This investigation uses fluorescent probe imaging of the two-dimensional viscosity field during reactive flow, as well as Schlieren imaging, to map how flow instabilities depend on the relative rates of hydrodynamic flow and chemical reactions. The proposed research includes: (1) development of molecular-probe fluorescence imaging technique for in situ monitoring of viscosity applied to a well-characterized miscible and Newtonian glycerol-water system in Hele-Shaw cells; (2) extension of this technique to measure the spatio-temporal evolution of the viscosity field for a chemically-reactive flow system of step-growth polymerization; and (3) investigation of the relative roles of rate of reaction to hydrodynamic flow rate.
Intellectual Merit When a high-mobility fluid displaces a fluid of lower mobility, the instability known as fingering occurs. If the two fluids are of comparable viscosity, then the mobility is dominated by density differences and buoyancy-driven convection occurs. If the source of the mobility difference is viscosity, then viscous fingering can occur in a horizontal Hele-Shaw cell. When fluids of differing viscosities and densities are brought together in a gravity field, then the outcome depends on the relative sizes and signs of the stabilizing and destabilizing effects of density and viscosity. This proposal focuses on viscous fingering (VF) in the absence of a gravity field, i.e., in a horizontal Hele-Shaw cell. Despite the central importance of the viscosity profile to experimental interpretation and theoretical models of VF, the viscosity field has yet to be measured in situ during flow. Hence, the actual viscosity gradient must be assumed or interpolated based on a given model. This work develops a technique addressing this issue using a viscosity-sensitive fluorescent probe. After gaining the viscosity field driving VF, one desires to control the field and the instability. A set of step-growth polymerization reactions will be used as model systems in horizontal Hele-Shaw cells because both rate of reactivity and viscosity of the reaction product can be controlled by varying the concentration of the initiator or catalyst or the functionality of the monomers. Schlieren imaging will be used to produce a phase diagram of resultant instability versus rate of reaction and hydrodynamic flow rate. Fluorescent-probe imaging of the viscosity field will provide quantitative data that will be related to theoretical models of the viscosity profile.
Broader Impacts Viscous fingering has been studied extensively in part due to its high impact in oil recovery and in pollution spreading in porous media. A large body of literature exists on experimental studies on one hand and on theoretical investigations that focus on computing the spatio-temporal evolution of viscosity fields. A gap exists however in quantitative comparisons between experiments and theory mainly due to the difficulty of quantitative measurements of the evolution in space and time of the local viscosity. This quantitative in-situ monitoring of 2D viscosity field enabling the tuning of the relative reaction and hydrodynamic time scales will broadly impact the field of hydrodynamic instabilities in porous media and will lead to controlling the instability. Additionally, as an outreach, Physics and Elementary Education students will implement a set of optics and fluids activities for middle school students. These activities will be primarily based on the Optics Discovery Kits prepared by the Optical Society of America but with additional demonstrations and activities drawn from fluid dynamics. Supplies will remain with a middle school science teacher in high-need school (such as an Hispanic urban charter school) to empower this teacher to excite future students.
