Effects of moderate Damköhler number on miscible viscous fingering involving viscosity decrease due to a chemical reaction

We have succeeded in experimentally investigating the effects of a moderate Damköhler number, Da (defined as the ratio between a characteristic time of fluid motion and that of a chemical reaction), for various Péclet numbers, Pe, on miscible viscous fingering involving a decrease in the viscosity of the displaced liquid due to a chemical reaction in Hele-Shaw cells. We achieved this by using a chemical reaction between a polymer solution and metal ions. Main analysis has been done for the radial fingering. In the range of Pe employed here, the fingering patterns without the reaction (Da = 0) were independent of Pe. The fingering patterns with the reaction depended on the single parameter, Da, and the area occupied by the fingering pattern near the injection hole increased with Da in the range of Da employed here. The ratio of the area occupied by the fingering pattern within the circle radius of which is the length of longest finger to the area of the circle increased with Da in the range of Da employed here. This result is opposite to that of Nagatsu et al. (J. Fluid Mech., vol. 571, 2007, p. 475), in which the area was decreased by the reaction decreasing the viscosity involving significantly high Da. Experiments in the linear geometry show that the shape of a single finger also depended on the single parameter, Da, and the finger width increased near the base with Da. This result is also opposite to that in the previous case in which the width of a single finger was considered to be decreased by the reaction. These results, interestingly, show that the effects of the decrease in the displaced liquid's viscosity due to chemical reaction on the fingering pattern for moderate Da are opposite to those for significantly high Da. A mechanism for the opposite effects on the fingering pattern depending on Da is discussed.