Abstract

The hydrodynamics of Brownian particles close to a wall is investigated using low-coherence dynamic light scattering. The diffusion coefficient of the particles in a suspension is measured as a function of distance from the wall. A sudden reduction in the diffusion coefficient near the interface is clearly observed using this method. The theoretically predicted wall-drag effect is experimentally confirmed when the influence of the spatial resolution due to the finite coherence length of the light source is accounted for. The space-dependent dynamics of Brownian particles under the wall-drag effect is obtained for the first time using our spatially resolved dynamic light scattering technique.

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  1. H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. 16(3-4), 242 – 251 (1961).
    [CrossRef]
  2. A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall – I Motion through a quiescent fluid,” Chem. Eng. Sci. 22(4), 637 – 651 (1967).
    [CrossRef]
  3. M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: A photon correlation study,” Phys. Rev. A 44(10), 6677 – 6685 (1991).
    [CrossRef] [PubMed]
  4. L. Lobry and N. Ostrowsky, “Diffusion of Brownian particles trapped between two walls: theory and dynamic-light scattering measurements,” Phys. Rev. B 53(18), 12050 – 12056 (1996).
    [CrossRef]
  5. P. G. Cummins and E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E Sci. Instrum. 14(10), 1171 – 1177 (1981).
    [CrossRef]
  6. K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17 – 20 (1986).
    [CrossRef] [PubMed]
  7. N. Garnier and N. Ostrowsky, “Brownian dynamics in a confined geometry. Experiments and numerical simulations,” J. Phys. II France 1(10), 1221 – 1232 (1991).
    [CrossRef]
  8. M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 6275 – 6280 (1998).
    [CrossRef]
  9. D. A. Boas, K. K. Bizheva, and A. M. Siegel, “Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media,” Opt. Lett. 23(5), 319 – 321 (1998).
    [CrossRef]
  10. G. Popescu and A. Dogariu, “Dynamic light scattering in localized coherence volumes,” Opt. Lett. 26(8), 551 – 553 (2001).
    [CrossRef]
  11. K. Ishii, R. Yoshida, and T. Iwai, “Single-scattering spectroscopy for extremely dense colloidal suspensions by use of a low-coherence interferometer,” Opt. Lett. 30(5), 555 – 557 (2005).
    [CrossRef] [PubMed]
  12. H. Xia, K. Ishii, and T. Iwai, “Hydrodynamic radius sizing of nanoparticles in dense polydisperse media by low-coherence dynamic light scattering,” Jpn. J. Appl. Phys. 44(8), 6261 – 6264 (2005).
    [CrossRef]
  13. K. Ishii, T. Iwai, and S. Nakamura, “Numerical analysis of a path-length-resolved spectrum of time-varying scattered light field,” J. Opt. Soc. Am. A 25(3), 718 – 724 (2008).
    [CrossRef]
  14. K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7664 – 7667 (1998).
    [CrossRef]
  15. G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74(01), 1 (1976).
    [CrossRef]
  16. H. Xia, K. Ishii, T. Iwaii, H. Li, and B. Yang, “Dynamics of interacting Brownian particles in concentrated colloidal suspensions,” Appl. Opt. 47(9), 1257 – 1262 (2008).
    [CrossRef] [PubMed]
  17. Y. Wang, Y. Zhao, J. S. Nelson, Z. Chen, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber,” Opt. Lett. 28(3), 182 – 184 (2003).
    [CrossRef] [PubMed]

2008 (2)

2005 (2)

K. Ishii, R. Yoshida, and T. Iwai, “Single-scattering spectroscopy for extremely dense colloidal suspensions by use of a low-coherence interferometer,” Opt. Lett. 30(5), 555 – 557 (2005).
[CrossRef] [PubMed]

H. Xia, K. Ishii, and T. Iwai, “Hydrodynamic radius sizing of nanoparticles in dense polydisperse media by low-coherence dynamic light scattering,” Jpn. J. Appl. Phys. 44(8), 6261 – 6264 (2005).
[CrossRef]

2003 (1)

2001 (1)

1998 (3)

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7664 – 7667 (1998).
[CrossRef]

M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 6275 – 6280 (1998).
[CrossRef]

D. A. Boas, K. K. Bizheva, and A. M. Siegel, “Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media,” Opt. Lett. 23(5), 319 – 321 (1998).
[CrossRef]

1996 (1)

L. Lobry and N. Ostrowsky, “Diffusion of Brownian particles trapped between two walls: theory and dynamic-light scattering measurements,” Phys. Rev. B 53(18), 12050 – 12056 (1996).
[CrossRef]

1991 (2)

M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: A photon correlation study,” Phys. Rev. A 44(10), 6677 – 6685 (1991).
[CrossRef] [PubMed]

N. Garnier and N. Ostrowsky, “Brownian dynamics in a confined geometry. Experiments and numerical simulations,” J. Phys. II France 1(10), 1221 – 1232 (1991).
[CrossRef]

1986 (1)

K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17 – 20 (1986).
[CrossRef] [PubMed]

1981 (1)

P. G. Cummins and E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E Sci. Instrum. 14(10), 1171 – 1177 (1981).
[CrossRef]

1976 (1)

G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74(01), 1 (1976).
[CrossRef]

1967 (1)

A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall – I Motion through a quiescent fluid,” Chem. Eng. Sci. 22(4), 637 – 651 (1967).
[CrossRef]

1961 (1)

H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. 16(3-4), 242 – 251 (1961).
[CrossRef]

Batchelor, G. K.

G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74(01), 1 (1976).
[CrossRef]

Bizheva, K. K.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7664 – 7667 (1998).
[CrossRef]

D. A. Boas, K. K. Bizheva, and A. M. Siegel, “Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media,” Opt. Lett. 23(5), 319 – 321 (1998).
[CrossRef]

Boas, D. A.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7664 – 7667 (1998).
[CrossRef]

D. A. Boas, K. K. Bizheva, and A. M. Siegel, “Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media,” Opt. Lett. 23(5), 319 – 321 (1998).
[CrossRef]

Brenner, H.

A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall – I Motion through a quiescent fluid,” Chem. Eng. Sci. 22(4), 637 – 651 (1967).
[CrossRef]

H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. 16(3-4), 242 – 251 (1961).
[CrossRef]

Chen, Z.

Cox, R. G.

A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall – I Motion through a quiescent fluid,” Chem. Eng. Sci. 22(4), 637 – 651 (1967).
[CrossRef]

Cummins, P. G.

P. G. Cummins and E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E Sci. Instrum. 14(10), 1171 – 1177 (1981).
[CrossRef]

Dogariu, A.

Feitosa, M. I. M.

M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: A photon correlation study,” Phys. Rev. A 44(10), 6677 – 6685 (1991).
[CrossRef] [PubMed]

Garnier, N.

N. Garnier and N. Ostrowsky, “Brownian dynamics in a confined geometry. Experiments and numerical simulations,” J. Phys. II France 1(10), 1221 – 1232 (1991).
[CrossRef]

Goldman, A. J.

A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall – I Motion through a quiescent fluid,” Chem. Eng. Sci. 22(4), 637 – 651 (1967).
[CrossRef]

Hosoda, M.

M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 6275 – 6280 (1998).
[CrossRef]

Ishii, K.

Iwai, T.

Iwaii, T.

Lan, K. H.

K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17 – 20 (1986).
[CrossRef] [PubMed]

Li, H.

Lobry, L.

L. Lobry and N. Ostrowsky, “Diffusion of Brownian particles trapped between two walls: theory and dynamic-light scattering measurements,” Phys. Rev. B 53(18), 12050 – 12056 (1996).
[CrossRef]

Mesquita, O. N.

M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: A photon correlation study,” Phys. Rev. A 44(10), 6677 – 6685 (1991).
[CrossRef] [PubMed]

Nakamura, S.

Nelson, J. S.

Ostrowsky, N.

L. Lobry and N. Ostrowsky, “Diffusion of Brownian particles trapped between two walls: theory and dynamic-light scattering measurements,” Phys. Rev. B 53(18), 12050 – 12056 (1996).
[CrossRef]

N. Garnier and N. Ostrowsky, “Brownian dynamics in a confined geometry. Experiments and numerical simulations,” J. Phys. II France 1(10), 1221 – 1232 (1991).
[CrossRef]

K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17 – 20 (1986).
[CrossRef] [PubMed]

Popescu, G.

Sakai, K.

M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 6275 – 6280 (1998).
[CrossRef]

Siegel, A. M.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7664 – 7667 (1998).
[CrossRef]

D. A. Boas, K. K. Bizheva, and A. M. Siegel, “Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media,” Opt. Lett. 23(5), 319 – 321 (1998).
[CrossRef]

Sornette, D.

K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17 – 20 (1986).
[CrossRef] [PubMed]

Staples, E. J.

P. G. Cummins and E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E Sci. Instrum. 14(10), 1171 – 1177 (1981).
[CrossRef]

Takagi, K.

M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 6275 – 6280 (1998).
[CrossRef]

Wang, Y.

Windeler, R. S.

Xia, H.

H. Xia, K. Ishii, T. Iwaii, H. Li, and B. Yang, “Dynamics of interacting Brownian particles in concentrated colloidal suspensions,” Appl. Opt. 47(9), 1257 – 1262 (2008).
[CrossRef] [PubMed]

H. Xia, K. Ishii, and T. Iwai, “Hydrodynamic radius sizing of nanoparticles in dense polydisperse media by low-coherence dynamic light scattering,” Jpn. J. Appl. Phys. 44(8), 6261 – 6264 (2005).
[CrossRef]

Yang, B.

Yoshida, R.

Zhao, Y.

Appl. Opt. (1)

Chem. Eng. Sci. (2)

H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. 16(3-4), 242 – 251 (1961).
[CrossRef]

A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall – I Motion through a quiescent fluid,” Chem. Eng. Sci. 22(4), 637 – 651 (1967).
[CrossRef]

J. Fluid Mech. (1)

G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74(01), 1 (1976).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. E Sci. Instrum. (1)

P. G. Cummins and E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E Sci. Instrum. 14(10), 1171 – 1177 (1981).
[CrossRef]

J. Phys. II France (1)

N. Garnier and N. Ostrowsky, “Brownian dynamics in a confined geometry. Experiments and numerical simulations,” J. Phys. II France 1(10), 1221 – 1232 (1991).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Xia, K. Ishii, and T. Iwai, “Hydrodynamic radius sizing of nanoparticles in dense polydisperse media by low-coherence dynamic light scattering,” Jpn. J. Appl. Phys. 44(8), 6261 – 6264 (2005).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: A photon correlation study,” Phys. Rev. A 44(10), 6677 – 6685 (1991).
[CrossRef] [PubMed]

Phys. Rev. B (1)

L. Lobry and N. Ostrowsky, “Diffusion of Brownian particles trapped between two walls: theory and dynamic-light scattering measurements,” Phys. Rev. B 53(18), 12050 – 12056 (1996).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (2)

M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 6275 – 6280 (1998).
[CrossRef]

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7664 – 7667 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17 – 20 (1986).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the low-coherence DLS experimental system.

Fig. 2
Fig. 2

Normalized amplitude autocorrelation functions obtained by low-coherence DLS measurements. A 10 vol% suspension of monodisperse polystyrene latex particles with a mean radius of 0.235 μm is used as the scattering medium. □, ●, and ∇ denote the experimental results for L = 4, 8, and 15 μm, respectively. The solid lines represent the results of fitting the experimental data with single exponential functions.

Fig. 3
Fig. 3

Anisotropic wall-drag effective diffusion coefficient of spherical particles with radii of 0.235 and 1.485 μm calculated using hydrodynamic theory [Eqs. (3) and (4)].

Fig. 4
Fig. 4

Measured coherence function and power spectrum distribution of a SLD. λ 0 ≈850 nm and l c ≈14 μm. The solid curve is a least-squares fit with a Gaussian function.

Fig. 5
Fig. 5

Normalized wall-drag effective diffusion coefficient along the direction normal to the interface as a function of distance from the interface s. □, ○, △, and ◇ represent experimental results for 10 vol% suspensions of monodisperse polystyrene latex particles with mean radii of 0.235, 0.403, 0.55, and 1.485 μm, respectively. The different lines represent the theoretical curves obtained from Eq. (7).

Equations (7)

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γ ( τ ) exp ( D q 2 τ ) ,
D 0 = k B T 6 π η 0 R ,
D h = [ ( 1 φ / 2 ) ( 1 φ ) 3 ] 1 D 0 ,
D w = { 4 3 sinh α n = 1 n ( n + 1 ) ( 2 n 1 ) ( 2 n + 3 ) [ 2 sinh ( 2 n + 1 ) α + ( 2 n + 1 ) sinh 2 α 4 sinh 2 ( n + 1 / 2 ) α ( 2 n + 1 ) 2 sinh 2 α 1 ] } 1 D h ,
γ ( Δ l ) exp [ 4 ln 2 ( Δ l / l c ) 2 ] ,
l c = 2 ln 2 / π ( λ 0 2 / Δ λ ) .
D w ( s ) = 0 D w ( l ) γ ( s l ) d l 0 γ ( s l ) d l D h .

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