Spiral pattern in a radial displacement in a Hele-Shaw cell

When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We have experimentally shown that the pattern created by the displacement of a more-viscous fluid by a less-viscous one in a radial Hele-Shaw cell develops not radially but spirally when a more-viscous sodium polyacrylate solution is displaced by a less-viscous trivalent iron ion (Fe$^{3+})$ solution with a sufficiently high concentration of Fe$^{3+}$. Another experiment in order to investigate the mechanism of spiral pattern formation revealed that an instantaneous chemical reaction takes place between the two fluids and at high Fe$^{3+}$ concentrations it produces a film of the gel at the contact plane. The gel is formed by three-dimensional network structures between the polyacrylate solution and the trivalent iron ion (Fe$^{3+})$ solution. We have proposed a physical model that the gel's film is responsible for the form of the spiral pattern.