https://doi.org/10.1140/epje/s10189-025-00537-9
Tips and Tricks - Flowing Matter
Shape of liquid meniscus in open cells of varying geometry: a combined study via simulation and experiment
1
Mathematical Modeling Lab, Astrakhan Tatishchev State University, 20a Tatishchev str., 414056, Astrakhan City, Astrakhan Region, Russia
2
Photonics and Microfluidics Lab, X-BIO Institute, University of Tyumen, 6 Volodarsky str., 625003, Tyumen City, Tyumen Region, Russia
Received:
10
September
2025
Accepted:
20
November
2025
Published online:
6
December
2025
Evaporative lithography in cells of arbitrary configuration allows for the creation of diverse particle deposition patterns due to the formation of a specific flow structure in the liquid caused by non-uniform evaporation. The latter in turn is determined by the shape of the liquid layer surface and the wetting menisci on the cell walls. Thus, predicting the shape of the wetting menisci can serve as a tool for controlling the process of creating desired particle deposition patterns and evaporation dynamics. Here, we propose a simple and sufficiently accurate methodology for determining the shape of the liquid meniscus in cells of arbitrary geometric shape, based on a combination of mathematical modeling and a series of experimental measurement techniques. The surface profiles of the liquid meniscus in cylindrical, square, and triangular cells were determined by measuring the change in the reflection angle of a laser beam from the free liquid surface while scanning from the cell wall to its center. The height of the wetting meniscus on the inner cell wall and the minimum liquid layer thickness at the center of the cell were measured by analyzing optical images and using a contact method, respectively. 3D meniscus profiles were obtained by numerically solving the Helmholtz equation. The boundary conditions and the unknown constant in the equation were determined based on experimental data obtained for several local points or cross sections. The simulated meniscus shapes showed satisfactory agreement with the experimental local measurements, with a maximum relative error of less than 14%.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
