氏名　Win Shwe Maw
学位の種類　博士（工学）
学位記番号　博甲第319号
学位授与の日付　平成16年8月31日
学位論文題目　Flow Behaviors of Viscoelastic Fluid Dominated by Elongational Stress（粘弾性流体の伸張応力支配の流動現象に関する研究）
論文審査委員
　主査　教授　白樫　正高
　副査　教授　五十野　善信
　副査　教授　古口　日出男
　副査　助教授　高橋　勉
　副査　鳴海　敬倫

• 論文目次
• 論文要旨

［平成16（2004）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

CONTENTS
Nomenclature　p.1
1. Introduction　p.1
　1.1 Background of this reserch　p.1
　1.2 Elongational flow of viscoelastic fluid　p.2
　1.3 Reserch works on elpngational flow　p.6
　1.4 Objectives of the present work　p.9
　References　p.11

2. Test Fluids　p.13
　2.1 Polyacrylamide solution　p.13
　2.2 Polyacrylamide with rice-syrup solution　p.15
　2.3 Polyethlene oxide solution　p.16
　2.4 Summary　p.17
　References　p.19

3. Hele-Shaw Flow of Viscoelastic Fluids　p.20
　3.1 Introduction　p.20
　References　p.22
　3.2 Hele-Shaw cell apparatus and flow visualization technique　p.23
　3.2.1 Hele-Shaw cell　p.23
　3.2.2 Inserted object plate　p.25
　3.2.3 Experimental layout and visualization technique　p.27
　3.3 Observation of flow patterns　p.29
　3.3.1 Newtonian fluid（Water）　p.29
　3.3.2 PAA/W solution　p.29
　3.3.3 PAA/W+RS solution　p.52
　3.3.4 PEO/W solution　p.55
　3.3.5 Summary　p.58
　References　p.60
　3.4 Basic equations for Hele-Shaw flow　p.61
　3.4.1 Equation of continuity（Similar gap-wise velocity profile）　p.61
　3.4.2 Equation of motion for incompressible fluids　p.64
　References　p.68
　3.5 Validity of potential flow analogy by Hele-Shaw flow　p.69
　3.5.1 Newtonnian fluid　p.69
　3.5.2 In-elastic fluid with non-Newtonian viscosity　p.70
　3.5.3 Discussion on critical conditions of potential flow analogy　p.74
　3.5.4 Summary　p.79
　References　p.80
　3.6 Principle of planar elongational viscosity measurement using slit entry flow　p.81
　3.6.1 Estimation of elongation rate　p.81
　3.6.2 Analysis on elongational stress　p.85
　3.6.3 Application to the power-law fluid　p.92
　3.7 Results and discussions on the planar elongational viscosity measurement　p.96
　3.7.1 Elongation rate　p.96
　3.7.2 Contribution of the first normal stress difference　p.100
　3.7.3 Elongational stress and elongational viscosity　p.103
　3.7.4 Discussions　p.105
　3.7.5 Summary　p.112
　3.8 Concluding remarks of Chapter3　p.113

4. Capillary Entry Flow　p.114
　4.1 Introduction　p.114
　References　p.118
　4.2 Experimental apparatus flow visualization techniques　p.119
　4.2.1 Test fluids　p.121
　4.2.2 Test section channel　p.123
　4.2.3 Experimental procedure and measurement　p.127
　References　p.128
　4.3 Experimental results on Newtonian fluid　p.128
　4.3.1 Start-up behavior　p.139
　4.3.2 Estimation of entry pressure loss in steady flow　p.144
　4.3.3 Summary on Newtonian fluid flow　p.144
　References　p.145
　4.4 Experimental results on viscoelastic fluid　p.145
　4.4.1 Transient behavior of capillary entry flow without upper wall　p.154
　4.4.2 Influence of the upper wall on transient behavior　p.166
　4.4.3 Influence of the upper wall on entry pressure loss in steady flow　p.170
　4.4.4 Summary of experimental results on viscoelastic on viscoelastic fluid flow　p.171
　References　p.172
　4.5 Analysis on entyry pressure loss of viscoelastic fluid　p.172
　4.5.1 Flow field and momentum equations　p.176
　4.5.2 Simplofocations of the momentum equations and the entry pressure loss equation　p.178
　4.5.3 Transient behavior of flow rate　p.183
　4.6 Discussions　p.185
　References　p.186

5. Concluding Remarks　p.187
　References　p.189

Appendix-A1　p.190
Appendix-A2　p.194

Acknowledgement
List of Author's Publications
Biography

Elongational flows of viscoelastic fluid are encountered in a flow passing through a contracting channel both of two-dimensional and three-dimensional geometries which are commonly applied in polymer processing. However, methods to measure the elongational viscosity and to predict flow behavior dominated by elongational stress are far from established, especially for mobile fluids. Therefore, the study of elongational flow of polymer materials is consecutively developing nowadays both in the science and the engineering of rheological field.
The specific aim of this work is to investigate the dominant role of the elongational stress both in the planar elongation and the uni-axial elongation flows. In chapter 1, the background of the present work, history and the present status of the research work on elongational flow and the motivation of this work are described. In chapter 2, properties of test fluids are presented. Three polymer solutions, i.e. PAA/W （0.2 wt% polyacrylamide solution in water）, PAA/W+RS （0.2 wt% polyacrylamide and 10 wt% rice-syrup solution in water） and PEO/W （1 wt% polyethylene oxide solution in water） are used as sample viscoelastic fluids. From steady shear flow rheometry data, the viscosity of these solutions is well modeled by the power-law, and the first normal stress difference is prominently higher than the shear stress. Water is used as a Newtonian fluid for comparison.
In chapter 3, effect of elongational stress on Hele-Shaw flow is investigated for several boundary geometries, i.e. a flow around a circular or a square cylinder and a flow passing through a slit. Based on the observation of flow and a theoretical analysis, it is proved that the Hele-Shaw flow well reproduces the potential streamlines in spite of the non-Newtonian viscosity and elasticity in shear flow when the flow rate is very small. When the flow rate increased, the flow pattern deviates from the potential flow pattern in the opposite way to the inertia effect due to the effect of elongational stress. Based on this understanding, a simple method is presented to estimate the planar elongational viscosity measurement using the slit entry flow in the Hele-Shaw cell. Although the uncertainty of the measured planar elongational viscosity is considerably large, the principle of this method is clear and the apparatus and procedure are quite simple and applicable to very mobile liquids.
In chapter 4, a three dimensional abruptly contracting channel flow is investigated using PAA/W, the same polymer solution in chapter 3. The test section channel is composed of a transparent square cross-section reservoir and a capillary attached flush to the center of the reservoir bottom. Since the contraction ratio is virtually infinite, influence of the side walls of the upstream reservoir can be taken to be negligible. In an experimental run, the fluid filling the test section is kept at rest for a while and then a valve below the capillary is quickly opened to start the flow. The driving pressure is kept constant during a test run. The transient behavior of flow from the start-up to the terminal steady stage is observed, and effect of the upper wall set parallel to the reservoir bottom upstream the capillary entrance is also investigated. The flow field in the reservoir develops toward upstream from the capillary entrance derived by the elongational stress. In consequence, the transition time to attain to the terminal stage is considerably longer than the flow of Newtonian fluid and an overshoot of flow rate and periodically spiraling flow appear when the driving pressure is higher than a certain value. The transient time and the spiraling period becomes shorter and the entry pressure loss higher due to the upper wall interrupting the inflow region. The uni-axial elongational viscosity estimated from the entry pressure loss is several times higher than the planar elongational viscosity obtained from the Hele-Shaw flow experiment.
In chapter 5, conclusions of this thesis are summarized and discussed.