Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-09T21:57:11.794Z Has data issue: false hasContentIssue false
  • English
  • Français

The effects of hindered mobility and depletion of particles in near-wall shear flows and the implications for nanovelocimetry

Published online by Cambridge University Press:  17 September 2009

PETER HUANG ,
JEFFREY S. GUASTO  and
KENNETH S. BREUER
PETER HUANG*
Affiliation:
Division of Engineering, Brown University, Providence, RI 02915, USA
JEFFREY S. GUASTO
Affiliation:
Division of Engineering, Brown University, Providence, RI 02915, USA
KENNETH S. BREUER
Affiliation:
Division of Engineering, Brown University, Providence, RI 02915, USA
*
†Present address: Department of Mechanical Engineering, Binghamton University, Binghamton, NY 13902, USA. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The behaviour of spherical Brownian particles in a near-wall shear flow is explored using Langevin simulations and experimental measurements, focusing on the effects of anisotropic hindered particle mobility and the formation of a particle depletion layer due to repulsive forces. The results are discussed in the context of particle velocity distributions obtained by near-wall image-based velocimetry. It is observed that the shear force and dispersion dominate at high Péclet number (Pe > 3), and the asymmetric shapes of particle velocity distributions are attributed to broken symmetry due to the presence of the wall. Furthermore, the excursions outside the observation depth between image acquisitions and the shear-induced slowdowns of tracer particles cause significant measurement bias for long and short inter-frame time intervals, respectively. Also impeding the measurement accuracy is the existence of a near-wall particle depletion layer that leads to an overestimation of the fluid velocity. An analytical protocol to infer the correct fluid velocity from biased measurements is presented.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 637 , 25 October 2009 , pp. 241 - 265
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Axelrod, D. 2001 Total internal reflection fluorescence microscopy in cell biology. Traffic 2, 764–774.CrossRefGoogle ScholarPubMed
Banerjee, A. & Kihm, K. D. 2005 Experimental verification of near-wall hindered diffusion for the Brownian motion of nanoparticles using evanescent wave microscopy. Phys. Rev. E 72, 042101.CrossRefGoogle ScholarPubMed
Bevan, M. A. & Prieve, D. C. 2000 Hindered diffusion of colloidal particles very near to a wall: revisited. J. Chem. Phys. 113, 1228–1236.CrossRefGoogle Scholar
Bouzigues, C. I., Tabeling, P. & Bocquet, L. 2008 Nanofluidics in the debye layer at hydrophilic and hydrophobic surfaces. Phys. Rev. Lett. 101, 114503.CrossRefGoogle ScholarPubMed
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane wall. Chem. Engng Sci. 16, 242–251.CrossRefGoogle Scholar
Chaoui, M. & Feuillebois, F. 2003 Creeping flow around a sphere in a shear flow close to a wall. Quart. J. Mech. Appl. Math. 56, 381–410.CrossRefGoogle Scholar
Cheezum, M. K., Walker, W. F. & Guilford, W. H. 2001 Quantitative comparison of algorithms for tracking single fluorescent particles. Biophys. J. 81, 2378–2388.CrossRefGoogle ScholarPubMed
Cherukat, P. & McLaughlin, J. B. 1994 The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263, 1–18.CrossRefGoogle Scholar
Deen, W. M. 1998 Analysis of Transport Phenomena. Oxford University Press.Google Scholar
Ermak, D. L. & McCammon, J. A. 1978 Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352–1360.CrossRefGoogle Scholar
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 a Slow viscous motion of a sphere parallel to a plane wall – I: motion through a quiescent fluid. Chem. Engng Sci. 22, 637–651.CrossRefGoogle Scholar
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 b Slow viscous motion of a sphere parallel to a plane wall – II: Couette flow. Chem. Engng Sci. 22, 653–660.CrossRefGoogle Scholar
Guasto, J. S. 2008 Micro- and nano-scale colloidal dynamics near surfaces. PhD thesis, Brown University, Providence, RI.Google Scholar
Guasto, J. S. & Breuer, K. S. 2009 High-speed quantum dot tracking using evanesent wave illumination. Exp. Fluids (in press).CrossRefGoogle Scholar
Guasto, J. S., Huang, P. & Breuer, K. S. 2006 Statistical particle tracking velocimetry using molecular and quantum dot tracer particles. Exp. Fluids 41, 869–880.CrossRefGoogle Scholar
Hohenegger, C. & Mucha, P. J. 2007 Statistical reconstruction of velocity profiles for nanoparticle image velocimetry. J. Appl. Math. 68, 239–252.Google Scholar
Huang, P. & Breuer, K. S. 2007 a Direct measurement of anisotropic near-wall hindered diffusion using total internal reflection velocimetry. Phys. Rev. E 76, 046307.CrossRefGoogle ScholarPubMed
Huang, P. & Breuer, K. S. 2007 b Direct measurement of slip length in electrolyte solutions. Phys. Fluids 19, 028104.CrossRefGoogle Scholar
Huang, P., Guasto, J. S. & Breuer, K. S. 2006 Direct measurement of slip velocities using three-dimensional total internal reflection velocimetry. J. Fluid Mech. 566, 447–464.CrossRefGoogle Scholar
Jin, S., Huang, P., Park, J., Yoo, J. Y. & Breuer, K. S. 2004 Near-surface velocimetry using evanescent wave illumination. Exp. Fluids 37, 825–833.CrossRefGoogle Scholar
Jones, R. A. L. 2002 Soft Condensed Matter. Oxford University Press.CrossRefGoogle Scholar
Joseph, P. & Tabeling, P. 2005 Direct measurement of the apparent slip length. Phys. Rev. E 71, 035303(R).CrossRefGoogle ScholarPubMed
King, M. R. & Leighton, D. T. 1997 Measurement of the inertial lift on a moving sphere in contact with a plane wall in a shear flow. Phys. Fluids 9, 1248–1255.CrossRefGoogle Scholar
Lauga, E. & Squires, T. M. 2005 Brownian motion near a partial-slip boundary: a local probe of the no-slip condition. Phys. Fluids 17, 103102.CrossRefGoogle Scholar
Li, H. & Yoda, M. 2008 Multilayer nano-particle image velocimetry (MnPIV) in microscale Poiseuille flows. Meas. Sci. Technol. 19, 075402.CrossRefGoogle Scholar
Lin, B., Yu, J. & Rice, S. A. 2000 Direct measurements of constrained Brownian motion of an isolated sphere between two walls. Phys. Rev. E 62, 3909–3919.CrossRefGoogle ScholarPubMed
Oberholzer, M. R., Wagner, N. J. & Lenhoff, A. M. 1997 Grand canonical Brownian dynamics simulation of colloidal adsorption. J. Chem. Phys. 107, 9157–9167.CrossRefGoogle Scholar
Oetama, R. J. & Walz, J. Y. 2006 Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface. J. Chem. Phys. 124, 164713.CrossRefGoogle ScholarPubMed
Peters, E. A. J. F. & Barenbrug, Th. M. A. O. M. 2002 a Efficient Brownian dynamics simulation of particles near wall. I. Reflecting and absorbing walls. Phys. Rev. E 66, 056701.CrossRefGoogle Scholar
Peters, E. A. J. F. & Barenbrug, Th. M. A. O. M. 2002 b Efficient Brownian dynamics simulation of particles near wall. II. Sticky walls. Phys. Rev. E 66, 056702.CrossRefGoogle ScholarPubMed
Pierres, A., Benoliel, A.-M., Zhu, C. & Bongrand, P. 2001 Diffusion of microspheres in shear flow near a wall: use to measure binding rates between attached molecules. Biophys. J. 81, 25–42.CrossRefGoogle Scholar
Pouya, S., Koochesfahani, M. M., Greytak, A. B., Bawendi, M. G. & Nocera, D. 2008 Experimental evidence of diffusion-induced bias in near-wall velocimetry using quantum dot measurements. Exp. Fluids 44, 1035–1038.CrossRefGoogle Scholar
Prieve, D. C. 1999 Measurement of colloidal forces with TIRM. Adv. Colloid Interface Sci. 82, 93–125.CrossRefGoogle Scholar
Sadr, R., Hohenegger, C., Li, H., Mucha, P. J. & Yoda, M. 2007 Diffusion-induced bias in near-wall velocimetry. J. Fluid Mech. 577, 443–456.CrossRefGoogle Scholar
Sadr, R., Li, H. & Yoda, M. 2005 Impact of hindered Brownian diffusion on the accuracy of particle-image velocimetry using evanescent-wave illumination. Exp. Fluids 38, 90–98.CrossRefGoogle Scholar
Santiago, J. G., Wereley, S. T., Meinhart, C. D., Beebe, D. J. & Adrian, R. J. 1998 A particle image velocimetry system for microfluidics. Exp. Fluids 25, 316–319.CrossRefGoogle Scholar
Sholl, D. S., Fenwick, M. K., Atman, E. & Prieve, D. C. 2000 Brownian dynamics simulation of the motion of a rigid sphere in a viscous fluid very near a wall. J. Chem. Phys. 113, 9268–9278.CrossRefGoogle Scholar
Unni, H. N. & Yang, C. 2005 Brownian dynamics simulation and experimental study of colloidal particle deposition in a microchannel flow. J. Colloid Interface Sci. 291, 28–36.CrossRefGoogle Scholar
Wereley, S. T. & Meinhart, C. D. 2005 Micron-resolution particle image velocimetry. In Microscale Diagnostic Techniques (ed. Breuer, K.), pp. 51–112. Springer.CrossRefGoogle Scholar
Xia, Y. & Whitesides, G. M. 1998 Soft lithography. Annu. Rev. Mater. Sci. 28, 153–184.CrossRefGoogle Scholar
Zettner, C. M. & Yoda, M. 2003 Particle velocity field measurements in a near-wall flow using evanescent wave illumination. Exp. Fluids 34, 115–121.CrossRefGoogle Scholar