Abstract
The phenomenon of phase separation has been observed in lipid membranes. This process is remarkable, since both in-membrane and solvent-mediated hydrodynamic effects affect separation dynamics. The Cahn–Hilliard model for phase separation is here considered, coupled with the overdamped (Stokes) fluid equations. The convection term of the Cahn–Hilliard equations, which is due to hydrodynamic effects, is here treated by a Lagrangian method, in which fluid particles move along the velocity field carrying the concentration field. The method is combined with a projection onto a fixed regular mesh, where the rest of the equations are solved in Fourier space. In this space, spatial derivatives are evaluated quite easily. Moreover, the effect of the underlying fluid is straightforward in Fourier space, through the modification of the Oseen tensor. This hybrid treatment is the main contribution of this work. Results are in good agreement with experimental findings. Some agreement is found with previous simulations, but some striking differences are present.
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Acknowledgements
I wish to thank Profs. Sarah Keller, Lutz Maibaum, and Michael Schick, and the Amphiphiliphiles Research Group at the University of Washington (UW) for kindly hosting the author during the initial stage of this research. Also, Dr. Camley has been very kind in providing additional details of their calculations. Financial support from Universidad Politécnica de Madrid (Programa Propio I+D+i), to fund this stay, in the Department of Physics, UW, from September 2016 until December 2016 is also acknowledged. HPC computing facilities have received funding from Project (Ministerio de Economía y Competitividad) UNPM13-4E-2075 “Mejora de clúster para estudios fluidomecánicos”, MINECO, Spain.
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Duque, D. Particle method for phase separation on membranes. Microfluid Nanofluid 22, 95 (2018). https://doi.org/10.1007/s10404-018-2115-8
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DOI: https://doi.org/10.1007/s10404-018-2115-8