1.Introduction

Bubbly flows are often used in environmental industry applications such as aeration, mixing or cleaning processes. The motion of those bubbles and the specific composition of the liquid phase generate foams. Among those processes, flotation is a technique that utilizes bubbles and foams to remove or to separate components present in the liquid phase. It is especially employed in wastewater treatment or within minerals processing industry; those methods have a small environmental load because they do not require adding chemical product. The motion of particles and liquid within foams has a major importance for the efficiency of those processes. Indeed, through the understanding of foam gas cells behavior and of liquid flow for different surfactant concentrations and particle sizes, those processes can be optimized.

Joseph Plateau (19th century), of the well-known Plateau's laws, is one of the first to define foam structure [1]. Foams are network of Plateau borders (connection of 3 gas cells) and nodes (connection of Plateau borders). A quasi two-dimensional foam is a layer of foam between two parallel plates and the junction of only three Plateau borders forms a node in order to reach dynamic equilibrium.

The flow of liquid within foams, called drainage, has been studied by many groups [2, 3, 4, 5]. The velocities profiles of flows within Plateau borders depend on the surface dissipation occurring at Plateau borders walls. This dissipation is in the form of a surface shear viscosity, μs [kg/s]. Therefore, depending on μs, two types of flows are occurring within Plateau borders. The first one is a Poiseuille-like flow for high value of μs which corresponds to rigid foams. The second one is a plug-like flow for small value of μs, which corresponds to mobile foams. They introduce a dimensionless parameter called mobility, defined as M=μr/μs, with μ [kg/m/s] the liquid viscosity, and r [m] the curvature radius of the Plateau border. Particles behavior within those two types of foams is presented in that study.

Concerning the motion of solids in rising foams, Neethling et al. (2002) [6] developed a numerical model for a high amount of solids in foams. They introduce viscous drag to predict the velocity the particles in the foam. They obtain realistic trends of the fractional liquid content and of the concentration of solids in foams. It is difficult to compare their results with our data because some parameters such as the volume fraction of liquid within Plateau borders are challenging to evaluate in our study.

In order to gain a better understanding of the particles motions in foams, here, we present the results of an experimental study of particles motion in quasi two-dimensional rising foams.

2. Experimental Set-Up

In the present study, we limit the case to quasi two-dimensional foams because visualization within three-dimensional ones is challenging [7].

As shown in Fig.1a, air was injected using a compressor and entered an acrylic water-filled channel (height H = 1 m, width W = 0.15 m and depth D = 4 mm) from its bottom part. The air went through a porous plate (beads size was 10 μm). We defined the height at which the bubbles were injected to be y=0 m.

Saponin and casein were used as surfactants. They had the same density as water. Polydispersed rising foams were generated. Saponin foams are known to have high mobility, therefore are mobile foams. Casein foams are known to have low mobility, therefore are rigid foams.

Particle Tracking Velocimetry was used to capture the trajectory of the falling particles. A laser sheet of 3 mm thickness was generated using an (2 Watts) argon laser (emission wavelength was 532 nm) and a combination of lenses. The position of the test section was at the height of y = 0.5 m. Hydrophilic fluorescent particles were used for the tracking. They were ion-exchange resin stained by the fluorescent dye Rhodamine-B (absorption and emission wavelengths are 540 nm and 600 nm respectively) from Diaion Mitsubishi and had a density of 974 kg/m3. They were chosen because of their light emission. The particle diameters were in the range of 50 to 150 μm. About one hundred particles were beforehand added to the liquid phase in order to observe particles motion from the bottom part of the foam. In order to capture only fluorescent particles, a cut-off filter (wavelength 560 nm) was attached to a CCD camera. The particle motions were obtained using MATLAB and camera photographs (Fig.1b). Foams generated with this set-up are polydispersed quasi two-dimensional ones. The diameter of tracked particles are within the same order as the Plateau border width since the ratio between the particle diameter and the encircled of cross-section of Plateau border is larger than 0.3.

3. Results and Discussion.

The physical chemistry of surfactant solutions have a real importance on the rheology of the interfaces Plateau borders and therefore on particle sedimentation. For that reason, two surfactants that have different properties have been used in this study: saponin and casein. Saponin Plateau borders are knows to have mobile walls. Therefore, the profile of liquid flow velocity within Plateau border is a plug-type flow. Whereas casein Plateau borders are knows to have rigid walls. Therefore, the profile of liquid flow velocity within Plateau border is a Poiseuille-type one. Particles were tracked within those two different foams that were generated with different gas flow rates and surfactant concentrations. They were tracked along a large amount of Plateau borders and nodes. And it was found that the velocity profiles of particles sedimenting with respect to the gas flow rates, within those foams are similar. At the scale of a Plateau border, if particles were tracked along several Plateau borders and nodes, we could observe different behaviour between saponin and casein Plateau border. Within saponin foams, particle velocities reach a local maximal when the particle is passing through a node. On the contrary, within casein foams, particle velocities reach a local minimal when the particle is passing through a node.

There are others parameters that characterise the type of foams and that influence particles sedimentation. They are the same for saponin and casein foams. One of them concerns the liquid content within foams. If the liquid content is large, the foam is a wet one, whereas if the liquid content is not large, the foam is rather a dry one. Determining the limit between dry and wet foams is challenging with our set-up, therefore, we used the width of Plateau border as a parameter. Indeed, the larger the width is, the more the foam is wet. This parameter depends one the gas flow rates that is used to generate the foam. Since the particles have a diameter that is within the same order of the Plateau border width, it will have some influence on their sedimentation. Hence, particles will flow more freely if the Plateau borders are larger. Therefore, particles sedimentation velocities within saponin and casein foams are larger within wet foams than within dry ones since Plateau borders are larger. Moreover, for the same gas flow rate, casein foams are wetter than saponin ones. Therefore, particles sedimentation velocities are larger within casein foams than the ones within saponin ones.

In addition to the influence on the liquid content, the gas flow rate is also influencing the shape of the foams. Since particles are meandering around foams gas cells, their sizes influence their paths and consequently, their velocities. Indeed, when foam gas cells have a large size, the paths of particles are longer and consequently, they have a smaller sedimentation velocity.

4. Conclusion

To conclude, the important parameter to control the efficiency of cleaning processes such as flotation process is the gas flow rate used to generate the foams. An optimal one should be finding, taking account of the concentration of the liquid to clean and the size of the particles to remove.

本論文は,気泡塔を用いた浮上分離による水処理技術と関連して,泡沫中を移動する微粒子に関して,泡沫の硬さや湿り度が微粒子の挙動に与える影響について実験的に調べ,より効率よく微粒子の浮上分離が行なえるための条件に関して知見を得ることを目的としている.

近年,水環境の急速な悪化に伴い,高効率で低環境負荷の水処理技術として,微細気泡の利用による浮上分離システムが大きな注目を集めている.本研究は,このような浮上分離システムにおいて,汚水物質を濃縮除去するプロセスで現れる気泡塔上部の泡沫部分に着目し,上昇泡沫中を下降する微粒子の挙動を詳細に解析しようとするものである.本論文は「The behaviour of tiny particles within rising foams (上昇する泡沫中における微小粒子の挙動)」と題し,全8章からなる.

第1章は「Introduction」であり,研究の背景と目的,また過去に行われた泡沫に関する研究を挙げ,これらに対する本論文の位置づけを述べている.ここでは特に浮上分離技術への応用を意識して研究の背景を説明し,泡沫の研究の重要性を説明している.

第2章は「Experimental System」と題して,本研究で行なった実験に関して,実験装置および実験方法の説明を行なっている.本研究では,泡沫に異なる特性を与える表面活性剤として,サポニンとカセインが用いられている.本章では,これらの表面活性剤に関する諸量および泡沫の生成法とレーザーシートを用いて粒子の追跡法などに関して,説明が与えられている.

第3章は「Behaviour of rising foams」と題して,泡沫が上昇していく挙動に関して実験結果が整理されている.サポニンとカセインの2種類の表面活性剤の特性の違いおよびその濃度に依存して,硬い-柔らかい,湿潤-乾燥,などの分類ができるが,ここではこれらの特性の違いと泡沫の上昇速度の関係について詳細に調べている.

第4章は「Sedimentation of particles within foams」と題して,上昇する泡沫中を下降する微小粒子の速度の測定に関して実験データが提供されている.

第5章は「Influence of particle sizes」と題して,第3章,第4章の結果を基に,解析を進め,微粒子サイズの影響について論じている.その結果,微粒子サイズの増加とともに沈降サイズは単調に減少し, 大きい微粒子の方がより簡単に除去できることが定量的に議論されている.

第6章は「Microscopic analysis」と題して,泡沫の微細構造と関連した議論が進められ,微粒子の沈降には泡沫の節点における微粒子の停留時間が重要となるが,柔らかいサポニン泡沫では微粒子は節点にとどまりづらく通過するのに対し,硬いカセイン泡沫では節点における微粒子の停留時間が長くなることが示されている.

第7章は「Modelling for particles behaviour」と題して,泡沫中を移動する微粒子の運動のモデル化が行なわれている.プラトー境界といわれる泡沫間の流路と泡沫中の節点における微粒子の挙動を分離してモデル化し,泡沫中の微粒子沈降をモデル化している.さらに,プラトー境界における流動構造をモデル化し,単純な理論では予測しきれない部分について考察を行なっている.

第8章は「Conclusion」であり,本研究で得られた結果を総括している.

以上,従来は浮上分離に対する泡沫の影響に関しては,泡沫全体としての粒子除去特性を評価する立場での研究が主流であり,泡沫の構造とその泡沫間の間隙を流れる液流および微粒子の挙動の観点から粒子除去について論じた論文は極めて少ない.本研究は,界面活性剤の種類および濃度を変化させることにより泡沫の特性を変え,そのもとで微粒子の挙動を詳細に調べることにより微粒子除去に対する影響を論じている点で独創性があり,優れた論文である.

よって本論文は博士(工学)の学位請求論文として合格と認められる。