F. C. MacKintosh and S. John, Phys. Rev. B 40, 2383 (1989).

[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63 (1988).

[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77 (1988).

[CrossRef]

P. Tong, W. I. Goldburg, C. K. Chan, and A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125 (1988).

[CrossRef]
[PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).

[CrossRef]
[PubMed]

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409 (1987).

[CrossRef]

P. Pieranski, “Colloidal crystals,” Contemp. Phys. 24, 25 (1983).

[CrossRef]

G. G. Fuller, J. M. Rallison, R. L. Schmidt, and L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555 (1980).

[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63 (1988).

[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77 (1988).

[CrossRef]

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge U. Press, Cambridge, 1977), p. 83.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).

[CrossRef]
[PubMed]

P. M. Chaikin, J. M. di Meglio, W. D. Dozier, H. M. Lindsay, and D. A. Weitz, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 65.

P. Tong, W. I. Goldburg, C. K. Chan, and A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125 (1988).

[CrossRef]
[PubMed]

S. H. Chen, T. L. Lin, and J. S. Huang, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 285.

B. Chu, Laser Light Scattering (Academic, New York, 1974), pp. 101–104.

P. M. Chaikin, J. M. di Meglio, W. D. Dozier, H. M. Lindsay, and D. A. Weitz, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 65.

P. M. Chaikin, J. M. di Meglio, W. D. Dozier, H. M. Lindsay, and D. A. Weitz, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 65.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, and L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555 (1980).

[CrossRef]

P. Tong, W. I. Goldburg, C. K. Chan, and A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125 (1988).

[CrossRef]
[PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).

[CrossRef]
[PubMed]

J. S. Huang and M. W. Kim, “Critical behavior of a microemulsion,” Phys. Rev. Lett. 47, 1462 (1981).

[CrossRef]

S. H. Chen, T. L. Lin, and J. S. Huang, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 285.

A. Ishimaru, Wave Propagation in Random Media (Academic, New York, 1978).

F. C. MacKintosh and S. John, Phys. Rev. B 40, 2383 (1989).

[CrossRef]

J. S. Huang and M. W. Kim, “Critical behavior of a microemulsion,” Phys. Rev. Lett. 47, 1462 (1981).

[CrossRef]

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1984), p. 55.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, and L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555 (1980).

[CrossRef]

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1984), p. 55.

S. H. Chen, T. L. Lin, and J. S. Huang, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 285.

P. M. Chaikin, J. M. di Meglio, W. D. Dozier, H. M. Lindsay, and D. A. Weitz, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 65.

F. C. MacKintosh and S. John, Phys. Rev. B 40, 2383 (1989).

[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63 (1988).

[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77 (1988).

[CrossRef]

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409 (1987).

[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77 (1988).

[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63 (1988).

[CrossRef]

P. Pieranski, “Colloidal crystals,” Contemp. Phys. 24, 25 (1983).

[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).

[CrossRef]
[PubMed]

G. G. Fuller, J. M. Rallison, R. L. Schmidt, and L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555 (1980).

[CrossRef]

G. G. Fuller, J. M. Rallison, R. L. Schmidt, and L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555 (1980).

[CrossRef]

P. Tong, W. I. Goldburg, C. K. Chan, and A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125 (1988).

[CrossRef]
[PubMed]

P. Tong, W. I. Goldburg, C. K. Chan, and A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125 (1988).

[CrossRef]
[PubMed]

D. J. Tritton, Physical Fluid Dynamics, 2nd ed. (Clarendon, Oxford, 1988), p. 20.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).

[CrossRef]
[PubMed]

P. M. Chaikin, J. M. di Meglio, W. D. Dozier, H. M. Lindsay, and D. A. Weitz, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 65.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63 (1988).

[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77 (1988).

[CrossRef]

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409 (1987).

[CrossRef]

P. Pieranski, “Colloidal crystals,” Contemp. Phys. 24, 25 (1983).

[CrossRef]

G. G. Fuller, J. M. Rallison, R. L. Schmidt, and L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555 (1980).

[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63 (1988).

[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77 (1988).

[CrossRef]

P. Tong, W. I. Goldburg, C. K. Chan, and A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125 (1988).

[CrossRef]
[PubMed]

F. C. MacKintosh and S. John, Phys. Rev. B 40, 2383 (1989).

[CrossRef]

J. S. Huang and M. W. Kim, “Critical behavior of a microemulsion,” Phys. Rev. Lett. 47, 1462 (1981).

[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).

[CrossRef]
[PubMed]

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409 (1987).

[CrossRef]

We note that the average intensity of transmitted light, 〈I〉, through the sample did not vary with Γ¯. Since 〈I〉 ∼ l*/L, we conclude that l*, and hence P(s), does not vary with Γ¯ for our samples (see Refs. 6 and 8). This also suggests that S(q) is essentially independent of Γ for the weakly interacting samples used in this study.

P. M. Chaikin, J. M. di Meglio, W. D. Dozier, H. M. Lindsay, and D. A. Weitz, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 65.

A. Ishimaru, Wave Propagation in Random Media (Academic, New York, 1978).

The correction to Brownian motion that is due to the convective flow is called Taylor dispersion. Taylor dispersion modifies particle diffusion in the direction of velocity gradient. In the entire range of shear rate in this experiment the correction (Γτ)2/3 is much smaller than 1. This justifies our approximation that the particle diffusion and convective shear are decoupled.

For some scattering geometries there will be an additional term in the sum corresponding to the difference between the input and output wave vectors. This term is proportional to the velocity (rather than to the velocity gradient) and does not contribute to the homodyne correlation function. We also note that for the common case that the flow direction is perpendicular to the input and output wave vectors, this term is identically zero.

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge U. Press, Cambridge, 1977), p. 83.

More generally, to include the effects of particle interactions, one must replace F(q) by the full scattering function S(q)F(q), where S(q) is the structure factor. We note that in these experiments, however, the volume fraction of PSS’s is low (ϕ= 0.02) and the Coulomb interaction between spheres is highly screened. Under these conditions, S(q) ≃ 1.

B. Chu, Laser Light Scattering (Academic, New York, 1974), pp. 101–104.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1984), p. 55.

Carboxylated polystyrene spheres were purchased from Duke Scientific, Palo Alto, California.

D. J. Tritton, Physical Fluid Dynamics, 2nd ed. (Clarendon, Oxford, 1988), p. 20.

S. H. Chen, T. L. Lin, and J. S. Huang, in Physics of Complex and Supermolecular Fluids (Wiley, New York, 1987), p. 285.