Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-07T09:26:05.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors

Published online by Cambridge University Press:  28 August 2013

Eligiusz Wajnryb ,
Krzysztof A. Mizerski ,
Pawel J. Zuk  and
Piotr Szymczak
Eligiusz Wajnryb
Affiliation:
Department of Mechanics and Physics of Fluids, Institute of Fundamental and Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106, Warsaw, Poland
Krzysztof A. Mizerski*
Affiliation:
Department of Magnetism, Institute of Geophysics, Polish Academy of Sciences, ul. Ksiecia Janusza 64, 01-452 Warsaw, Poland
Pawel J. Zuk
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681, Warsaw, Poland
Piotr Szymczak
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681, Warsaw, Poland
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation are that it includes all long-range terms (i.e. decaying as ${R}^{- 3} $ or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne–Prager–Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne–Prager–Yamakawa approximation can be generalized for other geometries and boundary conditions.

JFM classification

Mathematical Foundations: Computational methods Low-Reynolds-number flows: Low-Reynolds-number flows Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , R3
Copyright
©2013 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

Adamczyk, Z., Cichocki, B., Ekiel-Jeżewska, M. L., Słowicka, A., Wajnryb, E. & Wasilewska, M. 2012 Fibrinogen conformations and charge in electrolyte solutions derived from DLS and dynamic viscosity measurements. J. Colloid Interface Sci. 385, 244–257.CrossRefGoogle ScholarPubMed
Ando, T. & Skolnick, J. 2013 On the importance of hydrodynamic interactions in lipid membrane formation. Biophys. J. 104 (1), 96–105.CrossRefGoogle ScholarPubMed
Bhattacharya, S., Bławzdziewicz, J. & Wajnryb, E. 2005 Hydrodynamic interactions of spherical particles in suspensions confined between two planar walls. J. Fluid Mech. 541, 263–292.Google Scholar
Blake, J. A. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303.CrossRefGoogle Scholar
Bossis, G., Meunier, A. & Sherwood, J. D. 1991 Stokesian dynamics simulations of particle trajectories near a plane. Phys. Fluids A 3, 1853–1858.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Cichocki, B., Felderhof, B. U., Hinsen, K., Wajnryb, E. & Bławzdziewicz, J. 1994 Friction and mobility of many spheres in Stokes flow. J. Chem. Phys. 100, 3780–3790.CrossRefGoogle Scholar
Cichocki, B., Jones, R. B., Kutteh, R. & Wajnryb, E. 2000 Friction and mobility for colloidal spheres in Stokes flow near a boundary: the multipole method and applications. J. Chem. Phys. 112, 2548–2561.Google Scholar
Dhont, J. K. G. 1996 An Introduction to Dynamics of Colloids. Studies in Interface Science, vol. 2, Elsevier.Google Scholar
Felderhof, B. U. 1988 Many-body hydrodynamic interactions in suspensions. Physica A 151, 1–16.Google Scholar
Frembgen-Kesner, T. & Elcock, A. H. 2009 Striking effects of hydrodynamic interactions on the simulated diffusion and folding of proteins. J. Chem. Theory Comput. 5, 242–256.CrossRefGoogle ScholarPubMed
Gauger, E. M., Downton, M. T. & Stark, H. 2009 Fluid transport at low Reynolds number with magnetically actuated artificial cilia. Eur. Phys. J. E 28 (2), 231–242.Google Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid. Mech. 5, 317–328.CrossRefGoogle Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Kim, Y. W. & Netz, R. R. 2006 Electro-osmosis at inhomogeneous charged surfaces: hydrodynamic versus electric friction. J. Chem. Phys. 124, 114709.Google Scholar
Larson, R. G. & Magda, J. J. 1989 Coil-stretch transitions in mixed shear and extensional flows of dilute polymer solutions. Macromolecules 22, 3004–3010.CrossRefGoogle Scholar
Liron, N. & Shahar, R. 1978 Stokes flow due to a Stokeslet in a pipe. J. Fluid. Mech. 86, 727–744.CrossRefGoogle Scholar
Lorentz, H. A. 1896 A general theorem concerning the motion of a viscous fluid and a few consequences derived from it. Versl. Konigl. Akad. Wetensch. Amst. 5, 168–175.Google Scholar
Mazur, P. & van Saarloos, W. 1982 Many-sphere hydrodynamic interactions and mobilities in a suspension. Physica A 115, 21–57.Google Scholar
Nägele, G. 2006 Brownian dynamics simulations. In Computational Condensed Matter Physics (ed. Blügel, S., Gompper, G., Koch, E., Müller-Krumbhaar, H., Spatschek, R. & Winkler, R. G.), Matter and Materials, vol. 32, Forschungszentrum Jülich.Google Scholar
Oseen, C. W. 1927 Neuere Methoden und Ergebnisse in der Hydrodynamik. Akademische Verlagsgesellschaft.Google Scholar
Pear, M. R. & McCammon, J. A. 1981 Hydrodynamic interaction effects on local motions of chain molecules. J. Chem. Phys. 74, 6922–6925.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.Google Scholar
Reichert, M. 2006 Hydrodynamic interactions in colloidal and biological systems. PhD thesis, University Konstanz.Google Scholar
Rotne, J. & Prager, S. 1969 Variational treatment of hydrodynamic interaction in polymers. J. Chem. Phys. 50, 4831–4837.Google Scholar
Shaqfeh, E. S. G. 2005 The dynamics of single-molecule DNA in flow. J. Non-Newtonian Fluid Mech. 130, 1–28.Google Scholar
Sing, C. E., Schmid, L., Schneider, M. F., Franke, T. & Alexander-Katz, A. 2010 Controlled surface-induced flows from the motion of self-assembled colloidal walkers. Proc. Natl Acad. Sci. 107 (2), 535–540.Google Scholar
Szymczak, P. & Cieplak, M. 2011 Hydrodynamic effects in proteins. J. Phys.: Condens. Matter 23, 033102.Google Scholar
Tanaka, H. 2001 Interplay between wetting and phase separation in binary fluid mixtures: roles of hydrodynamics. J. Phys.: Condens. Matt. 13, 4637–4674.Google Scholar
de la Torre, G. J., del Rio Echenique, G. & Ortega, A. 2007 Improved calculation of rotational diffusion and intrinsic viscosity of bead models for macromolecules and nanoparticles. J. Phys. Chem. B 111, 955–961.CrossRefGoogle ScholarPubMed
Usta, O. B., Butler, J. E. & Ladd, A. J. C. 2007 Transverse migration of a confined polymer driven by an external force. Phys. Rev. Lett. 98, 098301.Google Scholar
Wojtaszczyk, P. & Avalos, J. B. 1998 Influence of hydrodynamic interactions on the kinetics of colloidal particles’ adsorption. Phys. Rev. Lett. 80, 754–757.CrossRefGoogle Scholar
Yamakawa, H. 1970 Transport properties of polymer chains in dilute solution: hydrodynamic interaction. J. Chem. Phys. 53, 436–443.Google Scholar
Supplementary material: PDF

Wajnryb et al. supplementary material

Supplementary data

Download Wajnryb et al. supplementary material(PDF)
PDF 68.9 KB