Abstract

Recently, the number of uses of bubbles has begun to increase dramatically, with medicine, biofuel production, and wastewater treatment just some of the industries taking advantage of bubble properties, such as high mass transfer. As a result, more and more focus is being placed on the understanding and control of bubble formation processes and there are currently numerous techniques utilized to facilitate this understanding. Acoustic bubble sizing (ABS) and laser scattering techniques are able to provide information regarding bubble size and size distribution with minimal data processing, a major advantage over current optical-based direct imaging approaches. This paper demonstrates how direct bubble-imaging methods can be improved upon to yield high levels of automation and thus data comparable to ABS and laser scattering. We also discuss the added benefits of the direct imaging approaches and how it is possible to obtain considerable additional information above and beyond that which ABS and laser scattering can supply. This work could easily be exploited by both industrial-scale operations and small-scale laboratory studies, as this straightforward and cost-effective approach is highly transferrable and intuitive to use.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article

Corrections

Daniel J. Wesley, Daniel T. W. Toolan, Stuart A. Brittle, Jonathan R. Howse, and William B. Zimmerman, "Development of an optical microscopy system for automated bubble cloud analysis: publisher’s note," Appl. Opt. 55, 7392-7392 (2016)
http://proxy.osapublishing.org/ao/abstract.cfm?uri=ao-55-26-7392

10 August 2016: Corrections were made to the author listing and funding.

7 September 2016: A correction was made to the copyright.


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References

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    [Crossref]
  2. J. C. Quinn and R. Davis, “The potentials and challenges of algae based biofuels: a review of the techno-economic, life cycle, and resource assessment modeling,” Bioresour. Technol. 184, 444–452 (2015).
    [Crossref]
  3. P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
    [Crossref]
  4. G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
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  5. D. Das and T. N. Veziroğlu, “Hydrogen production by biological processes: a survey of literature,” Int. J. Hydrogen Energy 26, 13–28 (2001).
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  6. H. Gaffron and J. Rubin, “Fermentative and photochemical production of hydrogen in algae,” J. Gen. Physiol. 26, 219–240 (1942).
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  7. B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
    [Crossref]
  8. A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
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  10. W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
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  11. J. Hanotu, “Algal growth enhancement mediated by CO2 enriched microbubbles,” M.Sc. dissertation (Environmental and Energy Engineering, University of Sheffield, 2009).
  12. K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
    [Crossref]
  13. C. Gudin and C. Thepenier, “Bioconversion of solar energy into organic chemicals by microalgae,” Adv. Biotechnol. Processes 6, 73–110 (1986).
  14. E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
    [Crossref]
  15. V. Tesař, C.-H. Hung, and W. B. Zimmerman, “No-moving-part hybrid-synthetic jet actuator,” Sens. Actuators A 125, 159–169 (2006).
    [Crossref]
  16. W. B. Zimmerman, V. Tesař, and H. C. H. Bandulasena, “Towards energy efficient nanobubble generation with fluidic oscillation,” Curr. Opin. Colloid Interface Sci. 16, 350–356 (2011).
    [Crossref]
  17. V. Tesař, “Configurations of fluidic actuators for generating hybrid-synthetic jets,” Sens. Actuators A 138, 394–403 (2007).
    [Crossref]
  18. V. Tesař, “Microbubble generation by fluidics. Part I: development of the oscillator,” in Colloquium Fluid Dynamics (2012).
  19. J. Hanotu, H. Bandulasena, and W. B. Zimmerman, “Microflotation performance for algal separation,” Biotechnol. Bioeng. 109, 1663–1673 (2012).
    [Crossref]
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    [Crossref]
  22. G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
    [Crossref]
  23. M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
    [Crossref]
  24. J. Lighthill, “Acoustic streaming,” J. Sound Vibration 61, 391–418 (1978).
    [Crossref]
  25. T. Leighton, The Acoustic Bubble (Academic, 1994).
  26. S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
    [Crossref]
  27. W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
    [Crossref]
  28. J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
    [Crossref]
  29. M. K. H. Al-Mashhadani, H. C. H. Bandulasena, and W. B. Zimmerman, “CO2 mass transfer induced through an airlift loop by a microbubble cloud generated by fluidic oscillation,” Ind. Eng. Chem. Res. 51, 1864–1877 (2012).
    [Crossref]
  30. J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
    [Crossref]
  31. Bubble analyzer JOSA.vi. file, figshare (2016). https://dx.doi.org/10.6084/m9.figshare.3462590.v1 .
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  33. Multi bubble calibration sub_v11 state machine.vi. file, figshare (2016). https://dx.doi.org/10.6084/m9.figshare.3462596.v1 .

2015 (3)

J. C. Quinn and R. Davis, “The potentials and challenges of algae based biofuels: a review of the techno-economic, life cycle, and resource assessment modeling,” Bioresour. Technol. 184, 444–452 (2015).
[Crossref]

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

2014 (1)

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

2013 (2)

J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
[Crossref]

K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
[Crossref]

2012 (3)

J. Hanotu, H. Bandulasena, and W. B. Zimmerman, “Microflotation performance for algal separation,” Biotechnol. Bioeng. 109, 1663–1673 (2012).
[Crossref]

M. K. H. Al-Mashhadani, H. C. H. Bandulasena, and W. B. Zimmerman, “CO2 mass transfer induced through an airlift loop by a microbubble cloud generated by fluidic oscillation,” Ind. Eng. Chem. Res. 51, 1864–1877 (2012).
[Crossref]

G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
[Crossref]

2011 (2)

W. B. Zimmerman, V. Tesař, and H. C. H. Bandulasena, “Towards energy efficient nanobubble generation with fluidic oscillation,” Curr. Opin. Colloid Interface Sci. 16, 350–356 (2011).
[Crossref]

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

2009 (1)

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

2008 (3)

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
[Crossref]

W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
[Crossref]

2007 (2)

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

V. Tesař, “Configurations of fluidic actuators for generating hybrid-synthetic jets,” Sens. Actuators A 138, 394–403 (2007).
[Crossref]

2006 (1)

V. Tesař, C.-H. Hung, and W. B. Zimmerman, “No-moving-part hybrid-synthetic jet actuator,” Sens. Actuators A 125, 159–169 (2006).
[Crossref]

2003 (1)

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

2001 (1)

D. Das and T. N. Veziroğlu, “Hydrogen production by biological processes: a survey of literature,” Int. J. Hydrogen Energy 26, 13–28 (2001).
[Crossref]

2000 (1)

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

1992 (1)

W. Sowa, “Interpreting mean drop diameters using distribution moments,” Atomization Sprays 2, 1–15, 1992.
[Crossref]

1986 (1)

C. Gudin and C. Thepenier, “Bioconversion of solar energy into organic chemicals by microalgae,” Adv. Biotechnol. Processes 6, 73–110 (1986).

1978 (1)

J. Lighthill, “Acoustic streaming,” J. Sound Vibration 61, 391–418 (1978).
[Crossref]

1942 (1)

H. Gaffron and J. Rubin, “Fermentative and photochemical production of hydrogen in algae,” J. Gen. Physiol. 26, 219–240 (1942).
[Crossref]

Al-Mashhadani, M. K. H.

M. K. H. Al-Mashhadani, H. C. H. Bandulasena, and W. B. Zimmerman, “CO2 mass transfer induced through an airlift loop by a microbubble cloud generated by fluidic oscillation,” Ind. Eng. Chem. Res. 51, 1864–1877 (2012).
[Crossref]

Bandulasena, H.

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

J. Hanotu, H. Bandulasena, and W. B. Zimmerman, “Microflotation performance for algal separation,” Biotechnol. Bioeng. 109, 1663–1673 (2012).
[Crossref]

Bandulasena, H. C.

W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
[Crossref]

Bandulasena, H. C. H.

J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
[Crossref]

M. K. H. Al-Mashhadani, H. C. H. Bandulasena, and W. B. Zimmerman, “CO2 mass transfer induced through an airlift loop by a microbubble cloud generated by fluidic oscillation,” Ind. Eng. Chem. Res. 51, 1864–1877 (2012).
[Crossref]

W. B. Zimmerman, V. Tesař, and H. C. H. Bandulasena, “Towards energy efficient nanobubble generation with fluidic oscillation,” Curr. Opin. Colloid Interface Sci. 16, 350–356 (2011).
[Crossref]

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

Belarbi, E.-H.

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

Biggs, C.

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

Brittle, S.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

Butler, S.

W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
[Crossref]

Chisti, Y.

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

Chiu, T. Y.

J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
[Crossref]

Das, D.

D. Das and T. N. Veziroğlu, “Hydrogen production by biological processes: a survey of literature,” Int. J. Hydrogen Energy 26, 13–28 (2001).
[Crossref]

Davis, R.

J. C. Quinn and R. Davis, “The potentials and challenges of algae based biofuels: a review of the techno-economic, life cycle, and resource assessment modeling,” Bioresour. Technol. 184, 444–452 (2015).
[Crossref]

Desai, P.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

Du, H.

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

Dunbar, A.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

Dunderdale, G.

G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
[Crossref]

Ebbens, S.

G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
[Crossref]

Fairclough, P.

G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
[Crossref]

Fernández, F. A.

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

Forestier, M.

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

Gaffron, H.

H. Gaffron and J. Rubin, “Fermentative and photochemical production of hydrogen in algae,” J. Gen. Physiol. 26, 219–240 (1942).
[Crossref]

Ghirardi, M. L.

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

Gilmour, D. J.

K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
[Crossref]

Grima, E. M.

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

Gudin, C.

C. Gudin and C. Thepenier, “Bioconversion of solar energy into organic chemicals by microalgae,” Adv. Biotechnol. Processes 6, 73–110 (1986).

Hankamer, B.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Hanotu, J.

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
[Crossref]

J. Hanotu, H. Bandulasena, and W. B. Zimmerman, “Microflotation performance for algal separation,” Biotechnol. Bioeng. 109, 1663–1673 (2012).
[Crossref]

J. Hanotu, “Algal growth enhancement mediated by CO2 enriched microbubbles,” M.Sc. dissertation (Environmental and Energy Engineering, University of Sheffield, 2009).

Hemaka Bandulasena, H. C.

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

Hewakandamby, B. N.

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

Howell, R.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

Howse, J.

G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
[Crossref]

Hung, C.-H.

V. Tesař, C.-H. Hung, and W. B. Zimmerman, “No-moving-part hybrid-synthetic jet actuator,” Sens. Actuators A 125, 159–169 (2006).
[Crossref]

James Gilmour, D.

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

Jones, S. T.

S. T. Jones, “Gas-liquid mass transfer in an external airlift loop reactor for syngas fermentation: ProQuest,” in Retrospective Theses and Dissertations (2007), paper 15547, http://lib.dr.iastate.edu/rtd/15547 .

Karunakaran, E.

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

Kruse, O.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Lehr, F.

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Leighton, T.

T. Leighton, The Acoustic Bubble (Academic, 1994).

Lighthill, J.

J. Lighthill, “Acoustic streaming,” J. Sound Vibration 61, 391–418 (1978).
[Crossref]

Liu, X.

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

Mao, G.

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

Marx, U. C.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

Medina, A. R.

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

Melis, A.

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

Mussgnug, J. H.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Ng, W. C.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

Omotowa, O. A.

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

Posten, C.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Quinn, J. C.

J. C. Quinn and R. Davis, “The potentials and challenges of algae based biofuels: a review of the techno-economic, life cycle, and resource assessment modeling,” Bioresour. Technol. 184, 444–452 (2015).
[Crossref]

Rubin, J.

H. Gaffron and J. Rubin, “Fermentative and photochemical production of hydrogen in algae,” J. Gen. Physiol. 26, 219–240 (1942).
[Crossref]

Rupprecht, J.

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Sanada, T.

M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
[Crossref]

Sato, A.

M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
[Crossref]

Schenk, P. M.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

Seibert, M.

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

Shi, Y.

K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
[Crossref]

Shirota, M.

M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
[Crossref]

Sowa, W.

W. Sowa, “Interpreting mean drop diameters using distribution moments,” Atomization Sprays 2, 1–15, 1992.
[Crossref]

Stephens, E.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

Tesar, V.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

W. B. Zimmerman, V. Tesař, and H. C. H. Bandulasena, “Towards energy efficient nanobubble generation with fluidic oscillation,” Curr. Opin. Colloid Interface Sci. 16, 350–356 (2011).
[Crossref]

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
[Crossref]

V. Tesař, “Configurations of fluidic actuators for generating hybrid-synthetic jets,” Sens. Actuators A 138, 394–403 (2007).
[Crossref]

V. Tesař, C.-H. Hung, and W. B. Zimmerman, “No-moving-part hybrid-synthetic jet actuator,” Sens. Actuators A 125, 159–169 (2006).
[Crossref]

V. Tesař, “Microbubble generation by fluidics. Part I: development of the oscillator,” in Colloquium Fluid Dynamics (2012).

Thepenier, C.

C. Gudin and C. Thepenier, “Bioconversion of solar energy into organic chemicals by microalgae,” Adv. Biotechnol. Processes 6, 73–110 (1986).

Thomas-Hall, S. R.

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

Veziroglu, T. N.

D. Das and T. N. Veziroğlu, “Hydrogen production by biological processes: a survey of literature,” Int. J. Hydrogen Energy 26, 13–28 (2001).
[Crossref]

Wang, L.

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

Watanabe, M.

M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
[Crossref]

Ying, K.

K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
[Crossref]

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

Zandi, M.

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

Zhang, L.

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

Zimmerman, W. B.

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
[Crossref]

K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
[Crossref]

J. Hanotu, H. Bandulasena, and W. B. Zimmerman, “Microflotation performance for algal separation,” Biotechnol. Bioeng. 109, 1663–1673 (2012).
[Crossref]

M. K. H. Al-Mashhadani, H. C. H. Bandulasena, and W. B. Zimmerman, “CO2 mass transfer induced through an airlift loop by a microbubble cloud generated by fluidic oscillation,” Ind. Eng. Chem. Res. 51, 1864–1877 (2012).
[Crossref]

W. B. Zimmerman, V. Tesař, and H. C. H. Bandulasena, “Towards energy efficient nanobubble generation with fluidic oscillation,” Curr. Opin. Colloid Interface Sci. 16, 350–356 (2011).
[Crossref]

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
[Crossref]

V. Tesař, C.-H. Hung, and W. B. Zimmerman, “No-moving-part hybrid-synthetic jet actuator,” Sens. Actuators A 125, 159–169 (2006).
[Crossref]

Zuo, J.

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

Adv. Biotechnol. Processes (1)

C. Gudin and C. Thepenier, “Bioconversion of solar energy into organic chemicals by microalgae,” Adv. Biotechnol. Processes 6, 73–110 (1986).

Appl. Energy (1)

W. B. Zimmerman, M. Zandi, H. C. Hemaka Bandulasena, V. Tesař, D. James Gilmour, and K. Ying, “Design of an airlift loop bioreactor and pilot scales studies with fluidic oscillator induced microbubbles for growth of a microalgae Dunaliella salina,” Appl. Energy 88, 3357–3369 (2011).
[Crossref]

Atomization Sprays (1)

W. Sowa, “Interpreting mean drop diameters using distribution moments,” Atomization Sprays 2, 1–15, 1992.
[Crossref]

Biochem. Eng. J. (1)

J. Hanotu, E. Karunakaran, H. Bandulasena, C. Biggs, and W. B. Zimmerman, “Harvesting and dewatering yeast by microflotation,” Biochem. Eng. J. 82, 174–182 (2014).
[Crossref]

BioEnergy Res. (1)

P. M. Schenk, S. R. Thomas-Hall, E. Stephens, U. C. Marx, J. H. Mussgnug, C. Posten, O. Kruse, and B. Hankamer, “Second generation biofuels: high-efficiency microalgae for biodiesel production,” BioEnergy Res. 1, 20–43 (2008).
[Crossref]

Bioresour. Technol. (1)

J. C. Quinn and R. Davis, “The potentials and challenges of algae based biofuels: a review of the techno-economic, life cycle, and resource assessment modeling,” Bioresour. Technol. 184, 444–452 (2015).
[Crossref]

Biotechnol. Adv. (1)

E. M. Grima, E.-H. Belarbi, F. A. Fernández, A. R. Medina, and Y. Chisti, “Recovery of microalgal biomass and metabolites: process options and economics,” Biotechnol. Adv. 20, 491–515 (2003).
[Crossref]

Biotechnol. Bioeng. (1)

J. Hanotu, H. Bandulasena, and W. B. Zimmerman, “Microflotation performance for algal separation,” Biotechnol. Bioeng. 109, 1663–1673 (2012).
[Crossref]

Chem. Eng. Res. Design (1)

S. Brittle, P. Desai, W. C. Ng, A. Dunbar, R. Howell, V. Tesař, and W. B. Zimmerman, “Minimising microbubble size through oscillation frequency control,” Chem. Eng. Res. Design 104, 357–366 (2015).
[Crossref]

Curr. Opin. Colloid Interface Sci. (1)

W. B. Zimmerman, V. Tesař, and H. C. H. Bandulasena, “Towards energy efficient nanobubble generation with fluidic oscillation,” Curr. Opin. Colloid Interface Sci. 16, 350–356 (2011).
[Crossref]

Food Bioprod. Process. (1)

W. B. Zimmerman, B. N. Hewakandamby, V. Tesař, H. C. H. Bandulasena, and O. A. Omotowa, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation,” Food Bioprod. Process. 87, 215–227 (2009).
[Crossref]

Ind. Eng. Chem. Res. (1)

M. K. H. Al-Mashhadani, H. C. H. Bandulasena, and W. B. Zimmerman, “CO2 mass transfer induced through an airlift loop by a microbubble cloud generated by fluidic oscillation,” Ind. Eng. Chem. Res. 51, 1864–1877 (2012).
[Crossref]

Int. J. Hydrogen Energy (1)

D. Das and T. N. Veziroğlu, “Hydrogen production by biological processes: a survey of literature,” Int. J. Hydrogen Energy 26, 13–28 (2001).
[Crossref]

Int. J. Multiphase Flow (1)

J. Hanotu, H. C. H. Bandulasena, T. Y. Chiu, and W. B. Zimmerman, “Oil emulsion separation with fluidic oscillator generated microbubbles,” Int. J. Multiphase Flow 56, 119–125 (2013).
[Crossref]

J. Biomater. Nanobiotechnol. (1)

K. Ying, D. J. Gilmour, Y. Shi, and W. B. Zimmerman, “Growth enhancement of Dunaliella salina by microbubble induced airlift loop bioreactor (ALB)—the relation between mass transfer and growth rate,” J. Biomater. Nanobiotechnol. 4, 1–9 (2013).
[Crossref]

J. Gen. Physiol. (1)

H. Gaffron and J. Rubin, “Fermentative and photochemical production of hydrogen in algae,” J. Gen. Physiol. 26, 219–240 (1942).
[Crossref]

J. Sound Vibration (1)

J. Lighthill, “Acoustic streaming,” J. Sound Vibration 61, 391–418 (1978).
[Crossref]

Langmuir (1)

G. Dunderdale, S. Ebbens, P. Fairclough, and J. Howse, “Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes,” Langmuir 28, 10997–11006 (2012).
[Crossref]

Phys. Fluids (1)

M. Shirota, T. Sanada, A. Sato, and M. Watanabe, “Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase,” Phys. Fluids (1994-present) 20, p. 043301 (2008).
[Crossref]

Physiol. Plant. (1)

B. Hankamer, F. Lehr, J. Rupprecht, J. H. Mussgnug, C. Posten, and O. Kruse, “Photosynthetic biomass and H2 production by green algae: from bioengineering to bioreactor scale‐up,” Physiol. Plant. 131, 10–21 (2007).
[Crossref]

Plant Physiol. (1)

A. Melis, L. Zhang, M. Forestier, M. L. Ghirardi, and M. Seibert, “Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green Alga Chlamydomonas reinhardtii,” Plant Physiol. 122, 127–136 (2000).
[Crossref]

Recent Pat. Eng. (1)

W. B. Zimmerman, V. Tesar, S. Butler, and H. C. Bandulasena, “Microbubble generation,” Recent Pat. Eng. 2, 1–8 (2008).
[Crossref]

Renewable Sustainable Energy Rev. (1)

G. Mao, X. Liu, H. Du, J. Zuo, and L. Wang, “Way forward for alternative energy research: a bibliometric analysis during 1994–2013,” Renewable Sustainable Energy Rev. 48, 276–286 (2015).
[Crossref]

Sens. Actuators A (2)

V. Tesař, “Configurations of fluidic actuators for generating hybrid-synthetic jets,” Sens. Actuators A 138, 394–403 (2007).
[Crossref]

V. Tesař, C.-H. Hung, and W. B. Zimmerman, “No-moving-part hybrid-synthetic jet actuator,” Sens. Actuators A 125, 159–169 (2006).
[Crossref]

Other (8)

J. Hanotu, “Algal growth enhancement mediated by CO2 enriched microbubbles,” M.Sc. dissertation (Environmental and Energy Engineering, University of Sheffield, 2009).

V. Tesař, “Microbubble generation by fluidics. Part I: development of the oscillator,” in Colloquium Fluid Dynamics (2012).

G. L. Chahine, (22nd October 2015). The ABS Acoustic Bubble Spectrometer (Dynaflow inc.). Available: http://www.dynaflow-inc.com/Products/ABS/ABS_General-Presentation.pdf

S. T. Jones, “Gas-liquid mass transfer in an external airlift loop reactor for syngas fermentation: ProQuest,” in Retrospective Theses and Dissertations (2007), paper 15547, http://lib.dr.iastate.edu/rtd/15547 .

T. Leighton, The Acoustic Bubble (Academic, 1994).

Bubble analyzer JOSA.vi. file, figshare (2016). https://dx.doi.org/10.6084/m9.figshare.3462590.v1 .

File to prompt user for input with enter key enabled_v2.vi., figshare (2016). https://dx.doi.org/10.6084/m9.figshare.3462593.v2 .

Multi bubble calibration sub_v11 state machine.vi. file, figshare (2016). https://dx.doi.org/10.6084/m9.figshare.3462596.v1 .

Supplementary Material (3)

NameDescription
» Code 1       Bubble analyzer JOSA.vi. file, figshare.
» Code 2       File to prompt user for input with enter key enabled_v2.vi. file, figshare.
» Code 3       Multi bubble calibration sub_v11 state machine.vi. file, figshare.

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic of microbubble imaging set-up and (b) high-contrast image of a bubble cloud.
Fig. 2.
Fig. 2. Danielsson reconstruction of particle forms from overlapping circular features. (a) The overlapping particles are extrapolated into separate ones by the algorithm (b).
Fig. 3.
Fig. 3. Bubble size distribution of a “pointfour” diffuser disk (25 mm diameter, 3 mm thick) under a steady 2.5    mL / min flow of air into water.
Fig. 4.
Fig. 4. Dependence of rise velocity on bubbles size (mm). Vertical travel was calculated from the ( X , Y ) coordinates of the rising bubble centers. Bubble size was taken as the mean of the largest and smallest radii of each bubble. A bubble with a diameter of 0.38 mm (black) has a rise velocity of 13.9    mm / s ; a 0.70 mm bubble (red) rises at 25.7    mm / s ; a 1.33 mm bubble (blue) rises at 41.6    mm / s ; a 1.95 mm bubble (pink) rises at 65.1    mm / s ; and a 2.25 mm bubble (green) rises at 98.2    mm / s .

Tables (1)

Tables Icon

Table 1. Comparison of the Three Major Bubble Sizing Techniques

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

J = K l S ( c g c l ) ,
SNR = P Q e t [ P Q e t + Dt + N r 2 ] 1 / 2 ,
[ P 8 P 1 P 2 P 7 P 0 P 3 P 6 P 5 P 4 ] .
D [ 1 , 0 ] = 1 n D n .
D [ 3 , 2 ] = 1 n 6 v / A n ,

Metrics