Abstract
The Schlieren method intends to reveal the elevation of a refractive fluid–fluid interface. The method is based on a comparison of images of a single pattern placed at the bottom of the container. Accurate measurements can be obtained with a simple and low-cost optical setup. However, it is restricted to weak interface deformations, weak slopes and weak paraxial angles. To overcome these limitations, we propose an enhanced optical setup that uses a bitelecentric objective and a double pattern. Thanks to this new setup, we avoid geometrical approximations and we extend the method to moderate/large deformations. Moreover, the proposed method does not depend on the liquid depth and could be used in various applications.
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Adrian R. J. (2005) Twenty years of particle image velocimetry. Exp Fluids 39(2):159–169. https://doi.org/10.1007/s00348-005-0991-7
Bornert M, Brémand F, Doumalin P et al (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech 49:353. https://doi.org/10.1007/s11340-008-9204-7
Chan DYC, Henry JD Jr, White LR (1981) The interaction of colloidal particles collected at fluid interfaces. J Colloid Interface Sci 79(2):410. https://doi.org/10.1016/0021-9797(81)90092-8
Dalziel SB, Hugues GO, Sutherland BR (2000) Whole-field density measurements by “synthetic schlieren.”. Exp Fluids 28:322. https://doi.org/10.1007/s003480050391
Damiano AP, Brun PT, Harris DM et al (2016) Surface topography measurements of the bouncing droplet experiment. Exp Fluids 57:163. https://doi.org/10.1007/s00348-016-2251-4
Eddi A, Fort E, Moisy F et al (2009) Unpredictable tunneling of a classical wave-particle association. Phys Rev Lett 102(240):401. https://doi.org/10.1103/PhysRevLett.102.240401
Eddi A, Sultan E, Moukhtar J et al (2011) Information stored in Faraday waves: the origin of a path memory. J Fluid Mech 674:433. https://doi.org/10.1017/S0022112011000176
Grédiac M, Blaysat B, Sur F (2020) Comparing several spectral methods used to extract displacement fields from checkerboard images. Opt Lasers Eng 127(105):984. https://doi.org/10.1016/j.optlaseng.2019.105984
Kolaas J, Riise BH, Sveen K et al (2018) Bichromatic synthetic Schlieren applied to surface wave measurements. Exp Fluids 59:128. https://doi.org/10.1007/s00348-018-2580-6
Kralchevsky PA, Denkov ND (2001) Capillary forces and structuring in layers of colloid particles. Curr Opin Colloid Interface Sci 6(4):383. https://doi.org/10.1016/S1359-0294(01)00105-4
Lau YM, Westerweel J, van de Water W (2020) Using Faraday waves to measure interfacial tension. Langmuir 36(21):5872. https://doi.org/10.1021/acs.langmuir.0c00622
Meinhardt-Llopis E, Sánchez J, Kondermann D (2013) Horn–Schunck optical flow with a multi-scale strategy. Image Proc On Line 3:151. https://doi.org/10.5201/ipol.2013.20
Meinhart CD, Wereley ST, Santiago JG (1999) PIV measurements of a microchannel flow. Exp Fluids 27:414. https://doi.org/10.1007/s003480050366
Metzmacher J, Poty M, Lumay G et al (2017) Self-assembly of smart mesoscopic objects. Eur Phys J E 40:108. https://doi.org/10.1140/epje/i2017-11599-y
Meunier P, Leweke T (2003) Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp Fluids 35:408. https://doi.org/10.1007/s00348-003-0673-2
Moisy F, Rabaud M, Salsac K (2009) A synthetic Schlieren method for the measurement of the topography of a liquid interface. Exp Fluids 46:1021. https://doi.org/10.1007/s00348-008-0608-z
Poty M, Vandewalle N (2021) Equilibrium distances for the capillary interaction between floating objects. Soft Matter 17:6718. https://doi.org/10.1039/D1SM00447F
Poty M, Lumay G, Vandewalle N (2014) Customizing mesoscale self-assembly with three-dimensional printing. New J Phys 16(2):013–023. https://doi.org/10.1088/1367-2630/16/2/023013
Raffel M (2015) Background-oriented Schlieren (BOS) techniques. Exp Fluids 56:60. https://doi.org/10.1007/s00348-015-1927-5
Rajendran LK, Bane SPM, Vlachos PP (2019) Dot tracking methodology for background-oriented Schlieren (BOS). Exp Fluids 60:162. https://doi.org/10.1007/s00348-019-2793-3
Sutherland BR, Dalziel SB, Hugues GO et al (1999) Visualization and measurement of internal waves by synthetic Schlieren. Part 1. Vertically oscillating cylinder. J Fluid Mech 390:93. https://doi.org/10.1017/S0022112099005017
Utami T, Blackwelder RE (1991) A cross-correlation technique for velocity field extraction from particulate visualization. Exp Fluids 10:213. https://doi.org/10.1007/BF00190391
Vandewalle N, Poty M, Vanesse N et al (2020) Switchable self-assembled capillary structures. Soft Matter 16(10):320. https://doi.org/10.1039/D0SM01251C
Vella D, Mahadevan L (2005) The “Cheerios effect.”. Am J Phys 73:817. https://doi.org/10.1119/1.1898523
Weinzaepfel P, Revaud J, Harchaoui Z, et al (2013) DeepFlow: large displacement optical flow with deep matching. In: Proceedings of the IEEE international conference on computer vision (ICCV), p 1385
Wildeman S (2018a) Matlab implementations of fcd and dic+of methods. https://github.com/swildeman/fcd, https://github.com/swildeman/dicflow
Wildeman Sander (2018) Real-time quantitative Schlieren imaging by fast Fourier demodulation of a checkered backdrop. Exp Fluids. https://doi.org/10.1007/s00348-018-2553-9
Acknowledgements
We thank Y. E. Corbisier for his support to draw 3D sketches and pictures for this paper.
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This work is financially supported by the University of Liège through the CESAM Research Unit.
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JM, GL and MP contributed to the conception of the proposed method. JM, MP and NV wrote the manuscript.
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Metzmacher, J., Lagubeau, G., Poty, M. et al. Double pattern improves the Schlieren methods for measuring liquid–air interface topography. Exp Fluids 63, 120 (2022). https://doi.org/10.1007/s00348-022-03467-w
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DOI: https://doi.org/10.1007/s00348-022-03467-w