  In this work, we study the role of viscoelastic instability in the mechanical
dispersion of fluid flow through porous media at high Peclet numbers. Using
microfluidic experiments and numerical simulations, we show that viscoelastic
instability in flow through a hexagonally ordered (staggered) medium strongly
enhances dispersion transverse to the mean flow direction with increasing
Weissenberg number (Wi). In contrast, preferential flow paths can quench the
elastic instability in disordered media, which has two important consequences
for transport: First, the lack of chaotic velocity fluctuations reduces
transverse dispersion relative to unstable flows. Second, the amplification of
flow along preferential paths with increasing Wi causes strongly-correlated
stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate
how the observed dispersion phenomena can be understood through the lens of
Lagrangian stretching manifolds, which act as advective transport barriers and
coincide with high stress regions in these viscoelastic porous media flows.
