PANDA-D: Interface-free determination of two dynamic contact angles

arXiv:2610.21996 · cond-mat.soft, cond-mat.mes-hall, physics.flu-dyn · Submitted 2026-10-15 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "PANDA-D: Interface-free determination of two dynamic contact angles".

Mira: The gist PANDA-D introduces an interface-free method to determine both dynamic contact angles of a driven liquid roll by jointly fitting molecular density and layerwise center-of-mass displacement profiles,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, moving on from how they do it, PANDA-D’s core thesis is that you can determine both dynamic contact angles without ever extracting an interface. It takes the ambiguity out of the measurement by jointly fitting two profiles instead of just one.

Mira: The paper argues that this approach is useful because hydrodynamic accounts don't always identify the same local angle, and a measured angle should really be reported with its observation scale and wall convention, which this method handles by measuring two angles consistently before asking which dynamical law describes them.

Lev: From a real hardware standpoint, that consistency is key when you're trying to map simulation results onto actual experimental observations where the conditions are never perfectly controlled.

Kai: It matters because it lets us measure the fluid and solid and their fluctuating interface simultaneously within molecular dynamics, which is a significant capability for researchers studying these systems.

Mira: They also mention that in a confined bridge, the two menisci can respond differently to forcing even if the liquid layers next to the walls don't look like a sharp continuum interface. That’s something this method is designed to handle.

Lev: It means we don't have to rely on approximations about what the interface *looks* like in a specific force regime; we get two angles directly from the underlying particle trajectories.

Conclusion: Kai: Thinking about the whole paper, PANDA-D is really about turning that asymmetric geometry of a moving liquid roll into a two-profile inverse problem. It yields both dynamic contact angles directly without needing to select a specific liquid-vapor contour for the main estimate.

Mira: The authors are looking at how we report these angles—how they should be reported with their observation scale and wall convention—and PANDA-D provides a way to measure those two angles consistently from particle trajectories before you even have to ask which dynamical law describes them.

Lev: For the future, this means that when we look at simulations, instead of having to manually pick a threshold or an extrapolation method for contact line analysis, this joint fitting approach becomes the primary tool for extracting those dynamic angles.

Kai: It’s about making the process of getting these angles from molecular data more reproducible by removing that dependency on interface detection methods.

Mira: That reproducibility is what makes it useful across different molecular trajectories and different wall-fluid attractions, as they show a consistent relationship between force and the two resulting angles.

Lev: So, for anyone working with these simulations, the implication is a more robust way to characterize the wetting behavior of these nanoscale systems using what’s already there in the data.

Georgii Konstantinovich Vandyshev, Grigorii Stanislavovich Gorkaev, Nikolay Dmitrievich Kondratyuk, Kirill Mironovich Gerke, Ilia Vladimirovich Kopanichuk

Moscow Institute of Physics and Technology (National Research University)

cond-mat.soft, cond-mat.mes-hall, physics.flu-dyn

Submitted: 2026-10-15

Updated: 2026-10-15

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: The gist PANDA-D introduces an interface-free method to determine both dynamic contact angles of a driven liquid roll by jointly fitting molecular density and layerwise center-of-mass displacement

Key concepts

PANDA-D: An extension of the PANDA method designed to determine both advancing and receding contact angles of a driven liquid roll by jointly fitting density and displacement profiles. It avoids the need to extract an explicit interface contour.
Density Profile ($ ho_k$): This profile measures the number density of molecules within specific layers ($k$) relative to the roll's center. It indicates how much space is occupied in different vertical positions, but it cannot tell which meniscus (advancing or receding) is moving.
Layerwise Center-of-Mass Displacement ($q_k$): This profile tracks the displacement of molecules in each layer relative to the roll's center of mass. By combining this with density, PANDA-D can distinguish between the two menisci and determine their respective angles.
Circular-Meniscus Model: A geometric model that maps the measured density and displacement profiles onto physical parameters like receding and advancing angles. It uses a circular arc parameterization to predict the roll's width and relate it to the contact line behavior.

Summary

The gist

PANDA-D introduces an interface-free method to determine both dynamic contact angles of a driven liquid roll by jointly fitting molecular density and layerwise center-of-mass displacement profiles, resolving ambiguity that arises from using only one profile

How it works

The PANDA-D method is an extension of the Predicting Angle from Nanoscale Density Analysis (PANDA) designed to determine both contact angles of a driven liquid roll without extracting an interface. It achieves this by jointly fitting density and the layerwise center-of-mass displacement relative to the roll. This joint fitting resolves the ambiguity that arises because a density profile measures occupied layer width but does not identify which meniscus is advancing.

The model maps these profiles to receding and advancing angles and an effective near-wall offset using a circular-meniscus model. The reconstruction error for synthetic rolls with prescribed angles was 0.29◦ root-mean-square. For force-driven Lennard–Jones rolls between crystalline walls, the joint fits reproduce both measured profiles, whereas density-only fits can match density while assigning incorrect asymmetry. The resulting angles agreed with independently determined circle-fit angles to 0.84◦ root-mean-square.

Profiles and Geometric Model

The method utilizes two observables for analysis: the number density profile and the layerwise displacement profile. The number density in scaled coordinates is defined as ρk = Nk / (l ly ∆z). The second observable is the layerwise displacement qk = 1 / Nk Σ X i i∈k xi − xCOM. For the fitting objective, the method uses Rk = ρk/ρl and Qk = qk.

The geometric model relates these profiles to apparent angles through a circular-arc parameterization. The local roll width and normalized density are predicted by the sum of the two meniscus bulges, w(z) = d + b1(z) + b2(z), R(z) = w(z)/l. The predicted center-of-mass displacement is given by Q(z) = b2(z) − b1(z) squared − dU2 + V2 − V1 / 2A.

Validation and Comparison

The synthetic validation involved testing recovery against known angles, using 45 geometries and 90 individual true angles. The joint-fit root-mean-square error was 0.29◦. In molecular dynamics validation, the joint model reproduced both measured profiles while density-only fits missed the observed asymmetry. The PANDA-D angles agreed with independent circle fits to 0.84◦ root-mean-square.

Force Dependence and Limitations

The results showed that across four wall–fluid attractions, the receding angle decreased and the advancing angle increased with force, approximately linearly over the studied ranges. The method's primary claim is an angle estimate that does not require contour extraction. However, it notes that close agreement with a circle fit is a consistency check, and proving universal superiority would require a separate matched benchmark with known truth. The method's performance depends on the assumptions of circular-meniscus and uniform core density. The fitted near-wall offset addresses some issues but cannot eliminate it.

The paper concludes that PANDA-D turns the asymmetric geometry of a moving liquid roll into a two-profile inverse problem, yielding both dynamic contact angles without selecting a liquid–vapor contour for the primary estimate. The method's practical advantage is that its primary estimate does not depend on choosing a two-dimensional density threshold, contour segment, or extrapolated tangent. Future work will test more complex meniscus shapes and transfer the analysis to GROMACS simulations of chemically realistic fluids and substrates. The results establish PANDA-D as a practical, reproducible method for extracting dynamic contact angles from molecular trajectories with less dependence on interface detection. The paper's findings are supported by the fact that the joint fit follows the observed profile within much of the temporal scatter in a representative driven case. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The empirical regressions show that the slopes krec and kadv depend on the wall–affinity dependence of these observed slopes, but slope differences alone cannot identify molecular contact-line friction or separate it from thermostat and interfacial-shape effects. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations. The PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states in the Langevin-yz series. The method's success is demonstrated through its ability to recover prescribed angles with a root-mean-square error of 0.29◦ on synthetic configurations.

Improvements for AI systems

textbfIncreased Robustness in Dynamic Wetting Analysis by Replacing Contour Extraction with Joint Profile Fitting:. The PANDA-D method determines both contact angles of a driven liquid roll without extracting an interface, which improves reproducibility compared to traditional methods that rely on selecting a two-dimensional liquid–vapor contour.
textbfHandling Ambiguity in Driving Forces via Center-of-Mass Displacement: The system can resolve the ambiguity between advancing and receding menisci by jointly fitting density and the layerwise center-of-mass displacement relative to the roll, which is crucial when the one-dimensional density is unchanged if only density profiles are used.
textbfReal-Time Dynamic Angle Estimation for Simulation Trajectories: The improved system can provide an angle estimate that does not require contour extraction, making it suitable for automated trajectory analysis and overcoming the difficulty of extracting interfaces manually in large simulation campaigns.
textbfExplicit Geometric Modeling of Meniscus Shape: The PANDA-D model utilizes a circular-meniscus model maps these profiles to receding and advancing angles and an effective near-wall offset, allowing for a geometric interpretation that is not a particular thermostat-dependent force balance.
textbfEnhanced Validation Against Known Truth: The system can perform an independent geometric comparison by fitting separate circles with vertical centers fixed at z = 0 to remaining contours, providing a check against the primary estimate, as the PANDA-D joint-fit estimates lie close to independent circle-fit angles over a broad range of advancing and receding states.

Abstract

Contact angles are central descriptors of wetting and capillary behavior at solid--fluid interfaces. Dynamic contact angles in molecular simulations are commonly extracted from two-dimensional liquid--vapor contours and near-wall tangent fits. We introduce PANDA-D, an extension of Predicting Angle from Nanoscale Density Analysis (PANDA) that determines both contact angles of a driven liquid roll without extracting an interface. The density profile measures occupied layer width but does not identify which meniscus is advancing. The method resolves this ambiguity by jointly fitting density and the layerwise center-of-mass displacement relative to the roll. A circular-meniscus model maps these profiles to receding and advancing angles and an effective near-wall offset. On synthetic rolls with prescribed angles, the reconstruction error is 0.29 root-mean-square. We then analyze force-driven Lennard--Jones rolls between crystalline walls. Joint fits reproduce both measured profiles, whereas density-only fits can match density while assigning incorrect asymmetry. The resulting angles agree with independently determined circle-fit angles to 0.84 root-mean-square. Across four wall--fluid attractions, the receding angle decreases and the advancing angle increases with force, approximately linearly over the studied ranges. By eliminating contour thresholds and near-wall tangent extrapolation from the primary estimate, the two-profile approach enables reproducible, automated angle analysis across molecular trajectories.