Intellectual Merit. This proposal focuses on a pore scale investigation of flow and transport in porous media, with a particular emphasis on dispersion at Reynolds numbers where inertial effects in the flow field become important. We are proposing a combination of experimental work, new theory development, and computation for exploring the importance of inertial contributions to flow and transport in porous media. Inertial flows in porous media have significance in a wide array of applications in the field from predicting the performance of packed bed reactors to understanding subsurface groundwater remediation. In such applications, the Reynolds number is often in the inertial range, but almost all theoretical studies of flow and transport in porous media have assumed Stokes (non-inertial) flow. In the proposed research, we plan to (i) make unique high resolution three dimensional and three component velocity measurements using particle imaging velocimetry (PIV) in index of refraction matched porous media to determine the influence of the inertial flows on dispersion, (ii) extend existing theory (via volume averaging) to describe the asymptotic and pre asymptotic flow and transport (dispersion) when inertial flows are present, and (iii) conduct high-resolution computational fluid dynamics simulations of the flow and transport processes at the sub-pore scale both as direct corroboration of the experimental work, and in support of the upscaling theoretical effort.. Our focus will be on moderate (non turbulent) particle Reynolds numbers in the range 10 < Rep < 150+, but we will also conduct more limited experimental and theoretical investigations in the unsteady laminar and turbulent flow regimes (Rep > 150+). The hypotheses associated with the proposed research are summarized as follows.
Hypothesis 1. The transition from Darcy flow to nonlinear (Forchheimer Ergun) flow can be explained by the pore scale redistribution of momentum that occurs when complex flow structures (helical vortexes, jets, regions of back-flow) are generated in the transition from Stokes to inertial flows.
Hypothesis 2. The complexity of flow structure during inertial flows will increase the dispersion tensor more than would an equivalent non inertial (Stokes) flow for the same Reynolds number. This will be most evident for the transverse dispersion component of the dispersion tensor.
Hypothesis 3. As the particle Reynolds number increases, the influence of the transient evolution of the dispersion tensor becomes greater (in the sense that the residence time of solutes will become correspondingly shorter in a finite bed). This influence will be manifest by the dependence of the dispersion tensor on bed location or bed length.
Broader Impacts. We have identified broader impacts that the proposed work will have in the areas of (i) promoting discovery and understanding while promoting training and learning, (ii) enhancing networks and partnerships, and (iii) participation of underrepresented groups. These are summarized as follows. Promoting Training and Learning. We have proposed efforts to promote training in learning at the undergraduate level (through an existing mentoring arrangement with the OSU NASA undergraduate Microgravity Flight Team [MGFT]), K-12 level (by expanding our existing interactions with the OSU SMILE outreach program, and providing visual fluid mechanics demonstrations that excite students to the power of scientific experimental measurements), and graduate level (by arranging to send a student to the Pacific Northwest National Laboratory [PNNL] for a summer research experience). These educational activities are described in greater detail in Section 4.1 of the proposal. Enhancing networks and partnerships. This proposal expands existing collaborations between the PIs and researchers at PNNL, and also establishes a new inter departmental interaction among PIs Wood and Liburdy. The collaboration with PNNL is important because (i) PNNL has proven to provide excellent opportunities for graduate students (as described in Section 4.1), (ii) there is a well equipped user facility at PNNL (EMSL) that has provided research equipment and expertise to PI Wood in the past, and (iii) the lab has the potential to provide employment opportunities to our students. These opportunities are described in additional detail in section 4.2 of the proposal. Participation of Underrepresented Groups. The PIs are committed to promoting diversity and encouraging the participation of underrepresented groups. The K-12 educational outreach described in section 4.1 is very effective at reaching under represented groups, particularly girls. The PIs have had particular success in encouraging women to pursue PhD studies, and this will remain a focus in the future.
Many components of technologies that we use every day involve flows of gasses or liquids through a porous medium. You can think of a porous medium as any kind of solid structure that has holes in it; sponges and buckets of sand would be two examples. As a more practical example, catalytic converters are installed on our cars involve a porous medium. These devices help keep the air clear by flowing the exhaust from our car engines through a porous material that reacts with polluting compounds to neutralize them. In order to design effective porous materials for applications in all kinds of technology, we need to understand the way that fluids flow through them. When fluids flow at low velocities, they act in very predictable ways. When they flow at very high velocities, however, fluid flows become very irregular and chaotic. Think about how creamer swirls around when added to coffee, or the eddies formed in fast-flowing rivers to get a sense for the structure of irregular flows. Irregular flows like this are called "turbulent" by those who study fluid motion. Irregular flows happen in porous materials, and their presence dramatically influences how those porous materials behave. In the research we conducted, we studied the details of how irregular flows look in porous media, and how we might represent their effects in applications. We measured the structure of irregular flows in porous media by using a "trick" of physics. We prepared a fluid that had the same optical properties as the solid that we used (pyrex beads) to construct our porous media. What this meant is that when the fluid was added to the solid porous media, it was essentially invisible. The combination looked and behaved optically like one uniform material. This allowed us to track particles that were released into the system using high-speed cameras, and, ultimately, to visualize the velocity field in the system. We also constructed models of the flow through the system on powerful computers. Part of the goal was to determine if the computer models of the fluid were accurate representations of the actual flow that was observed. Our results indicated that the computer models were, in fact, good representations of what actually occurred in our experimental porous media. This in itself is a useful result- it indicates that we can conduct computer "experiments" to help answer questions about how porous media behave when turbulence is involved. This has the potential benefit of allowing us to better design the structure of porous materials so that they are even more effective. In addition to the technical results that were obtained, this research also provided the support to train two students (both graduating with graduate degrees in engineering) who will form the next generation of fluid scientists to work on problems like these. One of these students is already applying the skills learned in this work to biomedical problems in industry. The other is continuing with related research as a post-doctoral researcher.
