PG02
フォトクロミック法による液柱マランゴニ対流の表面流速測定—深層学習による宇宙実験データの再解析
Surface Velocity Measurement of Marangoni Convection
in a Liquid bridge using Photochromic Dye Activation
Method—Reanalysis of Data from Space Experiment by
Deep Learning
矢野大志 1, 中西裕二 1, 西野耕一 2
Taishi YANO1, Yuji NAKANISHI2 and Koichi NISHINO2
12

神奈川大学，Kanagawa University
横浜国立大学，Yokohama National University

1. Introduction
It has been more than 15 years since the first series of Marangoni Experiment in Space (MEIS, hereinafter)
was carried out aboard the International Space Station (ISS, hereinafter)1,2). This space experiment is widely
known as the first Marangoni-convection experiment on the ISS as well as the first science mission in the Kibo
Japanese Experiment Module. Marangoni convection (or thermocapillary convection) in a liquid bridge,
shown in Figure 1(a), is the flow driven by the surface tension difference, which is caused by the temperature
gradient along the free surface. One of the most important features of this fluid phenomenon is thehydrodynamical or hydrothermal-wave instability. As demonstrated by many previous studies3–5), Marangoni
convection in liquid bridges transitions from an axisymmetric steady state to either a non-axisymmetricoscillatory state due to hydrothermal-wave instability (in the case of high Prandtl numbers) or a nonaxisymmetric steady state due to hydrodynamical instability (in the case of low Prandtl numbers) as thedriving force of convection increases. Our space experiment MEIS focused on the former instability and aimed
to determine the transition conditions of the flow regime (i.e., steady or oscillatory) of Marangoni convection
in a liquid bridge of high-Prandtl-number fluid under a wide variety of experimental condition. Additionally,
it measured the flow and temperature fields to understand the spatiotemporal structure of both steady andoscillatory Marangoni convection.
All the experiments were performed in the Fluid Physics Experiment Facility (FPEF, hereinafter) mounted
on the Kibo module. This facility was equipped with various instruments such as the particle tracking
velocimetry (PTV, hereinafter)6,7) and the photochromic dye activation (PDA, hereinafter) method1,8). These
measurement techniques greatly contributed to the success of the space experiments, with the former being
primarily used to measure the internal bulk flow and the latter being primarily used to measure the surface
flow. However, there are somewhat fewer reports on the results of the PDA method compared to those of
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Figure 1. (a) Schematic diagram of Marangoni convection in a liquid bridge together with gaseous nitrogenlaser beam for photochromic dye activation method and (b) photochromic dye trace image obtained in the spaceexperiment.

PTV due to the following reasons: (1) PTV was performed in all series of MEIS, whereas PDA method wasemployed in a limited number of series; (2) there are difficulties in the automatic analysis of data acquired by
the PDA method in MEIS; (3) a shortage of analysis personnel. This study aims to revisit the data of PDA
method obtained in past MEIS experiments through a new data analysis method, namely deep learning withthe convolution neural network (CNN, hereinafter).
2. Photochromic dye activation (PDA) method
The PDA method is one of the molecular tagging velocimetry techniques originally developed by Popovichand Hummel9). In this method, the photochromic dye is dissolved in the working liquid, and the excitation
light, such as a pulsed ultraviolet laser, is irradiated at the point where the velocity is to be measured. The
photochromic dye irradiated by the excitation light changes color, and the flow velocity can be obtained bytracking the movement of the colored region. Since the activated dye returns to its original color within a shortperiod (typically several seconds), the measurement can be repeated. Since the PDA method is a contactless
velocimetry technique suitable for measuring the flow velocity near a wall or a liquid-gas interface, it has
sometimes been used to measure the surface velocity of Marangoni convection in a liquid bridge10,11).
Surface velocity measurements using the PDA method were performed in the second and the third series ofMEIS (i.e., MEIS-2 and MEIS-3, respectively) out of a total of five series. The diameter of the supporting disks
was 30 mm for both series. Silicone oils with the typical kinematic viscosities of 5 and 20 cSt, resulting in
Prandtl numbers of Pr = 67 and 207, were used as the working liquids. The photochromic dye TNSB11–13)—
1,3,3-trimethyl-6’-nitrospiro[indoline-2,2’-chromene]—was dissolved in silicone oils at a concentration of
0.05% by weight, and a pulsed gaseous nitrogen (GN2, hereinafter) laser beam with a wavelength of 337.1 nm
and a pulse energy of 300 J was used to activate it. As shown in Figure 1(a), the GN2 laser beam was split into
two, reflected by a prism, and irradiated two spots on the liquid-bridge surface at the same axial position but
different azimuthal positions. Figure 1(b) shows an image captured by a CCD camera for the PDA method,
obtained during MEIS-2, and referred to hereinafter as a photochromic image. As can be seen from this image,the irradiated regions appear dark pink or purple against a light pink background. The surface velocity canbe measured by tracking these colored regions; however, there is an issue because the tracer particles for thePTV also appear purple, similar to the photochromic dye traces. In the previous studies1,8), activated
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photochromic dyes and tracer particles were distinguished manually. However, such manual operations
require an enormous amount of time for data analysis. Therefore, in this study, the process was automated(actually semi-automated) using deep learning with CNN. The details of the analysis procedure are describedin the next section.
3. Deep learning Photochromic dye activation (PDA) method
Before using deep learning, it is necessary to detect candidates of activated photochromic dye on the image.
In the previous studies1,8), the analysis region was limited to the vicinity of the laser beam irradiation points,
and activated photochromic dyes were detected only based on brightness levels. In contrast, this study
employs the following morphological image processing: (1) invert image colors; (2) create a background byaveraging a time series of inverted images; (3) subtract the background from the inverted images; (4) binarize
the subtracted images with an appropriate threshold; (5) fill holes (i.e., small black regions); (6) remove
connected objects (pixels) smaller than a specified area; (7) computes the Euclidean distance transform; (8)suppress regional minima using the H-minima transform; (9) separate clustered objects by watershedtransform. Figures 2(a) and 2(b) show the original photochromic image and the background-subtracted
photochromic image, respectively. In Figure 2(b), purple rectangles indicate objects detected by the above
operations. Through morphological image processing, purple (or dark pink) objects can be detected
automatically not only in the vicinity of the laser beam irradiation points but also in the entire photochromic
image. Additionally, it becomes possible to detect photochromic dye traces whose color is returning to theoriginal after some time has elapsed since the color change. However, it follows from Figure 2 that otherobjects, such as tracer particles and noise, are also detected in addition to the activated photochromic dyetraces. In order to classify these detected objects into photochromic dyes, tracer particles, and others, deep learningwith CNN is used.
The architecture of the CNN used for classification is shown in Figure 3. This network is designed based on
the VGGNet14) proposed by the Visual Geometry Group at the University of Oxford, which consists of many
convolutional layers with small filter sizes. The input to this CNN is volume data consisting of five layers.
The first three layers represent the red, green, and blue components of an image with a size of 49×51 pixels,
cropped around the objects detected with the aforementioned morphology image processing. The last two

Figure 2. (a) Original and (b) background subtracted and brightness adjusted photochromic dye trace images.
Purple rectangles in (b) indicate objects detected by the morphological image processing.
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Figure 3. Architecture of the convolution neural network for classifying the detected objects into photochromicdyes, tracer particles, and others.

layers represent the vertical and horizontal positions of each pixel on the photochromic image. Figures 4(a)–4(c) show visualizations of input data for photochromic dyes, tracer particles, and others. If the CNN is sufficientlyoptimized, it will output correct classification results for the inputs. In order to optimize the CNN (or todetermine the weighting coefficients and biases for each layer), it is necessary to prepare a large set of training
data, as shown in Figure 4. In this study, 300 training data are manually prepared for each category—
photochromic dyes, tracer particles, and others—totaling 900 training data. Such manual operations are onlyperformed at the beginning, with subsequent analysis conducted automatically; therefore, it is described as“actually semi-automated” in the previous section. Figure 5 shows the training history for each iteration,
wherein the red line indicates the accuracy of classification (see left vertical axis), and the green line indicatesthe cross-entropy loss (i.e., the indicator of the CNN’s poor performance, see right vertical axis). The algorithm
known as stochastic gradient descent with momentum15) is used to optimize the CNN, with the batch size andthe maximum number of epochs set to 15 and 100, respectively. The initial learning rate is set to 1×10−5 and isupdated (decreased) periodically. Through iterative computation, the classification accuracy increases tonearly 100%, while the cross-entropy loss significantly decreases. There results indicate that the CNN used inthis study is well-optimized for the training data. In the subsequent data analysis, the objects detected bymorphological image processing are classified into three categories (i.e., photochromic dyes, tracer particles, andothers), and the surface velocity is obtained by tracking those classified as photochromic dye.

Figure 4. Examples of training data used for optimizing the convolution neural network: (a) photochromic dyes,(b) tracer particles, and (c) others.
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Figure 5. Training history of convolutional neural network: classification accuracy (red line, see left verticalaxis) and cross-entropy loss (green line, see right vertical axis).

4. Surface velocity of steady Marangoni convection
The surface velocity of Marangoni convection in a liquid bridge observed in MEIS-2 is measured using a
newly developed method. The experimental conditions considered here are as follows: the liquid bridge heightis H = 15 mm, and the temperature difference between the supporting disks is ∆T = 5.7 K, which results insteady Marangoni convection because this ∆T is sufficiently lower than the instability threshold (i.e., 7.5 K).
The axial component uz of the surface velocity measured with the present method is plotted as a function of
the axial position z in Figure 6, along with those evaluated using the previous method1,8) and the numericalsimulation1,8). In the FPEF, the measurement position of the PDA method could be changed by moving thelaser beam irradiation points along the z direction. However, in the corresponding experiment, the laser beamirradiation positions were limited to four points due to time limitations, and therefore, the previous PDA
method could only measure the velocity at these specific locations. As shown in Figure 6, the newly developed
method can detect photochrome dye traces that have moved downstream and improves spatial resolution in
the z direction. The magnitude of uz tends to be slightly larger than the previous measurement and thenumerical simulation. However, the obtained surface velocities are reasonably consistent each other and show
the well-known tendency that the magnitude of the surface velocity increases with approaching the warmerside, except in the very vicinity of the disk. Additionally, it is confirmed that the azimuthal velocity converges
to zero, which is characteristic of steady Marangoni convection. These results demonstrate that the data
analysis developed in this study is effective for application to the PDA method in MEIS.

Figure 6. Axial distributions of the negative z-direction component of the surface velocity obtained by present
method (red dots), previous method (white circles), and numerical simulation (black line).
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5. Summary
This study aims to develop a new data analysist technique for the photochromic dye activation method inspace experiments on Marangoni convection in a high-Prandtl-number liquid bridge. To achieve this goal,
object detection using morphology image processing and data classification using deep learning withconvolutional neural network are employed. The developed method is applied to the data obtained from thepast space experiment (i.e., MEIS-2), and the surface velocity of axisymmetric steady Marangoni convection ismeasured. The newly developed method provides reasonable results and improves spatial resolution in theaxial direction of the liquid bridge. This method is expected to analyze previously untouched data from spaceexperiments and enhance understanding of Marangoni convection in a liquid bridge of high-Prandtl-number
fluid.
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