  Intricate fluid displacement patterns, arising from the unstable growth of
interfacial perturbations, can be driven by fluid viscoelasticity and surface
tension. A soft glassy suspension ages, $i.e.$ its mechanical moduli evolve
with time, due to the spontaneous formation of suspension microstructures. The
shear and time-dependent rheology of an aging suspension can be exploited to
generate a wide variety of interfacial patterns during its displacement by a
Newtonian fluid. Using video imaging, we report a rich array of interfacial
pattern morphologies: dense viscous, dendritic, viscoelastic fracture,
flower-shaped, jagged and stable, during the miscible and immiscible
displacements of an aging colloidal clay suspension by Newtonian fluids
injected into a radial quasi-two-dimensional geometry at different flow rates.
We propose a new parameter, the areal ratio, which we define as the
fully-developed pattern area normalized by the area of the smallest circle
enclosing it. We show that the natural logarithms of the areal ratios uniquely
identify the distinct pattern morphologies, such that each pattern can be
segregated in a three-dimensional phase diagram spanned by the suspension aging
time, the displacing fluid flow rate, and interfacial tension. Besides being of
fundamental interest, our results are useful in predicting and controlling the
growth of interfaces during fluid displacements.
