InterPore2023

A Fourier-transform approach for fringe pattern analysis for a Mach-Zehnder interferometry measurement on surface evaporation of saturated porous media

23 May 2023, 10:30

1h 30m

Poster Presentation (MS17) Thermal Processes, Thermal Coupling and Thermal Properties of Porous Media: modeling and experiments at different scales Poster

Speaker

Julian Härter (Universtity of Stuttgart)

Description

The interaction of fluids with different types of porous media plays an important role not only on our daily lives, but also understanding natural and industrial processes. Detailed studies of evaporation processes in porous materials are required not only to increase the fundamental understanding but also to enhance performance in engineering terms. The efficient design, operation and optimization of such engineering applications rely on detailed and thorough understanding of the interaction in terms of exchange of mass, momentum and energy. Several different techniques have been implemented to study this behaviour experimentally. Most experimental investigations are conducted using weight measurements, where a completely saturated porous probe is placed on a balance. However, local values of the surface evaporation flux are difficult to determine using this measurement technique. For this reason, we want to use an existing measurement technique, which is the interferometry, to estimate these local evaporation rates at the interface of a porous medium. This measurement technique has already been used to investigate drying processes on porous media [1, 2], but also to determine concentration gradients on evaporating droplets [3] and the evaporation of binary water-ethanol mixtures [4].

In this work, the evaporation of different fluids in a fully saturated porous medium is examined with a Mach-Zehnder interferometer. The latter uses the phase shift between two collimated light beams that results from splitting the light from a single light source due to a change in density or refractive index. The evaporation of moisture from the porous surface causes a deflection of the interference fringes, which thus leads to a phase shift. From this phase shift $\mathrm{\Delta }\varphi$, the change of refractive index $\mathrm{\Delta }n$ is computed using $\mathrm{\Delta }n=\frac{\mathrm{\Delta }\varphi \lambda }{2\pi t}$ where $\lambda$ is the wavelength of the light source, and $t$ the depth of the measurement region. To extract the two-dimensional phase shift from the interferogram, the Fourier transform based approach by [6] is used. However, one of the problems of the approach used is that the phase-retrieval technique give the detected phase wrapped into the interval $[-\pi ,\pi ]$. This is due to the non-linear wrapping function involved in the phase-estimation process. Unwrapping is the process by which these discontinuities are resolved and the result is transformed into the desired continuous phase ${\varphi }_{con}(x,y)=\varphi (x,y)+2\mathrm{\Pi }k(x,y)$ where $k(x,y)$ is an array of integers. The unwrapping problem has been an important research topic for over decades [5]. For phase maps composed from consistent phase maps fringe data, there are many different algorithms, but there is none used for our type of problem. The questions that needs to be addressed to resolve the unwrapping problem is: under what circumstances can this lost information be recovered? The main objective of this work are these phase discontinuities and how they can be solved to reproduce the local evaporation rates at the surface of the porous models as accurately as possible.

References

[1] A. Bhatia, N. Roth, and B. Weigand. A Mach-Zehnder interferometry study of moisture evaporation from porous media. In 9th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, Iguazu Falls, Brazil, June 2017.
[2] A. Bhatia, N. Roth, and B. Weigand. Mach-Zehnder interferometry investigations in drying of water-saturated porous materials. Journal of Applied Physics, 125(18):184901, 2019.
[3] S. Dehaeck, A. Rednikov, and P. Colinet. Vapor-based interferometric measurement of local evaporation rate and interfacial temperature of evaporating droplets. Langmuir, 30(8):2002–2008, 2014.
[4] S. Dehaeck, C. Wylock, and P. Colinet. A Mach-Zehnder interferometer-based study of evaporation of binary mixtures in Hele-Shaw cells. In Proceeding of the 13th International Symposium on Flow Visualisation ISFV, Nice, France, July 2008.
[5] D. Ghiglia, D. Ghiglia, M. Pritt, and M. Pritt. Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software. Living Away from Home: Studies. Wiley, 1998.
[6] T. Kreis. Digital holographic interference-phase measurement using the Fourier-transform method. J. Opt. Soc. Am. A, 3(6):847–855, 1986.