Researchers Discover Singular Drainage Patterns Form at Saddle Points on Curved Surfaces
Researchers have shown that thin liquid films draining over saddle-shaped curved surfaces develop a mathematically singular thickness distribution, even in the absence of contact lines or surface defects. The singularity arises from competing converging and diverging flows and is stabilized by a balance among drainage, hydrostatic pressure, and capillarity. The finding identifies saddle points as fundamental building blocks for understanding thin-film behavior on complex surfaces, with implications for coating, manufacturing, and geophysical flows.
A new preprint posted to arXiv by Simeon Djambov and colleagues demonstrates that smooth saddle-shaped topographies can independently generate singular drainage thickness distributions in thin liquid films — a phenomenon previously associated only with contact lines, boundaries, or surface defects. The singularity emerges from the interplay of converging and diverging flow directions inherent to saddle geometry, and is regularized within a dynamically selected region where drainage, hydrostatic pressure, and surface tension (capillarity) reach a local balance. This result suggests that saddle points are generic, structurally important features governing how thin films accumulate or thin on topographically complex surfaces. The work has potential relevance across a range of applied domains, including industrial coating processes, manufacturing quality control, and the dynamics of geophysical fluid layers. The paper was submitted on June 10, 2026, and carries a pending arXiv-issued DOI.
What's missing
As a preprint, this work has not yet undergone formal peer review, so the theoretical framework and any numerical or experimental validations have not been independently assessed. The abstract does not specify whether the findings are supported by laboratory experiments or solely by analytical and computational methods, nor does it detail the range of fluid properties or surface geometries over which the results are expected to hold.
What different sources said
- arXiv physicsCenter
Thin-film drainage becomes singular at saddles
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