Power Law Model Adaptation to Fingering of Non-newtonian Fluids

The growth rate of fingers of a Newtonian fluid can be modeled by a power law dependence on time. In this experiment, we examine whether the model can be adapted to describe a fluid with changing viscosity. We provide two possible interpretations. For PVA and a PVA/glycerol solution, we show that by assuming a constant exponent, the changing behavior of the fluid can be captured by a coefficient that changes with time. In addition, because the PVA/glycerol solution exhibits dual behavior matching both the Newtonian and non-Newtonian fluids, we propose a piecewise model of two power laws to capture both behaviors.