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helfrich

Mathematical Modelling of Natural Phenomena (1)

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Dynamics of Biomembranes: Effect of the BulkFluid
A. Bonito, R.H. Nochetto, M.S. Pauletti
Journal:

Mathematical Modelling of Natural Phenomena / Volume 6 / Issue 5 / 2011

Published online by Cambridge University Press:

10 August 2011, pp. 25-43

Print publication:

2011
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We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. Themembrane is characterized by its Canham-Helfrich energy (Willmore energy with areaconstraint) and acts as a boundary force on the Navier-Stokes system modeling anincompressible fluid. We give a concise description of the model and of the associatednumerical scheme. We provide numerical simulations with emphasis on the comparisonsbetween different types of flow: the geometric model which does not take into account thebulk fluid and the biomembrane model for two different regimes of parameters.