Abstract
We study the dynamics and formation of differently ordered lateral phases of interfacial lipid layers for two types of lipid systems, a vesicle-supported bilayer and a Langmuir–Blodgett monolayer, both in experiment and by simulation. Similarly, we investigate the dynamics of objects embedded in a simpler interface given by an air–water surface and demonstrate the surface-acoustic-wave-actuated separation of enantiomers (chiral objects) on the surface of the carrier fluid. It turns out that the dynamics and the separation of the phases do not only depend on parameters such as temperature, mobilities and line tension but also on the mechanics of the lipid layers subjected to exterior forces as, for instance, compression, extensional and shear forces in film-balance experiments. Since the mechanical behavior of lipid layers is viscoelastic, we use a modeling approach based on the incompressible Navier–Stokes equations with a viscoelastic stress term and a capillary term, a convective Jeffrey (Oldroyd) equation of viscoelasticity, and the Cahn–Hilliard equation with a transport term. The numerical simulations are based on C 0-interior-penalty discontinuous-Galerkin methods for the Cahn–Hilliard equation. Model-validation results and the verification of the simulation results by experimental data are presented. The feasibility of enantiomer separation by surface-acoustic-wave-generated vorticity patterns is shown both experimentally and through numerical simulations. This technique is cost-effective and provides an extremely high time resolution of the dynamics of the separation process compared to more traditional approaches. The experimental setup is an enhanced Langmuir–Blodgett film balance with a surface-acoustic-wave-generated vorticity pattern of the fluid, where model enantiomers (custom-made photoresist particles) float on the surface of the carrier fluid. For the simulations, we propose a finite element immersed boundary method (FEIBM) for deformable enantiomers and a fictitious-domain approach based on a distributed Lagrangian multiplier finite element immersed boundary method (DLM-FEIBM) for rigid chiral objects, both of which lead to simulation results consistent with experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Angelova, M., Soléau, S., Méléard, Ph., Faucon, F., Bothorel, P.: Preparation of giant vesicles by external AC electric fields. Kinetics and applications. In: Helm, C., Lösche, M., Möhwald, H. (eds.) Trends in Colloid and Interface Science, vol. VI. Progress in Colloid and Polymer Science, vol. 89, pp. 127–131. Springer, Berlin (1992)
Bagatolli, L.A., Gratton, E.: Two photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of binary phospholipid mixtures. Biophys. J. 78, 290–305 (2000)
Baoukina, S., Mendez-Villuendas, E., Bennett, W., Tieleman, D.: Computer simulations of the phase separation in model membranes. Faraday Discuss. 161, 63–75 (2013)
Baumgart, T., Hess, S., Webb, W.: Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425, 821–824 (2003)
Beleke-Maxwell, K., Franke, T., Hoppe, R.H.W., Linsenmann, C.: Numerical simulation of surface acoustic wave actuated enantiomer separation by the finite element immersed boundary method. Comput. Fluids 112, 50–60 (2015)
Bertozzi, A., Esedoglu, S., Gillette, A.: Inpainting of binary images using the Cahn-Hilliard equation. IEEE Trans. Image Process. 16, 285–291 (2007)
Boffi, D., Gastaldi, L.: A finite element approach for the immersed boundary method. Comput. Struct. 81, 491–501 (2003)
Boyer, F.: A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31, 41–68 (2002)
Boyer, F., Chupin, L., Fabrie, P.: Numerical study of viscoelastic mixtures through a Cahn-Hilliard flow model. Eur. J. Mech. B Fluids 23, 759–780 (2004)
Brooks, C.F., Fuller, G.G., Frank, C.W., Robertson, C.R.: Transitions in monolayers at the air-water interface. Langmuir 5, 2450–2459 (1999)
Burger, S., Fraunholz, T., Hoppe, R.H.W., Leirer, C., Wixforth, A., Peter, M.A., Franke, T.: Comparative study of the dynamics of lipid membrane phase decomposition in experiment and simulation. Langmuir 29(25), 7565–7570 (2013)
Burger, S., Franke, T., Fraunholz, T., Hoppe, R.H.W., Peter, M.A., Wixforth, A.: Numerical simulation of surface acoustic wave actuated separation of rigid enantiomers by the fictitious domain Lagrange multiplier method. Comput. Methods Appl. Math. 15(3), 247–258 (2015)
Cahn, J.W., Hilliard, J.E.: Free energy of a non-uniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958)
Chen, L.: Phase-field models for microstructural evolution. Annu. Rev. Mater. Res. 32, 113–140 (2002)
Choi, S.Q., Steltenkamp, S., Zasadzinski, J.A., Squires, T.M.: Active microrheology and simultaneous visualization of sheared phospholipid monolayers. Nat. Commun. 2, 312–316 (2011)
Chorin, A.J.: The numerical solution of the Navier-Stokes equations for an incompressible fluid. Bull. Am. Soc. 73, 928–931 (1967)
Chupin, L.: Existence result for a mixture of non-Newtonian flows with stress diffusion using the Cahn-Hilliard formulation. Discrete Continuous Dyn. Syst. B 3, 45–68 (2003)
Chupin, L.: Existence results for the flow of viscoelastic fluids with an integral constitutive law. J. Math. Fluid Mech. 15, 783–806 (2013)
Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. SIAM, Philadelphia (2002)
Dietrich, C., Bagatolli, L., Volovyk, Z., Thompson, N., Levi, M., Jacobson, K., Gratton, E.: Lipid rafts reconstituted in model membranes. Biophys. J. 80, 1417–1428 (2001)
Ding, J., Warriner, H.E., Zasadzinski, J.A., Schwartz, D.K.: Magnetic needle viscometer for Langmuir monolayers. Langmuir 18, 2800–2806 (2002)
Einstein, A.: Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 324, 289–306 (1906)
Elliott, C.: The Cahn-Hilliard model for the kinetics of phase separation. In: Rodrigues, J. (ed.) Mathematical Models for Phase Change Problems, International Series of Numerical Mathematics, vol. 88, pp. 35–74. Birkhauser, Basel (1989)
Espinosa, G., López-Montero, I., Monroy, F., Langevin, D.: Shear rheology of lipid monolayers and insights on membrane fluidity. Proc. Natl. Acad. Sci. 108, 6008–6013 (2011)
Fernandéz-Cara, E., Guillén, F., Ortega, R.R.: Some theoretical results concerning non-Newtonian fluids of the Oldroyd kind. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 26, 1–26 (1998)
Filippov, A., Orädd, G., Lindblom, G.: Lipid lateral diffusion in ordered and disordered phases in raft mixtures. Biophys. J. 86, 891–896 (2004)
Franke, T., Hoppe, R.H.W., Linsenmann, C., Schmidt, L., Willbold, C.: Numerical simulation of the motion of red blood cells and vesicles in microfluidic flows. Comput. Vis. Sci. 14, 167–180, 2011.
Fraunholz, T.: Transport at interfaces in lipid membranes and enantiomer separation. PhD dissertation, University of Augsburg, Germany, 2014
Fraunholz, T., Hoppe, R.H.W., Peter, M.A.: Convergence analysis of an adaptive interior penalty discontinuous Galerkin method for the biharmonic problem. J. Numer. Math. 23, 317–330 (2015)
Glowinski, R., Pan, T.-W., Hesla, T.I., Joseph, D.D., Periaux, J.: A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169, 363–427 (2001)
Gordon, R.J., Showalter, W.R.: Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions. Trans. Soc. Rheol. 16, 79–97 (1972)
Guth, E., Simha, R.: Untersuchungen über die Viskosität von Suspensionen und Lösungen. 3. Über die Viskosität von Kugelsuspensionen. Colloid Polym. Sci. 74, 266–275 (1936)
Helm, C., Möhwald, H., Kjaer, K., Als-Nielsen, J.: Phospholipid monolayers between fluid and solid states. Biophys. J. 52, 381–390 (1987)
Hernandez, C.J., Mason, T.G.: Colloidal alphabet soup: monodisperse dispersions of shape-designed lithoparticles. J. Phys. Chem. C 111, 4477–4480 (2007)
Hoppe, R.H.W., Linsenmann, C.: An adaptive Newton continuation strategy for the fully implicit finite element immersed boundary method. J. Comput. Phys. 231, 4676–4693 (2012)
Jacobson, K., Mouritsen, O., Anderson, R.: Lipid rafts: at a crossroad between cell biology and physics. Nat. Cell Biol. 9, 7–14 (2007)
Jeffreys, H.: The Earth, Its Origin, History and Physical Constitution. Cambridge University Press, Cambridge (1924)
Jørgensen, K., Mouritsen, O.: Phase separation dynamics and lateral organization of two-component lipid membranes. Biophys. J. 95, 942–954 (1995)
Joseph, D.D.: Fluid Dynamics of Viscoelastic Liquids. Springer, Berlin (1990)
Kahya, N., Scherfeld, D., Bacia, K., Poolman, B., Schwille, P.: Probing lipid mobility of raft-exhibiting model membranes by fluorescence correlation spectroscopy. J. Biol. Chem. 278, 28109–28115 (2003)
Krägel, J., Kretzschmar, G., Li, J.B., Loglio, G., Miller, R., Möhwald, H.: Surface rheology of monolayers. Thin Solid Films 284–285, 361–364 (1996)
Krüger, P., Lösche, M.: Molecular chirality and domain shapes in lipid monolayers on aqueous surfaces. Phys. Rev. E 62, 7031–7043 (2000)
Kostur, M., Schindler, M., Talkner, P., Hänggi, P.: Chiral separation in microflows. Phys. Rev. Lett. 96, 014502-1–014502-4 (2006)
Larson, R.G.: The Structure and Rheology of Complex Fluids. Oxford University Press, Oxford (1999)
Letherish, W.: The mechanical behavior of Bitumen. J. Soc. Chem. Ind. 59, 1–26 (1940)
Li, P.C.H.: Microfluidic Lab-on-a-Chip for Chemical and Biological Analysis and Discovery. CRC Press, Boca Raton (2006)
Lions, P.L., Masmoudi, N.: Global solutions for some Oldroyd models of non-Newtonian fluids. Chinese Ann. Math. Ser. B 21, 131–146 (2000)
Marcos, Fu, H.C., Powers, T.R., Stocker, R.: Separation of microscale chiral objects by shear flow. Phys. Rev. Lett. 102, 158103-1–158103-4 (2009)
Miller, A., Möhwald, H.: Diffusion limited growth of crystalline domains in phospholipid monolayers. J. Chem. Phys. 86, 4258–4265 (1987)
Miller, A., Knol, W., Möhwald, H.: Fractal growth of crystalline phospholipid domains in monomolecular layers. Phys. Rev. Lett. 56, 2633–2638 (1986)
Möhwald, H.: Phospholipid monolayers. In: Lipowsky, R., Sackmann, E. (eds.) Handbook of Biological Physics, vol. 1, pp. 161–211. Elsevier Science, Amsterdam (1995)
Novick-Cohen, A.: The Cahn-Hilliard equation: mathematical and modeling perspectives. Adv. Math. Sci. Appl. 8, 965–985 (1998)
Oldroyd, J.G.: On the formulation of rheological equations of state. Proc. R. Soc. A 200, 523–541 (1950)
Orädd, G., Westerman, P., Lindblom, G.: Lateral diffusion coefficients of separate lipid species in a ternary raft-forming bilayer: a Pfg-NMR multinuclear study. Biophys. J. 89, 315–320 (2005)
Pichot, R., Watson, R.L., Norton, I.T.: Phospholipids at the interface: current trends and challenges. Int. J. Mol. Sci. 14, 11767–11794 (2013)
Relini, A., Ciuchi, F., Rolandi, R.: Surface shear viscosity and phase transitions of monolayers at the air-water interface. J. Phys. II 5, 1209–1221 (1995)
Rowlinson, J., Widom, B.: Molecular Theory of Capillarity. Clarendon Press, Oxford (1982)
Sacchetti, M., Yu, H., Zografi, G.: In-plane steady shear viscosity of monolayers at the air/water interface and its dependence on free area. Langmuir 9, 2168–2171 (1993)
Sadoughi, A.H., Lopez, J.M., Hirsa, A.H.: Transition from Newtonian to non-Newtonian surface shear viscosity of phospholipid monolayers. Phys. Fluids 25, 032107 (2013)
Sickert, M., Rondelez, F.: Shear viscosity of Langmuir monolayers in the low-density limit. Phys. Rev. Lett. 90, 126104 (2003)
Simons, K., Ikonen, E.: Functional rafts in cell membranes. Nature 387, 569–572 (1997)
Singer, S.J., Nicolson, J.L.: The fluid mosaic model of the structure of cell membranes. Science 175, 720–735 (1972)
Steppich, D., Griesbauer, J., Frommelt, T., Appelt, W., Wixforth, A., Schneider, M.F.: Thermomechanic-electrical coupling in phospholipid monolayers near the critical point. Phys. Rev. E 81, 061123 (2010)
Temam, R.: Remark on the pressure boundary condition for the projection method. Theor. Comput. Fluid Mech. 3, 181–184 (1991)
Temam, R.: Navier-Stokes Equations: Theory and Numerical Analysis. AMS Chelsea Publications, Providence, RI (2000)
Tremaine, S.: On the origin of irregular structure in Saturn’s rings. Astron. J. 125, 894–901 (2003)
Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior. Springer, Berlin (1989)
Veatch, S., Keller, S.: Organization in lipid membranes containing cholesterol. Phys. Rev. Lett. 89, 268101 (2002)
Veatch, S., Keller, S.: Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys. J. 85, 3074–3083 (2003)
Veatch, S., Keller, S.: Seeing spots: complex phase behavior in simple membranes. Biochim. Biophys. Acta 1746, 172–185 (2005)
Wells, G.N., Kuhl, E., Garikipati, K.: A discontinuous Galerkin method for the Cahn-Hilliard equation. J. Comput. Phys. 218, 860–877 (2006)
Zener, C.: Elasticity and Anelasticity of Metals. University of Chicago Press, Chicago (1948)
Acknowledgements
This work was supported by the DFG Priority Program SPP 1506, by the German Cluster of Excellence “Nanosystems Initiative Munich (NIM)”, and by the NSF under grant DMS-1520886.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Boyarkin, O. et al. (2017). Transport at Interfaces in Lipid Membranes and Enantiomer Separation. In: Bothe, D., Reusken, A. (eds) Transport Processes at Fluidic Interfaces. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-56602-3_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-56602-3_17
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-56601-6
Online ISBN: 978-3-319-56602-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)