Correlation time and diffusion coefficient imaging: Application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R-u(tau) = [u(t)u(t + tau)], expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R-u(tau) = [u(2)]e(-\tau\/tau c), where tau(c) is the correlation time and D = [u(2)]tau(c) is the diffusion coefficient. The pulsed-held-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature [u(2)] was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows. (C) 2000 Academic Press.