Pattern selection in radial displacements of a confined aging viscoelastic fluid

Abstract

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.