimitriou and Holger Steeb. The collaboration showcases how a well-crafted blend of theory, computation, and careful experimentation can illuminate the wetting of real substances and their mixtures in a way that feels both fundamental and practically useful.
