17th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 07 – 10, 2014

1.4.2

Measuring the local and global evaporation rate of fast evaporating droplets with interferometry

S. Dehaeck1,*, A. Ye. Rednikov1, P. Colinet1,*

1: Transfers, Interfaces and Processes department (TIPs), Fluid Physics group, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Brussels, Belgium

* Correspondent author: sam.dehaeck@gmail.com, pcolinet@ulb.ac.be

Keywords: Interferometry, digital holography, evaporation, vapor concentration

In the current work, digital holographic interferometry is used to measure the refractive index field surrounding evaporating droplets. From this measurement, several key quantities can be extracted. These are the vapour mole fraction distribution surrounding the droplet, the temperature and local evaporation rate all along the interface of the droplet and finally, the global evaporation rate. All these measurements can be extracted from a single image. This work was recently published in Langmuir [4]. Measuring the vapour concentration field surrounding

evaporating droplets has been performed with several different techniques in the past. Laser induced fluorescence and phosphorescence is a tested technique (e.g. [1-2]) and Fourier Transform Infrared Absorption (FTIR) techniques has also been used to that end ([5]). However, these techniques have not been able to yield the required resolution near the liquid interface up till now in order to yield a measurement of the vapour concentration close to the interface which is required for measuring the interfacial temperature and local evaporation rate. Previously, Toker and Stricker [6] have used interferometry to measure the vapour concentration field surrounding an evaporating droplet and were able to extract interfacial temperatures of the droplet from the measurement of the vapour concentration at the interface. However, they did not continue to measure the local evaporation rate nor did they extract the global evaporation rate from these measurements. In the present contribution, we will revisit this technique and show that it is now capable of delivering much more information about the evaporating drop.

In the above image, the experimental setup is sketched

together with a typical raw image. It is a simple Mach-Zehnder interferometer with a liquid drop pending from a regular 2” silicon wafer. The typical droplet radius varies from 2mm to 0mm during the evaporation process. The liquid used here is 3M Novec HFE-7000, which is a highly volatile liquid with a boiling temperature around 35°C. Processing the interferometric image using standard

digital holographic image processing routines, one can obtain the optical phase delay information in each pixel. As this phase delay is the result of a projection along a supposedly axisymmetric configuration, a tomographic reconstruction process (inverse Abel Transform) is then performed so as to obtain the full 3D refractive index difference field surrounding the droplet. For the current configuration, we have demonstrated in [4] that the obtained refractive index difference field (with respect to a reference/calibration image) can be reasonably assumed to be proportional to the vapour mole fraction.

In the above image, the thus-obtained vapour mole

fraction field is shown together with two isoconcentration lines of 0.1 and 0.3 respectively. As can be understood from this image, the vapour generated at the droplet interface is ‘falling’ down along the axisymmetry-axis. This is due to the fact that the generated air-vapour mixture at the interface is up to 4 times heavier than the ambient air, leading to strong natural convection. From this vapour mole fraction field and the detection of

the droplet interface in the image, one can extract the mole fraction along the interface and in addition also the normal gradient of mole fraction at the interface. From the first quantity one can extract the interfacial temperature of the droplet when assuming that chemical equilibrium is achieved at the interface. When using additionally the normal gradient, the local evaporation rate can be extracted. As anticipated based on the description of the coffee-ring effect [3], the measured local evaporation rate increases drastically when approaching the contact line although not in the same way as in the case of pure vapour diffusion. Integrating the local evaporation rate along the entire interface then allows for an instantaneous global evaporation rate. This global evaporation rate was successfully validated by side view measurements. This showed that natural convection in the present case could boost the global evaporation rate by a factor 4 as compared to the rate predicted by pure diffusion.

[1] Bazile R and Stepowski D, "Measurements of vaporized and

liquid fuel concentration fields in a burning spray jet of acetone using planar laser induced fluorescence", Exp. Fluids 20 (1995), pp. 1-9.

[2] Charogiannis A and Beyrau F, "Laser induced phosphorescence imaging for the investigation of evaporating liquid flows", Exp. Fluids 54 (2013), pp. 1518.

[3] Deegan RD, Bakajin O, Dupont TF, Huber G, Nagel SR and Witten TA, "Capillary flow as the cause of ring stains from dried liquid drops", Nature 389 (1997), pp. 827-829.

[4] Dehaeck S, Rednikov A and Colinet P, "Vapor-Based Interferometric Measurement of Local Evaporation Rate and Interfacial Temperature of Evaporating Droplets", Langmuir 30, 8 (2014), pp. 2002-2008.

[5] Kelly-Zion PL, Pursell CJ, Hasbamrer N, Cardozo B, Gaughan K and Nickels K, "Vapor distribution above an evaporating sessile drop", Int. J. Heat and Mass Transfer 65 (2013), pp. 165-172.

[6] Toker GR and Stricker J, "Holographic study of suspended vaporizing volatile liquid droplets in still air", Int. J. Heat and Mass Transfer 39, 16 (1996), pp. 3475-3482.