Experimental and numerical investigations of gas-liquid and gas-liquid-liquid flows in microchannels

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EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF GAS−LIQUID AND GAS−LIQUID−LIQUID FLOWS IN

MICROCHANNELS

V. M. RAJESH

DEPARTMENT OF CHEMICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

NEW DELHI - 110016

AUGUST 2015

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c Indian Institute of Technology Delhi (IITD), New delhi, 2015.

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EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF GAS−LIQUID AND GAS−LIQUID−LIQUID FLOWS IN

MICROCHANNELS

by

V. M. RAJESH

Department of Chemical Engineering

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI

AUGUST 2015

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Dedicated to My Parents, Wife and My Sons.

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Certificate

This is to certify that the thesis entitled “Experimental and Numerical Inves- tigations of Gas-Liquid and Gas-Liquid-Liquid Flows in Microchannels”, being submitted byV. M. Rajeshto the Indian Institute of Technology Delhi, is worthy of consideration for the award of the degree ofDoctor of Philosophyand is a record of the original bonafide research work carried out by him under my guidance and supervi- sion. The results contained in the thesis have not been submitted in part or full, to any other University or Institute for the award of any degree or diploma.

I certify that he has pursued the prescribed course of research.

Dr. Vivek V Buwa

Associate Professor, (Supervisor of Student) Department of Chemical Engineering Indian Institute of Technology Delhi Hauz Khas, New Delhi – 110016

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Acknowledgments

This thesis would not have been possible without the help and support of many people in all my tough times. Without them it would be a dream. I placed my immense gratitude for their kindness, support, contribution and ideas.

I owe my deepest gratitude to my Professor, Dr. Vivek V. Buwa for his encourage- ment and support in each phase of my research endeavor. As a supervisor, he acts as a driving force of my research work from the beginning of the doctoral program. Personally as a well-wisher he helped me to overcome numerous obstacles. He supported me not only for guiding my research, but also emotionally, giving ample of moral support and freedom. With his insightful discussions and constructive feedback, he channelized my research work in proper direction. Being my source of inspiration, he taught how to make things in a perfect manner. Without his positive demeanour and continuous optimism, this dissertation would not have been possible. I owe my profound thanks to him for his flexibility in scheduling and his effort to shape my dissertation till the last moment. He is an unrivalled mentor who accompanied me throughout the gestation of my work. I am very grateful to his trust in me and his positive stimulation.

I am pleased to acknowledge my Ph.D. research committee members, Prof. K.K.

Pant, Prof. Ratan Mohan and Prof. Anupam Dewan for their significant influence in formulating the ideas. Their insight evaluation and detailed critique helped me to progress

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myself.

I thank Prof. Shantanu Roy for his insight evaluation and valuable suggestions in many phases of my research work and it intends me to have a meticulous effort to get expertise. I owe my profound gratitude to Prof. Rajesh Khanna, HOD, Department of Chemical Engineering, IIT Delhi, who gave access to make use of his laboratory instru- ments and other research facilities that have been utilized to gain some fruitful results for my dissertation.

I am indebted to my wonderful colleagues, for their friendship and support, who were ready to extend their helping hands when ever needed. I thank my first lab colleagues, Swapna Rabha, Lakshay Mahindroo, Nikita Mathur, Taru Kapoor, Richa Raj, Varun and Srikanth for their help at initial stages of my research. I would like to owe my heartfelt gratitude towards my friends and colleagues Abdul and Brajesh, whose constructive and intellectual discussions were fruitful in transferring the knowledge. We had many interesting and informative interactions to understand certain concepts crystal clear. I owe my invariably special thanks to my colleagues Abdul, Brajesh and Ekta Jain during the thesis-writing phase.

I express many thanks to my colleague B. M. Ningegowda from Department of Me- chanical Engineering, for his open discussion about CFD modeling. Many thanks also to Dr. Kiran from Department of Mechanical Engineering for sharing his acquaintance in CNC machining during my early stages of research. I owe my gratitude towards Rajagopal for sharing his knowledge on OpenFoam. I once again thank all my lab colleagues Saroj, Parul, Ritubhan and Vishal for their generous help and for making such an enthusiastic environment.

I owe my heartiest thanks to my dear friend Mr. Arun (Senior Research Officer, Re-

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search and Development, IOCL, Faridabad) for his timely financial help and support. He is ready to extend his helping hand whenever there is a need. I surprised of his generosity and thoughtfulness. I thanked him from the bottom of my heart for his unsolicited help.

I am profoundly obliged to him throughout my life for his unconditional friendship and support.

I feel so grateful to my Professor, Dr. Vivek V. Buwa for providing me well-equipped, rich and fertile environment for my research work. I would like to thank Indian Institute of Technology Delhi, for providing me an opportunity as a Research Scholar and for their financial support. This work is a concerted effort of my professors, friends, colleagues and every single individual who provide their unconditional generous help and support. Their encouragements gave me an impetus to finish my dissertation.

Last but not the least, I thank my parents for giving me such a good foundation and knowledge. Their moral support and persistent prayers helped me to over come many hindrances that I have gone through during my research work. I thank my wife Mrs.

Jeyanthi for her great moral support and unwavering belief in me. I thank my family for their sacrifices and bearing with me in many excruciating moments throughout my research work. I also thank my sons, Shri Ragav and Krithick Ragav for their tolerance in all my absence and for their unconditional love. They have given me a much-needed reprieve from work and re-energized me.

Above all I extended my deepest gratitude towards GOD, who gifted me the knowledge, the health to work consistently, the patience to withstand pressure and a good eco system.

– V. M. Rajesh

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Abstract

In chemical process industry; the need of cost competitive, energy efficient and envi- ronmentally benign processes initiated the development of micro-structured reactors and process equipment. Microreactors offered the controlled fluid manipulations and were used to perform the reactions in microchannels with typical dimensions of tens of micrometers up to a millimeter. Microreactors have broadly been employed to intensify chemical and biological processes, because of significant increase in quick analysis of products, reduc- tion in sample volume and reactant consumptions. Microreactors enhanced the reactor performance and functionality by integrating the different components (microchannels) on to individual reactors. The high surface-area-to-volume ratio of microreactors leads to enhanced heat and mass transfer and interfacial transport phenomena. As a consequence, high conversion and selectivity can be achieved in comparison to conventional reactors.

The present thesis focused on experimental and numerical investigations on gas−liquid and gas−liquid−liquid flows in microchannels. Gas−liquid two−phase flows experiments were performed to investigate the effect of flow rates of continuous (water) and dispersed phases (air) on flow regimes, formation mechanisms of air bubbles/slugs and their corresponding lengths in T−and Y−junction microchannels. High speed imaging experiments were performed to identify and to map the gas−liquid−liquid flow regimes and to understand the effect of flow rates of continuous (kerosene) and dispersed phases (air and water), addition of surfactant in aqueous phase with various concentrations on the flow regimes,

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formation mechanisms of air bubbles/slugs and water drops/slugs and also their lengths.

Experiments were also performed to control the generation of air bubbles and water drops with embedded capillary needles of different sizes for air and water inlets. This particular study was done to investigate the effect of inlet distributors on three−phase flow regimes, formation mechanisms of bubbles and drops and their corresponding lengths. A variety of interesting three-phase gas−in−water−in−oil emulsions were also generated using flow focusing devise to increase the interfacial area of air bubbles per unit volume of water slug in continuous oil phase.

In addition to the experiments, numerical simulations of three−dimensional (3D) gas−liquid microchannel flow using the volume-of-fluid (VOF) method, as implemented in OpenFOAM were performed. Simulations were performed for a 1) prediction of gas−liquid flow regimes and their formation mechanisms in T−and Y−junction microchannels, and 2) the prediction of lengths of air bubbles/slugs. In addition, an unified correlation was developed to predict the lengths of air bubbles and slugs in T− and Y−junction microchannels.

For the first time, 3D VOF simulations were also performed to simulate the gas- liquid-liquid flows in a T−junction microchannel using the commercial CFD solver Flu- ent 14.0. The predictive capability of VOF method was tested to predict the three phase gas−liquid−liquid flow regimes. The numerical predictions for two−phase (gas−liquid) and three−phase (gas−liquid−liquid) flow regimes, formation mechanisms of bubble/drop or slugs and their corresponding lengths showed an excellent agreement with the experimental data. The results presented in this thesis will be important to understand the hydrodynamics of three−phase gas−liquid−liquid flows in microchannels which in turns to device microreactor systems for catalytic reactions involving gas−liquid−liquid flows.

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List of Figures

1.1 (a) Process intensification and its components ((Stankiewicz and Moulijn, 2000)) (b) Fundamental view on process intensification ((Gerven and Stankiewicz,

2009)) . . . 3

1.2 Different types of microreactors (a and b) Falling film microreactors (source : IMM catalogue) (c) Micro packed bed reactor (Guangwen and Jun,2008) (d) Mesh microreactor (Abdallah et al.,2004) (e) Micro mixer (Pelleter and Renaud, 2009a) (f) Parallel microreactor (Coyle and Oelgemoller,2008). . 5

1.3 (a and b) Microreactors developed to perform the hazardous reactions in safer environment on industrial scale (Elvira et al.,2013). . . 6

1.4 Gas−liquid−liquid flow in a capillary reactor ((Onal et al., 2005b). . . 7

2.1 Experimental set-up. . . 22

2.2 Schematic of the experimental set-up . . . 23

2.3 Photographs of the typical microchannels used in the present work. . . 24

2.4 Formation dynamics of air bubbles/slugs in T−junction microchannel for air−water system . . . 27

2.5 Typical gas−liquid flow regimes observed at fixedQ_air = 5.12 ml/min in a T−junction microchannel A . . . 29

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2.6 Typical gas-liquid flow regimes observed at fixed Q_air = 5.12 ml/min in a Y−junction microchannel B . . . 29 2.7 Effect of Q_water, expressed in terms of Ca, on dimensionless length of air

bubbles/slugs for T−and Y−junction microchannels (microchannel A and B, Q_air = 5.12 ml/min) . . . 31 2.8 Formation dynamics of water drop/slugs at the 2^nd T−junction . . . 33 2.9 Gas−liquid−liquid flow regimes observed for microchannel C . . . 35 2.10 Flow regimes map for gas−liquid−liquid flows in microchannel C at fixed

Q_oil = 6 ml/min (Ca_oil = 5.5×10⁻³). . . 37 2.11 Effect of Q_oil, expressed in terms of Ca_oil, on length of air bubbles/slugs

and water drops/slugs . . . 39 2.12 Effect of Q_air, expressed in terms of We_air, on length of air bubbles/slugs

and water drops/slugs . . . 40 2.13 Effect of Q_water, expressed in terms of We_water, on length of air bub-

bles/slugs and water drops/slugs . . . 42 2.14 Formation dynamics of water drop/slugs at the 2^nd T−junction at Q_oil =

5 ml/min . . . 44 2.15 Formation dynamics of water drop/slugs at the 2^nd T−junction at Q_oil =

15 ml/min . . . 45 2.16 Observed gas-liquid-liquid flow regimes in presence of 0.3 wt/wt % SDS in

water . . . 47 2.17 Effect of surfactant (SDS) concentrations on length of air bubbles/slugs

(microchannel A, Q_water = 2.76 ml/min, Q_air = 5.42 ml/min) . . . 49

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2.18 Effect of surfactant (SDS) concentrations on length of water drops/slugs (microchannel C, at fixed Q_water = 2.76 ml/min, Q_air = 5.42 ml/min) . . . 50 2.19 Effect ofQ_air for 0.3 and 2 wt/wt/% SDS concentrations on lengths of (a)

bubbles/Slugs (b) drops/slugs (at fixed Q_water= 2.76 ml/min and Q_oil= 5, 15 ml/min) . . . 53 2.20 Effect of Q_water for 0.3 and 2 wt/wt/% SDS concentrations on lengths of

(a) bubbles/Slugs (b) drops/slugs (at fixed Q_air= 5.24 ml/min and Q_oil= 5, 15 ml/min) . . . 56

3.1 (a) A photograph of the test section (b) Schematic of the T−junction micro−channel used in the present work (W=1000 µm; H= 950 µm). . . . 65 3.2 Formation dynamics of a slug at 1^st T−junction in the ”Squeezing regime”

(D4 distributor (Q_oil= 2 ml/min (Ca_oil(1^st_T₎= 1.75×10⁻³) ; Q_water = 0.854 ml/min (We_water = 0.318); Q_air = 1.789 ml/min (We_air = 5.09×10⁻⁵)) (a) t = 23 ms (b) 70 ms (c) 103 ms (d) 128 ms . . . 67 3.3 Formation dynamics of a bubble at 1^st T−junction in the ”Transition

regime” (D1 distributor (Q_oil = 4 ml/min (Ca_oil(1^st_T₎ = 3.51 ×10⁻³) ; Q_water = 0.854 ml/min (We_water = 0.318); Q_air = 1.789 ml/min (We_air

= 1.41 ×10⁻²)) . . . 70 3.4 Formation dynamics of bubbles at 1^stT−junction in the ”Dripping regime”

(a) D1 distributor (Q_oil = 12 ml/min (Ca_oil(1^st_T₎ = 1.05 ×10⁻²) ; Q_water

= 0.854 ml/min (We_water = 0.318); Q_air = 1.789 ml/min (We_air = 1.41

×10⁻²)) (b) D3 distributor (Q_oil = 12 ml/min (Ca_oil(1^st_T₎ = 1.05 ×10⁻²) ; Q_water = 0.854 ml/min (We_water = 0.318); Q_air = 1.789 ml/min (We_air = 3.58 ×10⁻³)). . . 71

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3.5 Effect of distributors on bubble formation frequencies, expressed in terms of Ca_oil(1^st_T₎ at fixed Q_water = 0.854 ml/min (We_water = 0.318)and Q_air = 1.789 ml/min (We_air = 5.09 ×10⁻⁵ − 1.41 ×10⁻²) . . . 72 3.6 Formation dynamics of drops at 2^nd T−junction in D3 distributor (Q_oil =

4 ml/min (Ca_oil(1^st_T₎ = 1.75 ×10⁻³) ; Q_water = 0.854 ml/min (We_water = 0.318); Q_air = 1.789 ml/min (We_air = 3.58 ×10⁻³)) . . . 73 3.7 Flow regimes observed for various capillary numbers at 2^nd T−junction (a,

c, e) D2 distributor (b, d, f) D6 distributor . . . 74 3.8 Effect of distributors on gas−liquid−liquid flow regimes for flow regimes

observed in D1 distributor (left side images) and flow regimes observed in D4 distributor (right side images) at Q_oil of (a) 2 ml/min (b) 4 ml/min (c) 6 ml/min (d) 8 ml/min (e) 10 ml/min (f) 12 ml/min (Ca_oil(2^nd_T₎ = 8.77

× 10⁻⁴ − 4.39 × 10⁻³ ; Ca_oil(1^st_T₎ = 1.75 × 10⁻³ − 8.77 × 10⁻³) at fixed Q_water = 0.854 ml/min (We_water = 0.318) and Q_air = 1.789 ml/min (We_air

= 5.09× 10⁻⁵ −1.41 × 10⁻²) . . . 76 3.9 Effect of distributors on gas−liquid−liquid flow regimes for flow regimes

observed in D5 distributor (left side images) and flow regimes observed in D3 distributor (right side images) at Q_oil of (a) 2 ml/min (b) 4 ml/min (c) 6 ml/min (d) 8 ml/min (e) 10 ml/min (f) 12 ml/min (Ca_oil(2^nd_T₎ = 8.77

× 10⁻⁴ − 4.39 × 10⁻³ ; Ca_oil(1^st_T₎ = 1.75 × 10⁻³ − 8.77 × 10⁻³) at fixed Q_water = 0.854 ml/min (We_water = 0.130−0.318) and Q_air = 1.789 ml/min (We_air = 3.58× 10⁻³ −1.41 × 10⁻² ) . . . 78

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3.10 Effect of distributors on dimensionless lengths of bubbles/drops or slugs expressed in terms of Ca_oil(1^st_T₎ and Ca_oil(2ndT) for Q_oil = 1−12 ml/min at fixed Q_water = 0.854 ml/min (We_water = 0.00453−0.318) and Q_air = 1.789 ml/min (We_air = 5.09 ×10⁻⁵ − 1.41 ×10⁻²)(a) Lengths of bubbles/slugs for Ca_oil(1^st_T₎ = 8.77 ×10⁻⁴ −1.05 × 10⁻³ (b) Lengths of drops/slugs for Ca_oil(2^nd_T₎ = 4.39× 10⁻⁴ − 5.26 × 10⁻³. . . 81 3.11 Schematic view of T−junction microchannel configurations to create three-

phase gas−in−water−in−oil emulsions (d_h = 0.97 mm). . . 83 3.12 Formation dynamics of double emulsions at 2^nd T−junction with Q_oil = 4

ml/min (Ca_oil(2^nd_T₎ = 1.61× 10⁻²), Q_air = 0.942 ml/min (We_air = 2.57× 10⁻³), Q_water+SDS = 1.330 ml/min (Ca_water(1^st_T₎ = 6.67 ×10⁻⁴; We_water = 1.51 × 10⁻²) for 0.3 wt/wt% water-SDS mixture. . . 84 3.13 Three-phase gas−in−water−in−oil emulsions observed in a T−junction

microchannel at fixed Q_air= 0.942 ml/min (a) Q_oil= 4 ml/min; Qwater+0.3wt/wt%SDS

= 1.807 ml/min (b)Q_oil = 2 ml/min; Qwater+0.3wt/wt%SDS = 1.807 ml/min (c) Q_oil = 4 ml/min ; Qwater+0.3wt/wt%SDS = 2.760 ml/min (d) Q_oil = 4

ml/min; Qwater+2wt/wt%SDS= 1.807 ml/min (e) Q_oil= 4 ml/min ; Qwater+2wt/wt%SDS

= 2.760 ml/min. . . 86

4.1 Solution domain and boundary conditions (a) T−junction (W_Ch = D_Ch = W_GI = D_GI = 1 mm for present work; W_Ch = D_Ch = W_GI = D_GI = 0.8 mm for (Vansteijn et al., 2008)) (b) Y−junction (W_Ch = D_Ch = W_GI = D_GI = 1 mm for present work. . . 102

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4.2 Bubble formation dynamics (a) experiments (Vansteijn et al., 2008) (T = 170 ms) (b) simulations (present work) (T = 167 ms) (Q_G = 0.6 ml/min, Q_L= 0.4 ml/min, A_GI = 0.8×0.8 mm²; A_Ch= 0.8×0.8 mm²; air−ethanol system). . . 104 4.3 Comparison of predicted (present work with OpenFoam v1.6 and Fluent

6.3) and measured (Vansteijn et al., 2008) L_B/W_Ch for different Q_G/Q_L (A_GI = 0.8× 0.8 mm²; A_Ch = 0.8× 0.8 mm² ; air−ethanol system. . . 105 4.4 Dynamics of bubble formation at different static contact angle values (a)0^◦

(b)30^◦ (c) 60^◦ (d)90^◦ (e)120^◦ (f)180^◦ . . . 106 4.5 Numerical predictions of flow regimes in a T−junction microchannel at

different gas and liquid velocities (a) bubbly flow (U_G = 0.085 m/s, U_L = 0.44 m/s), (b) slug flow (U_G = 0.085 m/s, U_L = 0.189 m/s), (c) slug flow (U_G = 0.085 m/s, U_L = 0.093 m/s) and (d) long slug flow (U_G = 0.085 m/s, U_L = 0.031 m/s) (A_GI = 1× 1 mm²; A_Ch = 1 × 1 mm² ; air−water system). . . 108 4.6 Numerical predictions of flow regimes in a Y−junction microchannel at

different gas and liquid velocities (a) bubbly flow (U_G =0.085 m/s, U_L = 0.792 m/s), (b) slug flow (U_G =0.0859 m/s, U_L= 0.189 m/s), (c) slug flow (U_G =0.085 m/s, U_L = 0.094 m/s), (d) long slug flow (U_G =0.085 m/s, U_L

= 0.030 m/s); (A_GI = 1 × 1 mm²; A_Ch = 1 × 1 mm² ; air−water system). 110 4.7 Comparision of observed and predicted lengths of air bubbles/slugs in T−

and Y−junction microchannel (at fixed Q_air = 5.07 ml/min, W e_air = 4.29×10⁻⁴).. . . 111

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4.8 Effect of channel size on the slug length (a) A_GI = A_Ch = 0.8×0.8 mm²,(b) A_GI = A_Ch = 0.4× 0.4 mm² and (c) A_GI = A_Ch = 0.2× 0.2 mm² (Q_G = 1.011 ml/min; Q_L = 1.6 ml/min; air−ethanol system). . . 112 4.9 Controlled generation of bubbles/slugs in a T−junction microchannel (a)

Q_L= 0.2 (b) Q_L = 0.4 (c) Q_L= 1 and (d) Q_L= 2.4 (Q_G= 0.6 (all ml/min

; A_GI = 0.2 × 0.2 mm²; A_Ch = 0.8 × 0.8 ²; air−ethanol system). . . 115 4.10 Effect of gas inlet cross section area on the slug length (a) A_GI = 0.4 ×0.8

mm², (b) A_GI = 0.8 ×0.8 mm² and (c) A_GI = 1.6 × 0.8 mm² (A_Ch = 0.8

× 0.8 mm²; Q_G = 1.011 ml/min; Q_L = 1.6 ml/min; air−ethanol system). . 115 4.11 . Effect of surface tension on gas slug length (a) _σ^σ? = 0.1; (b) _σ^σ? = 0.5;

(c) _σ^σ? = 1; (d) _σ^σ? = 5; (e) _σ^σ? = 10 (Q_G = 0.6 ml/min; Q_L = 0.4 ml/min, A_GI = 0.8 ×0.8 mm², A_Ch = 0.8 ×0.8 mm², σ^? for air−ethanol system is 0.0224 N/m). . . 116 4.12 A parity plot of dimensionless gas slug lengths observed in experiments and

simulation and predicted using the unified correlation (Equation. 4.13) . . 118

5.1 Solution domain and boundary conditions used in the numerical simulations (a) Geometry−1 (b) Geometry−2 . . . 127 5.2 Different T−orientations(a) T−orientation−1 (b) Tee−orientation−2 . . . 128 5.3 Point pressure locations (a) 1^st−T with point pressure P1 (b) 2^nd−T with

point pressure P2 . . . 128

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5.4 (a) Predicted formation dynamics of a air slug at 1^st T−junction for Q_oil= 5 ml/min (Ca_oil(1^st_T₎ = 4.39×10⁻³),Q_water= 2.76 ml/min (We_water = 4.54

× 10⁻¹) Q_air= 5.24 ml/min (We_air = 4.37 × 10⁻⁴) for 0.3 wt/wt % of water+SDS mixture. In this and all subsequent images, gas bubbles/slugs are seen in yellow. (b) Effect of Ca_oil(1^st_T₎ on point pressure at 1^st T−junction130 5.5 Predicted formation dynamics of a air bubble at 1^st T−junction for Q_oil=

15 ml/min (Ca_oil(1^st_T₎ = 0.0132), Q_water= 2.76 ml/min (We_water = 4.54

× 10⁻¹) Q_air= 5.24 ml/min (We_air = 4.37 × 10⁻⁴) for 0.3 wt/wt % of water+SDS mixture. . . 132 5.6 (a) Predicted formation dynamics of a water slug at the 2^nd T−junction

(a) 0.3 wt/wt% and (b) 2 wt/wt% water+SDS mixture (Q_oil= 5 ml/min (Ca_oil(2^nd_T₎ = 0.020, 0.036),Q_water= 2.76 ml/min (We_water = 0.454, 0.757) Q_air= 5.24 ml/min (We_air= 4.37×10⁻⁴) In this and all subsequent images, air bubbles/slugs are seen in yellow color and water drops/slugs are seen in blue color. . . 134 5.7 Pressure flutuations at the at 2^nd T−junction . . . 135 5.8 (a) Predicted formation dynamics of a water slug at the 2^nd T−junction

(a) 0.3 wt/wt% and (b) 2 wt/wt% water+SDS mixture (Q_oil= 15 ml/min (Ca_oil(2^nd_T₎ = 0.060, 1.01), Q_water= 2.76 ml/min (We_water = 0.454, 0.757) Q_air= 5.24 ml/min (We_air = 4.37× 10⁻⁴). . . 138 5.9 A comparison of experimental and predicted flow regimes (Q_water= 2.76

ml/min;Q_air = 5.42 ml/min, 0.3 wt/wt % of water−SDS mixture) (a) Q_oil

=15; (b) Q_oil=10; (c) Q_oil=5; (d) Q_oil =3 (all in ml/min) . . . 140

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5.10 A comparison of experimental and predicted flow regimes (Q_water= 2.76 ml/min; Q_air = 5.42 ml/min, 2 wt/wt % of water−SDS mixture) (a) Q_oil

=15; (b) Q_oil=10; (c) Q_oil=5; (d)Q_oil =3 (all in ml/min) . . . 141 5.11 3D view of predicted flow regimes (Q_water= 2.76 ml/min; Q_air = 5.42

ml/min, 0.3 wt/wt % of water−SDS mixture) (a) Q_oil =15; (b) Q_oil=10;

(c) Q_oil=5; (d)Q_oil =3 (all in ml/min). . . 142 5.12 3D view of predicted flow regimes (Q_water= 2.76 ml/min; Q_air = 5.42

ml/min, 2 wt/wt % of water−SDS mixture) (a) Q_oil =15; (b) Q_oil=10;

(c) Q_oil=5; (d)Q_oil =3 (all in ml/min). . . 142 5.13 A comparison of predicted and measured lengths for of (a) air bubbles/slugs

(b) water drop/slugs at fixedQ_water= 2.76 ml/min (We_water = 4.54× 10⁻¹ for 0.3 wt/wt% SDS mixture and 7.57× 10⁻¹ for 2 wt/wt% SDS mixture) and Q_air= 5.24 ml/min (We_air = 4.37 × 10⁻⁴). . . 144 5.14 A comparison of predicted and measured lengths for effect of We_air on

(a) gas bubbles/slugs (b) water drop/slugs at fixed Q_water= 2.76 ml/min (We_water = 4.54 × 10⁻¹ for 0.3 wt/wt% SDS mixture and 7.57 × 10⁻¹ for 2 wt/wt% SDS mixture), and Q_oil= 5 and 15 ml/min (Ca_oil,(1^st_T₎ = 4.39 x 10⁻³, 1.32 x 10⁻²; Ca_oil,2^nd_T = 2.02 x 10⁻², 6.05 x 10⁻² for 0.3 wt/wt%

SDS mixture and Ca_oil,2^nd_T = 3.36 x 10⁻², 1.01 x 10⁻¹ for 2 wt/wt% SDS mixture) . . . 147

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5.15 A comparison of predicted and measured lengths for effect of We_water (=4.31×10⁻² −4.29 for 0.3 wt/wt% SDS mixture and 7.18×10⁻² −7.14 for 2 wt/wt% SDS mixture) of (a) gas bubbles/slugs (b) water drop/slugs at fixed Q_air= 5.24 ml/min (We_air = 4.37 × 10⁻⁴)and Q_oil= 5 and 15 ml/min (Ca_oil,(1^st_T₎ = 4.39 x 10⁻³, 1.32 x 10⁻²; Ca_oil,2ndT = 2.02 x 10⁻², 6.05 x 10⁻² for 0.3 wt/wt% SDS mixture and Ca_oil,2^nd_T = 3.36 x 10⁻², 1.01 x 10⁻¹ for 2 wt/wt% SDS mixture) . . . 149 5.16 Predicted formation dynamics of air slug at 1^nd T−junction (a) D1 dis-

tributor and (b) D2 distributor (Q_oil = 0.6 ml/min (Ca_oil(1^st_T₎ = 2 × 10⁻³),Q_air = 0.5 ml/min (We_air = 1.36 ×10⁻⁴, 2.95×10⁻⁵), Q_water = 0.3 ml/min (We_water = 0.184, 3.99×10⁻²), 0.3 wt/wt % of water−SDS mixture.153 5.17 Predicted formation dynamics of water slug at 2^ndT−junction (a) T−Orientation−1

(b) T−Orientation−2 (Q_oil = 0.6 ml/min (Ca_oil(2^nd_T₎ = 2.55 × 10⁻²),Q_air

= 0.5 ml/min (We_air = 1.36 × 10⁻⁴), Q_water = 0.3 ml/min (We_water = 0.184), 0.3 wt/wt % of water−SDS mixture. . . 155 5.18 A predicted 3−D view of two Drop−Slug (2D−S) gas−liquid−liquid flow

regime at Q_water = 0.3 ml/min, Q_air = 0.5 ml/min and Q_oil = 0.6 ml/min (0.3 wt/wt % of water−SDS mixture) . . . 156 5.19 Effect of inlet distributors on dimensionless lengths of air and water slugs

expressed in terms of Ca_oil(1^st_T₎ (= 1.33 × 10⁻³ − 2.67 × 10⁻³) and Ca_oil(2^nd_T₎ (= 6.13 × 10⁻³ − 1.22 × 10⁻²) for Q_oil = 0.4 − 0.8 ml/min, at fixed Q_water = 0.3 ml/min (We_water = 0.1848 and 0.0399) and Q_air = 0.5 ml/min (We_air= 1.36×10⁻⁴ and 2.95×10⁻⁵), 0.3 wt/wt % of water−SDS mixture. . . 158

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5.20 Effect of T−orientations on dimensionless lengths of air and water slugs expressed in terms of Ca_oil(1^st_T₎(= 1.85×10⁻³ −7.40×10⁻³) and Ca_oil(2ndT)

(= 8.51×10⁻³ −3.40×10⁻²) for Q_oil = 0.2−0.8 ml/min, at fixed Q_water

= 0.3 ml/min (We_water = 0.1848 and 0.0399) and Q_air = 0.5 ml/min(We_air

= 1.36 × 10⁻⁴ and 2.95 × 10⁻⁵), 0.3 wt/wt % of water−SDS mixture.. . . 159 5.21 Effect of channel aspect ratios on dimensionless lengths for for Q_oil = 0.4

− 0.8 ml/min at fixed Q_water = 0.3 ml/min (We_water = 0.1848 and 0.0399) and Q_air = 0.5 ml/min(We_air = 1.36× 10⁻⁴ and 2.95 × 10⁻⁵), 0.3 wt/wt

% of water−SDS mixture (a) air bubbles/slugs (Ca_oil(1^st_T₎ (= 3.70 × 10⁻³

− 7.40 × 10⁻³ for CH2, 1.33 × 10⁻³ − 2.67 × 10⁻³ for CH1) (b) water drops/slugs (Ca_oil(2ndT) (= 1.70 × 10⁻² − 3.41 × 10⁻² for CH2, 6.13 × 10⁻³ −1.23 ×10⁻² for CH1) . . . 161

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List of Tables

2.1 Physical properties of fluids . . . 25

2.2 Surface/interfacial tension of fluids . . . 26

2.3 Measured contact angles on PMMA surface . . . 26

2.4 Microchannel dimensions . . . 26

3.1 Distributor configurations used in present work . . . 64

4.1 Summary of correlations for prediction of gas and liquid slug lengths avail- able in the literature . . . 94

4.2 Boundary conditions used in the present work . . . 101

4.3 Discretization schemes used in present work . . . 101

4.4 Effect of grid resolution on slug formation period and gas slug length . . . 105

4.5 Effect channel size on predicted gas slug length for air−ethanol flow in T−junction microchannel . . . 112

4.6 Effect of gas−liquid distributor on predicted gas slug length for air−ethanol flow in T−junction microchannel . . . 114

5.1 Flow rates and Dimensionless Numbers used in the present G/L/L simulations . . . 128

5.2 Microchannel Configurations . . . 152 xix

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Nomenclature

Notations

U_G superficial velocity of gas phase, m/s UL superficial velocity of liquid phase, m/s Q_water volumetric flowrate of water, m³/s Q_oil volumetric flowrate of oil, m³/s dh hydraulic diameter, mm

Ca capillary number, (Ca=µ∗U/σ)

Ca_oil capillary number for oil phase-defined at 1^st T-junction as Caoil = µoilUoil/σail−oil

and at the 2^nd T-junction as Ca_oil= µ_oilU_oil/σwater−oil

AGI cross sectional area of gas inlet distributor, mm²

A_ch cross sectional area of channel, mm²

we_water weber number of water, (we_water =

d_hU²_waterρ_water)/σwater−oil)

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we_air weber number of air, (we_air= d_hU²_airρ_air /σair−oil))

ρ_air density of air

ρ_air−oil density of air and oil, kg/m³

d diameter of channel, m

D channel depth, m

w channel width, m

H channel hight, m

L length of main channel/solution domain, m F frequency of bubble of slug formation, 1/s T bubble formation period, s

R curvature

g gravitational constant, m/s²

n surface normal vector

P pressure, Pa

t time, s

U superficial velocity, m/s u mean liquid velocity, m/s

Re Reynolds number (=ρ∗d∗U/µ)

W_i gas inlet

Greek letters

α volume fraction, dimensionless xxii

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µ molecular visocity, Pa.s

θ contact angle

ρ density, kg/m³

σ surface tension, N/m

φ line constant

ε gas hold-up or volumetric fraction

Υ ratio of gas inlet width and channel width β geometrical angle of entry of gas in main

channel at junction

Subscripts

g, G, Air gas phase l, L, liquid liquid phase

oil oil phase

B bubble

a axial curvature

r radial curvature

L laplace

Ch channel

GI gas inlet

GI gas inlet distributor air−oil air and oil

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Acronyms

SDS Sodium Dodecyl Sulfate PMMA Polymethyl methacrylate

VOF Volume-of-Fluid

OpenFOAM Open Field Operation and Manipulation

xxiv

Experimental and numerical investigations of gas-liquid and gas-liquid-liquid flows in microchannels

EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF GAS−LIQUID AND GAS−LIQUID−LIQUID FLOWS IN

MICROCHANNELS

V. M. RAJESH

DEPARTMENT OF CHEMICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

NEW DELHI - 110016

AUGUST 2015

EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF GAS−LIQUID AND GAS−LIQUID−LIQUID FLOWS IN

MICROCHANNELS

by

V. M. RAJESH

Department of Chemical Engineering

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI

AUGUST 2015

Dedicated to My Parents, Wife and My Sons.

Certificate

Acknowledgments

Abstract

Contents

List of Figures

List of Tables

Nomenclature

Notations

Greek letters

Subscripts

Acronyms