Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-19T19:58:43.470Z Has data issue: false hasContentIssue false
  • English
  • Français

Mobility of membrane-trapped particles

Published online by Cambridge University Press:  24 September 2015

Howard A. Stone  and
Hassan Masoud
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Hassan Masoud
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Department of Mechanical Engineering, University of Nevada, Reno, NV 89557, USA
*
†Email address for correspondence: hastone@princeton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Rheological and transport studies of model thin films and membranes, often inspired by biological systems, make use of translational or rotational motion or diffusion of particles trapped in the surface film. Here, we consider the translational mobility of spherical and oblate spheroidal particles protruding into the surrounding subphase liquid. Both the subphase and surface film contribute to the resistance experienced by the particle, which is calculated as a function of the degree of protrusion as well as the viscosity contrast between the surface film and the surrounding fluid. The calculations are based on a combination of a perturbation expansion involving the particle shape and the Lorentz reciprocal theorem.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 494 - 505
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alberts, B., Johnson, A., Lewis, J., Morgan, D., Raff, M., Roberts, K. & Walter, P. 2002 Molecular Biology of the Cell. Garland Science.Google Scholar
Ally, J. & Amirfazli, A. 2010 Magnetophoretic measurement of the drag force on partially immersed microparticles at air–liquid interfaces. Colloids Surf. A 360, 120–128.CrossRefGoogle Scholar
Barentin, C., Muller, P., Ybert, C., Joanny, J. F. & di Meglio, J. M. 2000 Shear viscosity of polymer and surfactant monolayers. Eur. Phys. J. E 2, 153–159.CrossRefGoogle Scholar
Barentin, C., Ybert, C., di Meglio, J. M. & Joanny, J. F. 1999 Surface shear viscosity of Gibbs and Langmuir monolayers. J. Fluid Mech. 397, 331–349.CrossRefGoogle Scholar
Choi, S. Q., Steltenkamp, S., Zasadzinski, J. A. & Squires, T. M. 2011 Active microrheology and simultaneous visualization of sheared phospholipid monolayers. Nat. Commun. 2, 1–6.CrossRefGoogle ScholarPubMed
Danov, K., Aust, R., Durst, F. & Lange, U. 1995 Influence of the surface viscosity on the hydrodynamic resistance and surface diffusivity of a large Brownian particle. J. Colloid Interface Sci. 175, 36–45.CrossRefGoogle Scholar
Danov, K. D., Dimova, R. & Pouligny, B. 2000 Viscous drag of a solid sphere straddling a spherical or flat surface. Phys. Fluids 12, 2711–2722.CrossRefGoogle Scholar
Davis, A. M. J. 1990 Stokes drag on a disk sedimenting toward a plane or with other disks; additional effects of a side wall or free surface. Phys. Fluids 2, 301–312.CrossRefGoogle Scholar
Dimova, R., Danov, K., Pouligny, B. & Ivanov, I. B. 2000 Drag of a solid particle trapped in a thin film or at an interface: influence of surface viscosity and elasticity. J. Colloid Interface Sci. 226, 35–43.CrossRefGoogle ScholarPubMed
Dodd, T. L., Hammer, D. A., Sangani, A. S. & Koch, D. L. 1995 Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins. J. Fluid Mech. 293, 147–180.CrossRefGoogle Scholar
Dörr, A., Hardt, S., Masoud, H. & Stone, H. A. 2015 Drag and diffusion coefficients of a spherical particle attached to a fluid–fluid interface. J. Fluid Mech. (submitted).Google Scholar
Evans, A. A. & Levine, A. J. 2015 Membrane Rheology. pp. 159–186. Springer.Google Scholar
Evans, E. & Sackmann, E. 1988 Translational and rotational drag coefficients for a disk moving in a liquid membrane associated with a rigid substrate. J. Fluid Mech. 194, 553–561.CrossRefGoogle Scholar
Fischer, T. M. 2004a Comment on ‘Shear viscosity of Langmuir monolayers in the low-density limit’. Phys. Rev. Lett. 92, 139603.CrossRefGoogle ScholarPubMed
Fischer, T. M. 2004b The drag on needles moving in a Langmuir monolayer. J. Fluid Mech. 498, 123–137.CrossRefGoogle Scholar
Fischer, T. M., Dhar, P. & Heinig, P. 2006 The viscous drag of spheres and filaments moving in membranes or monolayers. J. Fluid Mech. 558, 451–475.CrossRefGoogle Scholar
Fitzgibbon, S., Shaqfeh, E. S. G., Fuller, G. G. & Walker, T. W. 2014 Scaling analysis and mathematical theory of the interfacial stress rheometer. J. Rheol. 58, 999–1038.CrossRefGoogle Scholar
Fuller, G. G. & Vermant, J. 2012 Complex fluid–fluid interfaces: rheology and structure. Annu. Rev. Chem. Biomol. 3, 519–543.CrossRefGoogle ScholarPubMed
Gambin, Y., Lopez-Esparza, R., Reffay, M., Sierecki, E., Gov, N. S., Genest, M., Hodges, R. S. & Urbach, W. 2006 Lateral mobility of proteins in liquid membranes revisited. Proc. Natl Acad. Sci. USA 103, 2098–2102.CrossRefGoogle ScholarPubMed
Haj-Hariri, H., Nadim, A. & Borhan, A. 1993 Reciprocal theorem for concentric compound drops in arbitrary Stokes flows. J. Fluid Mech. 252, 265–277.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics, with Special Applications to Particulate Media. Prentice-Hall.CrossRefGoogle Scholar
Hughes, B. D., Pailthorpe, B. A. & White, L. R. 1981 The translational and rotational drag on a cylinder moving in a membrane. J. Fluid Mech. 110, 349–372.CrossRefGoogle Scholar
Kim, K. K., Choi, S. Q., Zasadzinski, J. A. & Squires, T. M. 2011 Interfacial microrheology of DPPC monolayers at the air–water interface. Soft Matt. 7, 7782–7789.CrossRefGoogle Scholar
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435–476.CrossRefGoogle Scholar
Levine, A. J., Liverpool, T. B. & MacKintosh, F. C. 2004 Mobility of extended bodies in viscous films and membranes. Phys. Rev. E 69, 021503.CrossRefGoogle ScholarPubMed
Lishchuk, S. V. 2014 Effective surface-shear viscosity of an incompressible particle-laden fluid interface. Phys. Rev. E 89, 043003.CrossRefGoogle ScholarPubMed
Maestro, A., Bonales, L. J., Ritacco, H., Fischer, T. M., Rubio, R. G. & Ortega, F. 2011 Surface rheology: macro- and microrheology of poly(tert-butyl acrylate) monolayers. Soft Matt. 7, 7761–7771.CrossRefGoogle Scholar
Masoud, H. & Shelley, M. J. 2014 Collective surfing of chemically active particles. Phys. Rev. Lett. 112, 128304.CrossRefGoogle ScholarPubMed
Masoud, H. & Stone, H. A. 2014 A reciprocal theorem for Marangoni propulsion. J. Fluid Mech. 741, R4.CrossRefGoogle Scholar
Mendoza, A. J., Guzman, E., Martinez-Pedrero, F., Ritacco, H., Rubio, R. G., Ortega, F., Starov, V. M. & Miller, R. 2014 Particle laden fluid interfaces: dynamics and interfacial rheology. Adv. Colloid Interface Sci. 206, 303–319.CrossRefGoogle ScholarPubMed
Ortega, F., Ritacco, H. & Rubio, R. G. 2010 Interfacial microrheology: particle tracking and related techniques. Curr. Opin. Colloid Interface Sci. 15, 237–245.CrossRefGoogle Scholar
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73, 593–602.CrossRefGoogle Scholar
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. USA 72, 3111–3113.CrossRefGoogle ScholarPubMed
Samaniuk, J. R. & Vermant, J. 2014 Micro and macrorheology at fluid–fluid interfaces. Soft Matt. 10, 7023–7033.CrossRefGoogle ScholarPubMed
Sickert, M., Rondelez, F. & Stone, H. A. 2007 Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers. Europhys. Lett. 79, 66005.CrossRefGoogle Scholar
Singh, P. & Joseph, D. D. 2005 Fluid dynamics of floating particles. J. Fluid Mech. 530, 31–80.CrossRefGoogle Scholar
Squires, T. M. & Mason, T. G. 2010 Fluid mechanics of microrheology. Annu. Rev. Fluid Mech. 42, 413–438.CrossRefGoogle Scholar
Stone, H. A. 2010 Interfaces: in fluid mechanics and across disciplines. J. Fluid Mech. 645, 1–25.CrossRefGoogle Scholar
Stone, H. A. & Ajdari, A. 1998 Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth. J. Fluid Mech. 369, 151–173.CrossRefGoogle Scholar
Stone, H. A. & McConnell, H. M. 1995 Hydrodynamics of quantized shape transitions of lipid domains. Proc. R. Soc. Lond. A 448, 97–111.Google Scholar
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77, 4102–4104.CrossRefGoogle ScholarPubMed
Tanzosh, J. P. & Stone, H. A. 1996 A general approach for analyzing the arbitrary motion of a circular disk in a Stokes flow. Chem. Engng Commun. 150, 333–346.CrossRefGoogle Scholar
Verwijlen, T., Moldenaers, P., Stone, H. A. & Vermant, J. 2011 Study of the flow field in the magnetic rod interfacial stress rheometer. Langmuir 27, 9345–9358.CrossRefGoogle ScholarPubMed
Wang, D., Yordanov, S., Paroor, H. M., Mukhopadhyay, A., Li, C. Y., Butt, H. J. & Koynov, K. 2011 Probing diffusion of single nanoparticles at water–oil interfaces. Small 7, 3502–3507.CrossRefGoogle ScholarPubMed