Transport in Porous Media

, Volume 104, Issue 1, pp 25–41 | Cite as

Vascular Structure Design of an Artificial Tree for Microbial Cell Cultivation and Biofuel Production

  • Thomas E. Murphy
  • Evan Fleming
  • Halil Berberoglu


This paper reports the design of a vascular structure for an artificial tree, also known as an evaporation-driven porous substrate bioreactor (PSBR), for efficient biofuel production using microalgae. This system consists of multiple vertical ribs, each of which is made of porous membrane and grows algal cells on its surface as a biofilm. Nutrient medium flow through the reactor is driven by evaporation at the terminal end of the porous membrane, and nutrients are delivered from the porous membrane to the cells by diffusion. Flow through the membrane was modeled as a function of the physico-chemical and morphological properties of the membrane, as well as the environmental parameters governing evaporation. It was determined that under typical operating conditions, the evaporative flux from the evaporator region ranged from about 14 to 66 mg/m\(^2\) s. Moreover, there was a membrane pore radius that maximized nutrient medium flow as a result of the competition between capillary, viscous, and gravitational forces. For the range of evaporative fluxes observed in this study, this pore radius was about 10 \(\upmu \)m. Furthermore, a design example is provided for artificial trees made of three different commercially available membrane materials. A design methodology was demonstrated for maximizing photosynthetic productivity by tuning the evaporation-driven flow rate to ensure sufficient nutrient delivery to cells without incurring large evaporative loss rates. It was observed that both the growth rate and the evaporation-driven nutrient delivery rate were directly related to the irradiance in outdoor artificial trees, which provides a passive and efficient nutrient delivery mechanism. It is expected that the design principles along with the physical models governing the fluid flow in these vascular structures will aid researchers in developing novel applications for artificial trees.


Algae cultivation Artificial tree Evaporation  Attached cultivation  Capillary physics 



Constant of proportionality for calculating nutrient delivery length


Diffusivity of water vapor in air (m\(^2\)/s)


Irradiance (W/m\(^2\))


Grashof number


Height (m)


Convection heat transfer coefficient (W/m\(^2\) K)


Heat of vaporization (J/kg)


Hydraulic permeability (m\(^2\))

\(k_\omega \)

Mass transfer coefficient (kg/m\(^2\) s)

\(\dot{m}^{\prime }\)

Mass flow rate per unit length (kg/s m)

\(\dot{m_\mathrm{e}}^{\prime \prime }\)

Evaporative flux (kg/m\(^2\) s)


Pressure (Pa)


Capillary pressure (Pa)


Pore radius


Reynolds number


Relative humidity


Schmidt number


Sherwood number


Temperature (K)


Rib thickness (m)


Wind speed (m/s)

\(\dot{X}_o^{\prime \prime }\)

Areal biomass production rate (kg/m\(^2\) s)


Distance in the direction of flow (m)


Critical wetting length (m)


Nutrient delivery length (m)


Biomass yield based on nutrient \(i\) (kg/kmol)

Greek Symbols

\(\alpha \)


\(\epsilon \)

Void fraction of porous membrane

\(\mu \)

Dynamic viscosity (Pa s)

\(\omega \)

Mass fraction

\(\rho \)

Mass density (kg/m\(^3\))

\(\sigma \)

Surface tension (N/m)

\(\theta \)

Contact angle (\(^{\circ }\))


\(\infty \)

Refers to ambient


Refers to air


Refers to exterior region


Refers to forced convection


Refers to interior region


Refers to limiting nutrient


Refers to natural convection


Refers to rib


  1. Adham, S., Chiu, K.-P., Lehman, G., Mysore, C., Clouet, J.: Optimization of Membrane Treatment for Direct and Clarified Water Filtration, 1st edn. American Waterworks Foundation, New York (2006)Google Scholar
  2. Andersen, R.A.: Algal Culturing Techniques. Elsevier Academic Press, London (2005)Google Scholar
  3. Beal, C.M., Smith, C.H., Webber, M.E., Ruoff, R.S., Hebner, R.E.: A framework to report the production of renewable diesel from algae. Bioenergy Res. 4, 36–60 (2011)CrossRefGoogle Scholar
  4. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 1st edn. Wiley, New York (1960)Google Scholar
  5. Borowitzka, M.A.: Commercial production of microalgae: ponds, tanks, tubes, and fermenters. J. Biotechnol. 70, 313–321 (1999)CrossRefGoogle Scholar
  6. Chisti, Y.: Biodiesel from algae. Biotechnol. Adv. 25, 294–306 (2007)CrossRefGoogle Scholar
  7. Chisti, Y., Yan, J.: Energy from algae: current status and future trends. Appl. Energy 88(10), 3277–3279 (2011)CrossRefGoogle Scholar
  8. Clarens, A.F., Resurreccion, E.P., White, M.A., Colosi, L.M.: Environmental life cycle comparison of algae to other bioenergy feedstocks. Environ. Sci. Technol. 44(5), 1813–1819 (2010)CrossRefGoogle Scholar
  9. Craggs, R.J., Heubeck, S., Lundquist, T.J., Benemann, J.R.: Algal biofuels from wastewater treatment high rate algal ponds. Water Sci. Technol. 63(4), 660–665 (2011)CrossRefGoogle Scholar
  10. Day, J.G., Benson, E.E., Fleck, R.A.: In vitro culture and conservation of microalgae: applications for aquaculture, biotechnology and environmental research. In Vitro Cell Dev. Biol. 35, 127–136 (1999)CrossRefGoogle Scholar
  11. de Gennes, P.-G., Brochard-Wyart, F., Quere, D.: Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, 1st edn. Springer, New York (2004)CrossRefGoogle Scholar
  12. Incropera, F.P., Dewitt, D.P., Bergman, T.L., Lavine, A.S.: Fundamentals of Heat and Mass Transfer, 6th edn. Wiley, Hoboken (2007)Google Scholar
  13. Jorquera, O., Kiperstok, A., Sales, E.A., Embiruçu, M., Ghirardi, M.L.: Comparative energy life-cycle analyses of microalgal biomass production in open ponds and photobioreactors. Bioresour. Technol. 101(4), 1406–1413 (2010)CrossRefGoogle Scholar
  14. Kaviany, M.: Principles of Heat Transfer in Porous Media, 2nd edn. Springer, New York (1999)Google Scholar
  15. Kumar, K., Dasgupta, C.N., Nayak, B., Lindblad, P., Das, D.: Development of suitable photobioreactors for \(\text{ CO }_{2}\) sequestration addressing global warming using green algae and cyanobacteria. Bioresour. Technol. 102(8), 4945–4953 (2011)CrossRefGoogle Scholar
  16. Liu, T., Wang, J., Hu, Q., Cheng, P., Ji, B., Liu, J., Chen, Y., Zhang, W., Chen, X., Chen, L., Gao, L., Ji, C., Wang, H.: Attached cultivation technology of microalgae for efficient biomass feedstock production. Bioresour. Technol. 127, 216–222 (2013)CrossRefGoogle Scholar
  17. Milledge, J.J.: Commercial application of microalgae other than as biofuels: a brief review. Rev. Environ. Sci. Biotechnol. 10(1), 31–41 (2010)CrossRefGoogle Scholar
  18. Millington, R.J., Quirk, J.P.: Permeability of porous solids. Trans. Faraday Soc. 57, 1200–1207 (1961)CrossRefGoogle Scholar
  19. Mills, A.F.: Heat Transfer, 5th edn. Prentice-Hall, Upper Saddle River (1999)Google Scholar
  20. Murphy, T.E., Berberoglu, H.: Flux balancing of light and nutrients in a biofilm pho- tobioreactor for maximizing photosynthetic productivity (accepted manuscript). Biotech- nol. Prog (2014)Google Scholar
  21. Murphy, T.E., Fleming, E., Bebout, L., Bebout, B., Berberoglu, H.: A novel micro- bial cultivation platform for space applications. In: 1st Annual International Space Station Research and Development Conference, Denver (2012)Google Scholar
  22. Naumann, T., Cebi, Z., Podola, B., Melkonian, M.: Growing microalgae as aquaculture feeds on twin-layers, a novel solid state photobioreactor. J. Appl. Phycol. 25, 1619 (2013)CrossRefGoogle Scholar
  23. Ozkan, A., Kinney, K., Katz, L., Berberoglu, H.: Reduction of water and energy requirement of algae cultivation using an algae biofilm photobioreactor. Bioresour. Technol. 114, 542–548 (2012)CrossRefGoogle Scholar
  24. Pasquini, D., Belgacem, M.N., Gandini, A., da Silva Curvelo, A.A.: Surface esterification of cellulose fibers: characterization by DRIFT and contact angle measurements. J. Colloid Interface Sci. 295(1), 79–83 (2006)CrossRefGoogle Scholar
  25. Pulz, O., Gross, W.: Valuable products from biotechnology of microalgae. Appl. Microbiol. Biotechnol. 65(6), 635–648 (2004)CrossRefGoogle Scholar
  26. Scott, S.A., Davey, M.P., Dennis, J.S., Horst, I., Howe, C.J., Lea-Smith, D.J., Smith, A.G.: Biodiesel from algae: challenges and prospects. Curr. Opin. Biotechnol. 21(3), 277–286 (2010)CrossRefGoogle Scholar
  27. Spolaore, P., Joannis-Cassan, C., Duran, E., Isambert, A.: Commercial applications of microalgae. J. Biosci. Bioeng. 101(2), 87–96 (2006)CrossRefGoogle Scholar
  28. Sumner, A.L., Menke, E.J., Dubowski, Y., Newberg, J.T., Penner, R.M., Hemminger, J.C., Wingen, L.M., Finlayson-Pitts, B.J.: The nature of water on surfaces of laboratory systems and implications for heterogeneous chemistry in the troposphere. Phys. Chem. Chem. Phys. 6, 604–613 (2004)CrossRefGoogle Scholar
  29. Wilcox, S., Marion, W.: Users manual for TMY3 data sets. Technical report, National Renewable Energy Laboratory, Golden (2008)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Thomas E. Murphy
    • 1
  • Evan Fleming
    • 1
  • Halil Berberoglu
    • 1
  1. 1.Mechanical Engineering DepartmentThe University of Texas at AustinAustinUSA

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