Reconstruction by fluorescence imaging of the spatio-temporal evolution of the viscosity field in Hele-Shaw flows

We study the spatio-temporal evolution of the viscosity field during stable and unstable radial flows of glycerol-water solutions in a horizontal Hele-Shaw cell where a localized temperature gradient is imposed. The viscosity field is reconstructed from the measurement of the fluorescence emitted by a viscosity-sensitive molecular probe (Auramine O). For an immiscible flow, the viscosity and temperature fields are obtained accurately. For miscible displacements, we show how the interplay between the viscosity changes of both fluids and the variation of the fluid thickness in the gap prevents obtaining strict quantitative reconstruction of the viscosity field. We explain how the reconstructed viscosity field can nevertheless be interpreted to obtain information about the fluid thickness and the local viscosity and temperature.