  Granular materials segregate by size under shear, and the ability to
quantitatively predict the time required to achieve complete segregation is a
key test of our understanding of the segregation process. In this paper, we
apply the Gray-Thornton model of segregation (developed for linear shear
profiles) to a granular flow with an exponential profile, and evaluate its
ability to describe the observed segregation dynamics. Our experiment is
conducted in an annular Couette cell with a moving lower boundary. The granular
material is initially prepared in an unstable configuration with a layer of
small particles above a layer of large particles. Under shear, the sample mixes
and then re-segregates so that the large particles are located in the top half
of the system in the final state. During this segregation process, we measure
the velocity profile and use the resulting exponential fit as input parameters
to the model. To make a direct comparison between the continuum model and the
observed segregation dynamics, we locally map the measured height of the
experimental sample (which indicates the degree of segregation) to the local
packing density. We observe that the model successfully captures the presence
of a fast mixing process and relatively slower re-segregation process, but the
model predicts a finite re-segregation time, while in the experiment
re-segregation occurs only exponentially in time.
