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The dynamics and rheology of a dilute suspension of hydrodynamically Janus spheres in a linear flow

Published online by Cambridge University Press:  25 August 2009

ARUN RAMACHANDRAN  and
ADITYA S. KHAIR
ARUN RAMACHANDRAN
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
ADITYA S. KHAIR*
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
*
†Email address for correspondence: akhair@engineering.uscb.edu
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Abstract

The creeping motion of a hydrodynamically ‘Janus’ spherical particle, whose surface is partitioned into two distinct regions, is investigated. On one region, fluid adjacent to the particle obeys the no-slip condition, whereas on the other, fluid slips past the particle. The fore-aft asymmetry of this ‘slip–stick’ sphere (Swan & Khair, J. Fluid Mech., vol. 606, 2008, p. 115) leads to a number of interesting results when it is placed in different flows, which is illustrated by computing the particle motion to first order in the ratio of slip length to particle radius. For example, in a pure straining field the sphere attains an equilibrium orientation either along the compressional or extensional axis of the flow, depending on the ratio of slip-to-stick surface areas. In a simple shear flow, on the other hand, the slip–stick sphere undergoes a periodic rotational motion, or Jeffrey orbit. Moreover, depending on its initial orientation, the particle can either follow a periodic {translational} orbit or undergo a net displacement along the flow direction. Lastly, to first order in the volume fraction of slip–stick spheres, the suspension rheology is non-Newtonian, with non-zero first and second normal stress differences.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 233 - 269
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Basset, A. B. 1961 A Treatise on Hydrodynamics. Dover.Google Scholar
Batchelor, G. K. 1970 Stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.CrossRefGoogle Scholar
Batchelor, G. K. 1973 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Behrend, C. J., Anker, J. N., McNaughton, B. H., & Kopelman, R. 2005 Microrheology with modulated optical nanoprobes (MOONs). J. Magn. Magn. Mater. 293, 663–670.CrossRefGoogle Scholar
Beitel, A. & Heideger, J. W. 1971 Surfactant effects on mass transfer from drops subject to interfacial instability. Chem. Engng Sci. 26, 711–717.CrossRefGoogle Scholar
Boehnke, U. C., Remmler, T., Motschmann, H., Wurlitzer, S., Hauwede, J. & Fischer, Th. M. 1999 Partial air wetting on solvophobic surfaces in polar liquids. J. Colloid Interface Sci. 211, 243–251.CrossRefGoogle ScholarPubMed
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284–304.CrossRefGoogle Scholar
Casagrande, C., Fabre, P., Raphael, E. & Veyssie, M. 1989 Janus beads: realization and behaviour at water/oil interfaces. Europhys. Lett. 9 (3), 251–255.CrossRefGoogle Scholar
Cayre, O., Paunov, V. N. & Velev, O. D. 2003 Fabrication of asymmetrically coated colloid particles by microcontact printing techniques. J. Mat. Chem. 13 (10), 2445–2450.CrossRefGoogle Scholar
Cheng, J. T. & Giordano, N. 2002 Fluid flow through nanometre-scale channels. Phys. Rev. E 65, 031206.CrossRefGoogle Scholar
Choi, C.-H., Westin, K.Johan, A. & Breuer, K. S. 2003 Apparent slip flows in hydrophilic and hydrophobic microchannels. Phys. Fluids 15 (10), 2897–2902.CrossRefGoogle Scholar
De Gennes, P. G. 1992 Soft Matter. Rev. Mod. Phys. 64, 645–648.CrossRefGoogle Scholar
Dietrich, C., Bagatolli, L. A., Volovyk, Z. N., Thompson, N. L., Levi, M., Jacobson, S. K. & Gratton, E. 2001 Lipid rafts reconstituted in model membranes. Biophys. J. 80, 1417–1428.CrossRefGoogle ScholarPubMed
Dorrepaal, J. M. 1978 The Stokes resistance of a spherical cap to translational and rotational motions in a linear shear flow. J. Fluid Mech. 84, 265–279.CrossRefGoogle Scholar
Einstein, A. 1906 A new determination of molecular dimensions. Ann. Phys. 19, 289–306.CrossRefGoogle Scholar
Ericksen, J. L. 1959 Anisotropic fluids. Arc. Rat. Mech. Anal. 4, 231–237.CrossRefGoogle Scholar
Gangwal, S., Cayre, O. J., Bazant, M. Z. & Velev, O. D. 2008 Induced-charge electrophoresis of metallodielectric particles. Phys. Rev. Lett. 100, 058302.CrossRefGoogle ScholarPubMed
Glaser, N., Adams, D. J., Boker, A. & Krausch, G. 2006 Janus particles and liquid–liquid interfaces. Langmuir 22, 5227–5229.CrossRefGoogle ScholarPubMed
Glotzer, S. C. & Solomon, M. J. 2007 Anisotropy of building blocks and their assembly into complex structures. Nat. Mater. 6, 557–562.CrossRefGoogle ScholarPubMed
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
Hinch, E. J. & Leal, L. G. 1972 The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52 (4), 683–712.CrossRefGoogle Scholar
Hong, L., Jiang, S. & Granick, S. 2006 Simple method to produce Janus colloidal particles in large quantity. Langmuir 22 (23), 9459–9499.CrossRefGoogle ScholarPubMed
Howse, J. R., Jones, R. A. L., Ryan, A. J., Gough, T., Vafabakhsh, R. & Golestanian, R. 2007 Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99, 048102.CrossRefGoogle ScholarPubMed
Kim, S. & Karrila, S. J. 2005 Microhydrodynamics: Principles and Selected Applications. Dover.Google Scholar
Korlach, J., Schwille, P., Webb, W. & Feigenson, G. 1999 Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. Proc. Natl. Acad. Sci. 96, 8461–8466.CrossRefGoogle ScholarPubMed
Lamb, H. 1932 Hydrodynamics. Dover.Google Scholar
Lauga, E., Brenner, M. P. & Stone, H. A. 2007 Microfluidics: the no-slip boundary condition. In Handbook of Experimental Fluid Dynamics (ed. Tropea, C., Yarin, A. & Foss, J. F.), pp. 1219–1240. Springer.Google Scholar
Lauga, E. & Stone, H. A. 2003 Effective slip in pressure-driven Stokes flow. J. Fluid Mech. 489, 55–77.CrossRefGoogle Scholar
Leal, L. G. 2007 Advanced Transport Phenomena. Cambridge University Press.CrossRefGoogle Scholar
Navier, C. L. M. H. 1823 Mémoire sur le lois du mouvement des fluides. Mémoires de l'Academie Royale des Sciences de l'Instituit de France IV, 389–440.Google Scholar
Nie, Z., Li, W., Seo, M., Xu, S. & Kumacheva, E. 2006 Janus and Ternary particles generated by microfluidic synthesis: design, synthesis and self-assembly. J. Am. Chem. Soc. 128 (29), 9408–9412.CrossRefGoogle ScholarPubMed
Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209–223.CrossRefGoogle Scholar
Nisisako, T., Torii, T., Takahashi, T. & Takizawa, Y. 2006 Synthesis of monodisperese bicolored Janus particles with electrical anisotropy using a microfluidic co-flow system. Adv. Mater. 18, 1152–1156.CrossRefGoogle Scholar
Perro, A., Reculusa, S., Ravaine, S., Bourgeat-Lami, E. B. & Duguet, E. 2005 Design and synthesis of Janus micro- and nanoparticles. J. Mat. Chem. 15, 3745–3760.CrossRefGoogle Scholar
Philip, J. R. 1972 a Flows satisfying mixed no-slip and no-shear conditions. Z. Agnew. Math. Phys. 23, 353–370.CrossRefGoogle Scholar
Philip, J. R. 1972 b Integral properties of flows satisfying mixed no-slip and no-shear conditions. Z. Agnew. Math. Phys. 23, 960–968.CrossRefGoogle Scholar
Priezjev, N. V., Darhuber, A. A. & Troian, S. M. 2005 Slip behaviour in liquid films on surfaces of patterned wettability: comparison between continuum and molecular dynamics simulations. Phys. Rev. E 71, 041608.CrossRefGoogle ScholarPubMed
Roh, K., Martin, D. C. & Lahann, J. 2005 Biphasic Janus particles with nanoscale anisotropy. Nat. Mater. 4, 759–763.CrossRefGoogle ScholarPubMed
Sadhal, S. S. & Johnson, R. E. 1983 Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film – exact solution. J. Fluid Mech. 126, 237–250.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2006 Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J. Fluid Mech. 560, 65–101.CrossRefGoogle Scholar
Swan, J. W. & Khair, A. S. 2008 On the hydrodynamics of “slip-stick” spheres. J. Fluid Mech. 606, 115–132.CrossRefGoogle Scholar
Takei, H. & Shimizu, N. 1997 Gradient sensitive microscopic probes prepared by gold evaporation and chemisorption on latex spheres. Langmuir 13 (7), 1865–1868.CrossRefGoogle Scholar
Taylor, G. I. 1971 A model for the boundary condition of a porous material. Part 1. J. Fluid Mech. 49, 319–326.CrossRefGoogle Scholar
Thompson, P. A. & Troian, S. M. 1997 A general boundary condition for liquid flow at solid surfaces. Nature 389, 360–362.CrossRefGoogle Scholar
Tyrrell, J. W. G. & Attard, P. 2001 Images of nanobubbles on hydrophobic surface and their interactions. Phys. Rev. Lett. 87 (17), 176104.CrossRefGoogle ScholarPubMed
Velev, O. D., Lenhoff, A. M. & Kaler, E. W. 2000 A class of microstructured particles through colloidal crystallization. Science 287, 2240–2243.CrossRefGoogle ScholarPubMed
Walther, A. & Muller, A. H. E. 2008 Janus particles. Soft Matter 4, 663–668.CrossRefGoogle ScholarPubMed