Diffusing wave spectroscopy in inhomogeneous flows

TLDR: In this article, a theoretical study of the time-dependent correlation function of multiply scattered light in laminar and stationary flow is presented, which is sensitive to the root mean square of velocity gradients weighted by the cloud of diffusive light paths.

Abstract: A theoretical study of the time-dependent correlation function of the multiply scattered light in laminar and stationary flow is presented. We study an inhomogeneous system of flow, i.e. when the strain tensor σ ij ( r ) depends on the space variables. Since in such flows the dephasing of light is space dependent, we introduce the useful function of the local density distribution of diffusion paths. We show that the time-dependent correlation function C1(t) of the scattered field is sensitive to the root mean square of velocity gradients weighted by the cloud of diffusive light paths. We establish a general formulation of C1(t) for laminar and stationary flow in the weak scattering limit kl ⪢ 1. The effects of the dimension of the inhomogeneous system and of the boundary conditions are also discussed. These results are applied to the cases of an infinitely thin and continuous sheet of vorticity, of a Rankine vortex, and of a Gaussian shaped velocity gradient.