Diffusing-wave spectroscopy in a shear flow

We present a new technique for measuring velocity gradients for laminar shear flow, using dynamic light scattering in the strongly multiple-scattering regime. We derive temporal autocorrelation functions for multiply scattered light, taking into account particle displacements arising from deterministic shear flow and random Brownian motion. The laminar shear flow and Brownian motion are characterized by the relaxation rates ${{\tau }_S}^{-1}=\overline{\mathrm{\Gamma }}{k}_{0}l*/\sqrt{30}$ and τ_B⁻¹ = Dk₀², respectively, where $\overline{\mathrm{\Gamma }}$ is the mean shear rate of the scatterers, k₀ = 2πn/λ is the wave number in the scattering medium, l* is the transport mean free path of the photons, and D is the diffusion coefficient of the scatterers. We obtain excellent agreement between theory and experiment over a wide range of shear rates, $0.5{sec}^{-1}<\overline{\mathrm{\Gamma }}<200{sec}^{-1}$. In addition, the autocorrelation function for forward scattering is independent of the scattering properties of the medium and depends only on the mean shear rate and sample thickness when τ_S is much less than τ_B. Thus the mean shear rate can be simply determined by a single measurement.