Spiral viscous fingering.

When a less-viscous fluid displaces a more-viscous fluid in a radial Hele-Shaw cell, viscous fingering pattern is believed to develop in a radial direction. We performed experiments on viscous fingering in a radial Hele-Shaw cell when a polymer solution, a sodium polyacrylate (SPA) solution is used as the more-viscous fluid and the trivalent iron (Fe$^{3+})$ solution is as the less-viscous fluid. The experiment was done by varying the concentration of Fe$^{3+}$, $c_{Fe3+}$. We have found that viscous fingering pattern develops spirally when $c_{Fe3+}$ is larger than a threshold value, while the pattern develops in a radial direction for small $c_{Fe3+}$. We confirmed from different experiments that an instantaneous chemical reaction takes place between SPA solution and Fe$^{3+}$ solution. The chemical reaction produces precipitation and significantly reduces the viscosity of the SPA solution. The quantity of the precipitation is increased with $c_{Fe3+}$. We will make a discussion on the relationship between the formation of spiral viscous fingering and the chemical reaction taking place between the two fluids.