P06
水処理システムにおける水電解気泡の重力依存性
Gravity Dependence of Water Electrolysis Bubbles inWater Treatment Systems
栗原 雄大 1, 松本 聡 2, 金子 暁子 3,Yudai KURIHARA1, Satoshi MATSUMOTO2 and Akiko KANEKO3
筑波大学大学院，Graduate School of Tsukuba#1,
宇宙航空研究開発機構，JAXA#2,
3 筑波大学，University of Tsukuba#3,
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1. Introduction
Space exploration has made tremendous progress to date, and long-duration missions to the Moon andMars are planned in the future. In such missions, life support is essential for human activities in space, andthe Japan Aerospace Exploration Agency (JAXA) is conducting research and development of theEnvironment Control and Life Support System (ECLSS). Water supply is essential for human activities inspace, but water transportation requires significant resources and is recognized as a major challenge formanned space activities. Therefore, some space ECLSS is equipped with autonomous water reclamation
systems to minimize the amount of additional transport from Earth 1). However, because of the different
environment (μG in space, 1/6G on the moon, and 1/3G on Mars), the expected performance in space will
likely not be achieved without an accurate evaluation of gravity dependence, which must be reflected in thedesign of the equipment to account for gravity dependence.
The water treatment system developed by JAXA1) uses electrolysis as part of the treatment process, and inelectrolysis, bubbles are generated around electrodes. In order for the oxidative decomposition process to beefficient, the bubbles attached to the electrodes must be quickly removed. On the ground, the buoyancy force
acting on the bubbles facilitates their release from the electrodes, but this is not expected to happen under
microgravity because the buoyancy force is not effective. Several studies of electrolysis under microgravity
have been reported, including a study of the gravity dependence of water electrolysis bubbles in a watertreatment system1) and a study of ammonia oxidation reaction measurements on the International Space
Station (ISS)2). However, with regard to the evaluation of forces acting on electrolysis bubbles, the former
only evaluates buoyancy and drag force due to flow, while the latter does not.
This study describes the results of modeling the forces acting on bubbles generated by electrolysis inforced flow and order evaluation. In water treatment systems, the effect of bubble release by water flow istargeted, but the quality of treated water varies depending on the balance between treatment speed and flow
velocity. The gravity dependence at the electrodes is examined from the hydrodynamic point of view as wellas electrochemical factors.

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Analysis Model Electrolysis Cell Overview
The electrolytic cell is modeled as shown in Figure 1, with a rod electrode of 6 mm diameter placed in thecenter of a circular tube of 10 mm inner diameter, with the rod electrode as the anode and the inner wall of
the circular tube as the cathode. Since organic carbon must be reduced to produce drinking water from urine,electrolysis is performed at high temperature (250°C) and high pressure (5 MPa).

Figure 1.

Schematic diagram of electrolytic cell2.1. Evaluation of forces acting on electrolysis bubbles
Water electrolysis generates bubbles from the electrodes, and the desorption and transport of bubbles fromthe electrodes affect electrolytic performance. On the electrode, there is an inert region formed bysupersaturation of dissolved components, which is a factor that reduces electrolytic performance. Therefore,
it is important to detach air bubbles from the electrode.
In this study, an analysis based on the hydrodynamic point of view is performed. In order to determine thebubble detachment diameter, the balance of forces acting on the electrolysis bubbles was investigated. In
doing so, the forces were resolved in the x- and y-directions in Figure 1.
The balance of forces at x-direction:∑ 𝐹𝑥 = 𝐹𝑑𝑢,𝑥 + 𝐹𝜎,𝑥 + 𝐹𝑞𝑠(1)

The balance of forces at y-direction:∑ 𝐹𝑦 = 𝐹𝑑𝑢,𝑦 + 𝐹𝜎,𝑦 + 𝐹ℎ + 𝐹𝐿 + 𝐹𝑐𝑝 + 𝐹𝐵

(2)

where 𝐹𝑑𝑢,𝑥 and 𝐹𝑑𝑢,𝑦 are each components of the unsteady growth force acting as drag force [N], 𝐹𝜎,𝑥 and𝐹𝜎,𝑦 are each components of the surface tension between the bubble and the electrode surface [N], 𝐹𝑞𝑠 is thedrag force due to flow [N], 𝐹ℎ is the fluid force due to hydrodynamic pressure [N], 𝐹𝐿 is the shear lift force[N], 𝐹𝑐𝑝 is the contact pressure [N], and 𝐹𝐵 is the buoyancy force [N]. The following equations from (3) to (11)are obtained for the forces under consideration.
3𝐹𝑑𝑢,𝑥 = −𝜌𝐿 π𝑟𝑏 2 ( 𝐶𝑠 𝑟𝑏̇ 2 + 𝑟𝑏 𝑟𝑏̈ ) sin𝜃𝑖2(3)3𝐹𝑑𝑢,𝑦 = −𝜌𝐿 π𝑟𝑏 2 ( 𝐶𝑠 𝑟𝑏̇ 2 + 𝑟𝑏 𝑟𝑏̈ ) 𝑐𝑜𝑠𝜃𝑖2(4)where 𝜌𝐿 is the density of the liquid [kg/m3], 𝑟𝑏 is the bubble radius associated with the bubble growth rate[m], 𝑟𝑏̇ and 𝑟𝑏̈ are first and second derivative with respect to time respectively, 𝐶𝑠 is the empirical coefficient,
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and 𝜃𝑖 is the angle between the y axis and the growth force [rad]. The bubble radius is generally expressedby Equation (5).
𝑟𝑏 = A𝑡 𝛾(5)where A is the coefficient for each condition, 𝑡 is the bubble growth time [s] and γ is the time coefficient.
𝐹𝜎,𝑥 = −1.25𝑑𝑤 𝜎𝐹𝜎,𝑦 = −𝑑𝑤 𝜎𝜋 (𝛼 − 𝛽 )𝜋 2 − (𝛼 − 𝛽 )2(𝑠𝑖𝑛𝛼 + 𝑠𝑖𝑛𝛽 )𝜋(𝑐𝑜𝑠𝛽 − 𝑐𝑜𝑠𝛼 )𝛼−𝛽(6)(7)

where 𝑑𝑤 is the contact diameter [m], 𝜎 is the surface tension coefficient [N/m], 𝛼 is the forward angle [rad],and 𝛽 is the backward angle [rad]. The contact diameter is expressed by Equation (8).
𝑑𝑤 = 𝑑𝑏 sin𝛽𝑚(8)where 𝑑𝑏 is the bubble diameter [m] and 𝛽𝑚 is the average contact angle [rad].
𝐹𝑞𝑠 =3𝐶𝐷 𝜋𝜇𝐿 𝑅𝑒𝑏
𝜌𝐿(9)where 𝐶𝐷 is the drag coefficient, 𝜇𝐿 is the viscosity coefficient of the liquid [Pa ･ s] and 𝑅𝑒𝑏 is the bubble
Reynolds number, which is expressed by Equation (10).
𝑅𝑒𝑏 =𝑑𝑏 𝑢𝑟 𝜌𝐿𝜇𝐿

(10)

where 𝑢𝑟 is the velocity of the center of the bubble [m/s].
𝐹𝐵 =𝜋 3𝑑 ∆𝜌𝑔6 𝑏(11)where ∆𝜌 is the difference in density between the liquid and the bubble [kg/m 3] and 𝑔 is the acceleration ofgravity [m/s2].
From the above, when the combined force of the components in each direction is zero, i.e., ∑ 𝐹𝑥 = 0 and∑ 𝐹𝑦 = 0 are calculated to determine the peel diameter.
The forces acting on the bubbles are other than those shown in Equations (3) through (11), and only single
bubbles are considered. In addition, at the present stage, we have not reached the point of order evaluation.
Therefore, in the future, we plan to present the forces acting on bubbles that have not yet been shown at thisstage, calculate the magnitude of each force, and conduct order evaluation by considering the existence ofmultiple bubbles. In this presentation, we will report the results of the order evaluation.

References
1)
2)

S. Matsumoto, M. Akashi, Y. Shido and H. Saruwatari: Gravity Effects on Bubble Behaviour during Electrolysis for
Water Purification: ISTS (2023).
C. Morales-Navas, R.A. Martínez-Rodríguez, et al: Autonomous electrochemical system for ammonia oxidation
reaction measurements at the International Space Station. npj Microgravity, 9 (2023) 20, DOI:
https://doi.org/10.1038/s41526-023-00265-4.

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