Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-29T16:45:58.566Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamic couplings of colloidal ellipsoids diffusing in channels

Published online by Cambridge University Press:  29 December 2021

Zhongyu Zheng Open the ORCID record for Zhongyu Zheng [Opens in a new window] ,
Xinliang Xu Open the ORCID record for Xinliang Xu [Opens in a new window] ,
Yuren Wang  and
Yilong Han Open the ORCID record for Yilong Han [Opens in a new window]
Zhongyu Zheng
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
Xinliang Xu
Affiliation:
Beijing Computational Science Research Center, Beijing 100193, China
Yuren Wang
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
Yilong Han*
Affiliation:
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China The Hong Kong University of Science and Technology, Shenzhen Research Institute, Shenzhen 518057, China
*
†Email address for correspondence: yilong@ust.hk
Get access Rights & Permissions [Opens in a new window]

Abstract

The hydrodynamic interactions (HIs) of two colloidal spheres characterized by the translation–translation (T–T) couplings have been studied under various confinements, but little is known regarding the HIs of anisotropic particles and rotational motions, which are common in nature and industry. Here, we study the T–T, rotation–rotation (R–R) and translation–rotation (T–R) hydrodynamic couplings of two colloidal ellipsoids sediment on the bottoms of channels in experiment, theory and simulation. We find that the degree of confinement and the particle shape anisotropy are critical tuning factors resulting in anomalous hydrodynamic and diffusive behaviours. The negative R–R coupling reflects the tendency of opposite rotations of two neighbouring ellipsoids. The positive T–R coupling reflects that an ellipsoid rotates away from the channel axis as another ellipsoid approaches. As the channel width increases, the positive T–T coupling changes to an abnormal negative coupling, indicating that the single-file diffusion can exist even in wide channels. By contrast, only positive T–T couplings were observed for spheres in channels. The T–T coupling increases with the aspect ratio p. The R–R coupling is the maximum at a moderate p ~ 2.8. The T–R coupling is the maximum at a moderate degree of confinement. The spatial range of HIs is longer than that of spheres and increases with p. We propose a simple model which reproduces some coupling phenomena between two ellipsoids, and it is further confirmed by low-Reynolds-number hydrodynamic simulation. These findings shed new light on anisotropic particle diffusion in porous media, transport through membranes, microfluidics and microrheology.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Stokesian dynamics Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A40
Check for updates
Copyright
© The Author(s), 2021. Published by 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

Batchelor, G.K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–440.CrossRefGoogle Scholar
Beatus, T., Tlusty, T. & Bar-Ziv, R. 2006 Phonons in a one-dimensional microfluidic crystal. Nat. Phys. 2, 743–748.CrossRefGoogle Scholar
Berlyand, L. & Panchenko, A. 2007 Strong and weak blow-up of the viscous dissipation rates for concentrated suspensions. J. Fluid Mech. 578, 1–34.CrossRefGoogle Scholar
Blake, J.R. 1971 A note on the image system for a stokeslet in a noslip boundary. Proc. Gamb. Phil. Soc. 70, 303–310.CrossRefGoogle Scholar
Blake, J.R. 1979 On the generation of viscous toroidal eddies in a cylinder. J. Fluid Mech. 95, 209–222.CrossRefGoogle Scholar
Bleibel, J., Domínguez, A., Günther, F., Harting, J. & Oettel, M. 2014 Hydrodynamic interactions induce anomalous diffusion under partial confinement. Soft Matter 10, 2945–2948.CrossRefGoogle ScholarPubMed
Brady, J.F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Braverman, L., Mowitz, A. & Witten, T.A. 2020 Chiral motion in colloidal electrophoresis. Phys. Rev. E 101, 062608.CrossRefGoogle ScholarPubMed
Brotto, T., Caussin, J.-B., Lauga, E. & Bartolo, D. 2013 Hydrodynamics of confined active fluids. Phys. Rev. Lett. 110, 038101.CrossRefGoogle ScholarPubMed
Bukowicki, M., Gruca, M. & Ekiel-Jeżewska, M.L. 2014 Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion. J. Fluid Mech. 767, 95–108.CrossRefGoogle Scholar
Cacciuto, A. & Luijten, E. 2006 Confinement-driven translocation of a flexible polymer. Phys. Rev. Lett. 96, 238104.CrossRefGoogle ScholarPubMed
Chwang, A.T. & Wu, T.Y. 1976 Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids. J. Fluid Mech. 75, 677–689.CrossRefGoogle Scholar
Crocker, J.C., Valentine, M.T., Weeks, E.R., Gisler, T., Kaplan, P.D., Yodh, A.G. & Weitz, D.A. 2000 Two-point microrheology of inhomogeneous soft materials. Phys. Rev. Lett. 85, 888.CrossRefGoogle ScholarPubMed
Cui, B., Diamant, H. & Lin, B. 2002 Screened hydrodynamic interaction in a narrow channel. Phys. Rev. Lett. 89, 188302.CrossRefGoogle Scholar
Cui, B., Diamant, H., Lin, B. & Rice, S.A. 2004 Anomalous hydrodynamic interaction in a quasi-two-dimensional suspension. Phys. Rev. Lett. 92, 258301.CrossRefGoogle Scholar
Dai, L., He, G., Zhang, X. & Zhang, X. 2018 Stable formations of self-propelled fish-like swimmers induced by hydrodynamic interactions. J. R. Soc. Interface 15, 20180490.CrossRefGoogle ScholarPubMed
Davidchack, R.L., Ouldridge, T.E. & Tretyakov, M.V. 2017 Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions. J. Chem. Phys. 147, 224103.CrossRefGoogle ScholarPubMed
Dettmer, S.L., Pagliara, S., Misiunas, K. & Keyser, U.F. 2014 Anisotropic diffusion of spherical particles in closely confining microchannels. Phys. Rev. E 89 (6), 062305.CrossRefGoogle ScholarPubMed
Dhont, J.K.G. 1996 An Introduction to Dynamics of Colloids. Elsevier, Amsterdam.Google Scholar
Diamant, H. 2009 Hydrodynamic interaction in confined geometries. J. Phys. Soc. Japan 78, 041002.CrossRefGoogle Scholar
Di Leonardo, R., Cammarota, E., Bolognesi, G., Schäfer, H. & Steinhart, M. 2011 Three-dimensional to two-dimensional crossover in the hydrodynamic interactions between micron-scale rods. Phys. Rev. Lett. 107, 044501.CrossRefGoogle ScholarPubMed
Doi, M. & Edwards, S.F. 1988 The Theory of Polymer Dynamics. Oxford University Press.Google Scholar
Domínguez, A. 2018 Theory of anomalous collective diffusion in colloidal monolayers on a spherical interface. Phys. Rev. E 97, 022607.CrossRefGoogle ScholarPubMed
Drescher, K., Dunkel, J., Cisneros, L.H., Ganguly, S. & Goldstein, R.E. 2011 Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc. Natl Acad. Sci. USA 108, 10940–10945.CrossRefGoogle ScholarPubMed
Dufresne, E.R., Squires, T.M., Brenner, M.P. & Grier, D.G. 2000 Hydrodynamic coupling of two Brownian spheres to a planar surface. Phys. Rev. Lett. 85, 3317.CrossRefGoogle ScholarPubMed
Duggal, R. & Pasquali, M. 2006 Dynamics of individual single-walled carbon nanotubes in water by real-time visualization. Phys. Rev. Lett. 96, 246104.CrossRefGoogle ScholarPubMed
Dunkel, J., Heidenreich, S., Drescher, K., Wensink, H.H., Bär, M. & Goldstein, R.E. 2013 Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102.CrossRefGoogle ScholarPubMed
Durlofsky, L., Brady, J.F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.CrossRefGoogle Scholar
Ermak, D.L. & McCammon, J.A. 1978 Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352–1360.CrossRefGoogle Scholar
Fleury, J.-B., Schiller, U.D., Thutupalli, S., Gompper, G. & Seemann, R. 2014 Mode coupling of phonons in a dense one-dimensional microfluidic crystal. New J. Phys. 16, 063029.CrossRefGoogle Scholar
Foss, D.R. & Brady, J.F. 2000 Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation. J. Fluid Mech. 407, 167–200.CrossRefGoogle Scholar
García de la Torre, 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 Scholar
Goddard, B.D., Nold, A. & Kalliadasis, S. 2016 Dynamical density functional theory with hydrodynamic interactions in confined geometries. J. Chem. Phys. 145, 214106.CrossRefGoogle ScholarPubMed
Goldfriend, T., Diamant, H. & Witten, T.A. 2015 Hydrodynamic interactions between two forced objects of arbitrary shape. I. Effect on alignment. Phys. Fluids 27, 123303.CrossRefGoogle Scholar
de Graaf, J., Menke, H., Mathijssen, A.J., Fabritius, M., Holm, C. & Shendruk, T.N. 2016 Lattice-Boltzmann hydrodynamics of anisotropic active matter. J. Chem. Phys. 144, 134106.CrossRefGoogle ScholarPubMed
Grünbaum, D. 1995 A model of feeding currents in encrusting bryozoans shows interference between zooids within a colony. J. Theor. Biol. 174, 409–425.CrossRefGoogle Scholar
Grzybowski, B.A., Stone, H.A. & Whitesides, G.M. 2000 Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface. Nature 405, 1033–1036.CrossRefGoogle Scholar
Han, Y., Alsayed, A., Nobili, M. & Yodh, A.G. 2009 Quasi-two-dimensional diffusion of single ellipsoids: aspect ratio and confinement effects. Phys. Rev. E 80, 011403.CrossRefGoogle ScholarPubMed
Han, Y., Alsayed, A.M., Nobili, M., Zhang, J., Lubensky, T.C. & Yodh, A.G. 2006 Brownian motion of an ellipsoid. Science 314, 626–630.CrossRefGoogle ScholarPubMed
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Kluwer Academic Publishers.Google Scholar
Hernández-Ortiz, J.P., de Pablo, J.J. & Graham, M.D. 2006 N log N method for hydrodynamic interactions of confined polymer systems: Brownian dynamics. J. Chem. Phys. 125, 164906.CrossRefGoogle ScholarPubMed
Huang, B., Wu, H., Bhaya, D., Grossman, A., Granier, S., Kobilka, B.K. & Zare, R.N. 2007 Counting low-copy number proteins in a single cell. Science 315, 81–84.CrossRefGoogle Scholar
Huh, D., Gu, W., Kamotani, Y., Grotberg, J.B. & Takayama, S. 2005 Microfluidics for flow cytometric analysis of cells and particles. Physiol. Meas. 26, R73–R98.CrossRefGoogle ScholarPubMed
Karrila, S.J., Fuentes, Y.O. & Kim, S. 1989 Parallel computational strategies for hydrodynamic interactions between rigid particles of arbitrary shape in a viscous fluid. J. Rheol. 33, 913–947.CrossRefGoogle Scholar
Keen, S., Yao, A., Leach, J., Di Leonardo, R., Saunter, C., Love, G., Cooper, J. & Padgett, M. 2009 Multipoint viscosity measurements in microfluidic channels using optical tweezers. Lab on a Chip 9, 2059–2062.CrossRefGoogle ScholarPubMed
Ladd, A.J.C. 1994 a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.CrossRefGoogle Scholar
Ladd, A.J.C. 1994 b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311–339.CrossRefGoogle Scholar
Levine, A.J. & Lubensky, T.C. 2000 One-and two-particle microrheology. Phys. Rev. Lett. 85, 1774.CrossRefGoogle ScholarPubMed
Lin, B., Cui, B., Lee, J.-H. & Yu, J. 2002 Hydrodynamic coupling in diffusion of quasi-one-dimensional Brownian particles. Europhys. Lett. 57, 724.CrossRefGoogle Scholar
Liron, N. & Shahar, R. 1978 Stokes flow due to a Stokeslet in a pipe. J. Fluid Mech. 86, 727–744.CrossRefGoogle Scholar
Lisicki, M., Cichocki, B. & Wajnryb, E. 2016 Near-wall diffusion tensor of an axisymmetric colloidal particle. J. Chem. Phys. 145, 034904.CrossRefGoogle ScholarPubMed
Martin, S., Reichert, M., Stark, H. & Gisler, T. 2006 Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres. Phys. Rev. Lett. 97, 248301.CrossRefGoogle ScholarPubMed
Mathijssen, A.J., Doostmohammadi, A., Yeomans, J.M. & Shendruk, T.N. 2016 Hotspots of boundary accumulation: dynamics and statistics of micro-swimmers in flowing films. J. R. Soc. Interface 13, 20150936.CrossRefGoogle ScholarPubMed
Mazo, R.M. 2002 Brownian Motion: Fluctuations, Dynamics, and Applications. Oxford University Press.Google Scholar
Mazur, P. & van Saarloos, W. 1982 Many-sphere hydrodynamic interactions and mobilities in a suspension. Physica A 115, 21–57.CrossRefGoogle Scholar
Meiners, J.-C. & Quake, S.R. 1999 Direct measurement of hydrodynamic cross correlations between two particles in an external potential. Phys. Rev. Lett. 82, 2211.CrossRefGoogle Scholar
Misiunas, K. & Keyser, U.F. 2019 Density-dependent speed-up of particle transport in channels. Phys. Rev. Lett. 122 (21), 214501.CrossRefGoogle ScholarPubMed
Misiunas, K., Pagliara, S., Lauga, E., Lister, J.R. & Keyser, U.F. 2015 Nondecaying hydrodynamic interactions along narrow channels. Phys. Rev. Lett. 115, 038301.CrossRefGoogle ScholarPubMed
Montgomery, J.A. Jr. & Berne, B.J. 1977 The effects of hydrodynamic interactions on translational and rotational relaxation. J. Chem. Phys. 67, 4589–4596.CrossRefGoogle Scholar
Mowitz, A.J. & Witten, T.A. 2017 Predicting tensorial electrophoretic effects in asymmetric colloids. Phys. Rev. E 96, 062613.CrossRefGoogle ScholarPubMed
Novikov, S., Rice, S.A., Cui, B., Diamant, H. & Lin, B. 2010 Hydrodynamic interactions in ribbon channels: from quasi-one-dimensional to quasi-two-dimensional behavior. Phys. Rev. E 82, 031403.CrossRefGoogle ScholarPubMed
Pagès, J.-M., James, C.E. & Winterhalter, M. 2008 The porin and the permeating antibiotic: a selective diffusion barrier in Gram-negative bacteria. Nat. Rev. Microbiol. 6, 893–903.CrossRefGoogle ScholarPubMed
Palanisamy, D. & den Otter, W.K. 2018 Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix. J. Chem. Phys. 148, 194112.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Raven, J.-P. & Marmottant, P. 2009 Microfluidic crystals: dynamic interplay between rearrangement waves and flow. Phys. Rev. Lett. 102, 084501.CrossRefGoogle ScholarPubMed
Reichert, M. & Stark, H. 2004 Hydrodynamic coupling of two rotating spheres trapped in harmonic potentials. Phys. Rev. E 69, 031407.CrossRefGoogle ScholarPubMed
Riley, K.F., Hobson, M.P. & Bence, S.J. 2006 Mathematical Methods for Physics and Engineering: a Comprehensive Guide. Cambridge university press.CrossRefGoogle Scholar
Sokolov, A., Aranson, I.S., Kessler, J.O. & Goldstein, R.E. 2007 Concentration dependence of the collective dynamics of swimming bacteria. Phys. Rev. Lett. 98, 158102.CrossRefGoogle ScholarPubMed
Somasi, M., Khomami, B., Woo, N.J., Hur, J.S. & Shaqfeh, E.S. 2002 Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues. J. Non-Newtonian Fluid Mech. 108, 227–255.CrossRefGoogle Scholar
Stroock, A.D., Weck, M., Chiu, D.T., Huck, W.T., Kenis, P.J., Ismagilov, R.F. & Whitesides, G.M. 2000 Patterning electro-osmotic flow with patterned surface charge. Phys. Rev. Lett. 84, 3314.CrossRefGoogle ScholarPubMed
Tanaka, H. 2001 Interplay between wetting and phase separation in binary fluid mixtures: roles of hydrodynamics. J. Phys: Condens. Matter 13, 4637.Google Scholar
Tanaka, H. 2005 Roles of hydrodynamic interactions in structure formation of soft matter: protein folding as an example. J. Phys: Condens. Matter 17, S2795.Google Scholar
Tran-Cong, T. & Phan-Thien, N. 1989 Stokes problems of multiparticle systems: a numerical method for arbitrary flows. Phys. Fluid A Fluid Dyn. 1, 453–461.CrossRefGoogle Scholar
Uspal, W.E. & Doyle, P.S. 2014 Self-organizing microfluidic crystals. Soft Matter 10, 5177–5191.CrossRefGoogle ScholarPubMed
Uspal, W.E., Eral, H.B. & Doyle, P.S. 2013 Engineering particle trajectories in microfluidic flows using particle shape. Nat. Commun. 4, 2666.CrossRefGoogle ScholarPubMed
Usta, O.B., Butler, J.E. & Ladd, A.J. 2007 Transverse migration of a confined polymer driven by an external force. Phys. Rev. Lett. 98, 098301.CrossRefGoogle ScholarPubMed
Usta, O.B., Ladd, A.J.C. & Butler, J.E. 2005 Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries. J. Chem. Phys. 122, 094902.CrossRefGoogle Scholar
Valley, D.T., Rice, S.A., Cui, B., Ho, H.M., Diamant, H. & Lin, B. 2007 Pair diffusion in quasi-one-and quasi-two-dimensional binary colloid suspensions. J. Chem. Phys. 126, 134908.CrossRefGoogle ScholarPubMed
Villanueva-Valencia, J.R., Santana-Solano, J., Sarmiento-Gómez, E., Herrera-Velarde, S., Arauz-Lara, J.L. & Castañeda-Priego, R. 2018 Long-time dynamics and hydrodynamic correlations in quasi-two-dimensional anisotropic colloidal mixtures. Phys. Rev. E 98, 062605.CrossRefGoogle Scholar
Wajnryb, E., Mizerski, K.A., Zuk, P.J. & Szymczak, P. 2013 Generalization of the Rotne-Prager-Yamakawa mobility and shear disturbance tensors. J. Fluid Mech. 731, R3.CrossRefGoogle Scholar
Wei, Q.-H., Bechinger, C. & Leiderer, P. 2000 Single-file diffusion of colloids in one-dimensional channels. Science 287, 625–627.CrossRefGoogle ScholarPubMed
Witten, T.A. & Diamant, H. 2020 A review of shaped colloidal particles in fluids: anisotropy and chirality. arXiv:2003.03698CrossRefGoogle Scholar
Witten, T.A. & Mowitz, A. 2019 Adapting the Teubner reciprocal relations for stokeslet objects. arXiv:1907.07444Google Scholar
Yang, H. & Kim, S. 1995 Boundary element analysis of particle mobilities in a cylindrical channel: network-based parallel computing with condor. Comput. Chem. Engng 19, 683–692.CrossRefGoogle Scholar
Zheng, Z. & Han, Y. 2010 Self-diffusion in two-dimensional hard ellipsoid suspensions. J. Chem. Phys. 133, 124509.CrossRefGoogle ScholarPubMed
Zheng, Z., Ni, R., Wang, F., Dijkstra, M., Wang, Y. & Han, Y. 2014 Structural signatures of dynamic heterogeneities in monolayers of colloidal ellipsoids. Nat. Commun. 5, 3829.CrossRefGoogle ScholarPubMed
Zheng, Z., Wang, F. & Han, Y. 2011 Glass transitions in quasi-two-dimensional suspensions of colloidal ellipsoids. Phys. Rev. Lett. 107, 065702.CrossRefGoogle ScholarPubMed