Fluid Dynamics of Phytoplankton with Spines in Shear Flow

Hoa NguyenCenter for Computational Science, Tulane University

CollaboratorsLisa Fauci, Department of Mathematics, Tulane University

Peter Jumars and Lee Karp-Boss, School of Marine Sciences, University of Maine

Magdalena Musielak, Department of Mathematics, The George Washington University

Phytoplankton

Copyright of Smithsonian Environmental Research Center

Phytoplankton are the foundation of the oceanic food chain.

Thalassiosira nordenskioeldiiCopyright of the Biodiversity Institute of

Ontario

IntroductionObject: Individual non-motile

diatom.

Goal: Understand the effects of spines on diatoms in shear flow.

Method: the Immersed Boundary Method (IBM) developed by Charles Peskin ([1], [2]).

Thalassiosira nordenskioeldiiCopyright of the Biodiversity Institute of

Ontario

Our simulation of a simplified model of the above diatom in

shear flow (Re = 8.26 x 10-4)

[1] C. S. Peskin; Numerical analysis of blood flow in the heart, J. Compu. Phys. 25, 1977, pp. 220 - 252.[2] C. S. Peskin; The immersed boundary method, Acta Numerica 11, 2002, pp. 459- 517.

Immersed Boundary Method (IBM)

Spring Force

Model of a plankter with eight spines (left) and detail of how the spines attach to the cell body (right).

Discretization:Spherical Centroidal Voronoi Tessellation

The triangulation on the unit sphere is the dual mesh of the Spherical Centroidal Voronoi Tessellation (SCVT), as coded by Lili Ju [6]. We map this triangulation to a surface (such as an ellipsoid, a flat disc or a plankter’s cell body) to create a discretization of the structure.

Fluid Solver:Immersed Boundary Method with

Adaptive Mesh Refinement (IBAMR)

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. Journal of Computational Physics. 223: 10-49 (2007).

Re = 8.26

Jeffery Orbit

Ellipsoid in Shear Flow

Variation of φ with time (where φ = rotation angle relative to the initial

position).

The period from the simulation is about 1.55

s, compared with the theoretical period

T = 1.59 s.

Flat Disc in Shear Flow

The period from the

simulation is about 6.4 s, compared with the

experimental period

T = 7.6 s in Goldsmith

and Mason’s paper [5]

from 1962. Re = 3.03 x 10-4 (oil) Re = 1.56 (water)

Plankter in Shear Flow

The cell body has the same diameter as the disc, except that the top and bottom are dome-shaped (height = 0.006 cm). The spine length = 0.052 cm.

Spine angle = 0o Spine angle = 45o

Plankter without spines (Re = 3.03 x 10-4)

Plankter with eight spines (Re = 8.26 x 10-4)

Observe that the plankter with spines at different angles has a

longer period than the one without spines.

Simulations and ResultsT = 6.5 s

T = 8.89 s

T = 7.17 s

Research ExtensionsDifferent morphologies and chains

of cells.

Nutrient transport and acquisition.

Computational models and laboratory experiments.

unsteady shear and vortical background flows.

Plankter without springs internal to the cell body and spines.

Special thanks to Hideki Fujioka and Ricardo Cortez at the Center for Computational Science, Tulane University.

Thanks for your

attention!

This work is supported by NSF OCE 0724598.