Richard M. Lueptow - US grants

This project involves the measurement of particle velocities in a rotating filter system by the Pulsed Light Velocimetry technique. Particular emphasis will be on the role of secondary flows (e.g. Taylor vortices) in preventing plugging, the effects of particle sedimentation in the separation, and the influence of particles on flow stability. Overcoming plugging should greatly improve the performance of filters, which are important to many industrial processes.

Abstract
CTS-0092584
R. Lueptow, Northwestern University


The 12th International Couette-Taylor Workshop will be held at Northwestern University in September 2001 with Dr. Lueptow as the organizer. Besides Couette-Taylor flow, the research topics to be discussed in the workshop will include non-linear dynamics, instability, Goertler/Dean vortices, and other vortical flows. It is anticipated the workshop will have 80-100 participants with 50-60 contributed papers. It provides an excellent opportunity for fluid dynamicists in this field of research to have an open exchange of ideas.

0403581
Lueptow
In response to both legislative and health related events, low-pressure membrane filtration (LPMF) is an emerging technology that is showing accelerated growth in the drinking water industry. There are a number of advantages to LPMF relative to conventional treatment such as superior treated water quality, little need for chemical additives, low energy requirements, and a compact, modular system. Yet, a major limitation associated with LPMF is its ineffectiveness in altering organic quality or quantity. Another problem common to all membrane systems, albeit in varying degrees, is fouling related to particle, organic, and microbial deposition at the membrane surface.

We propose to create a novel reactive membrane system by coupling TiO2 photocatalysis and rotating ceramic membrane filtration. The principle of this process is that robust water treatment is achieved by integrating the physical separation of particles and chemical oxidation of organic and microbial constituents in combination with physical and chemical control of surface fouling. The proposed research is based on the activation of TiO2 nanoparticles by UV light to produce HO. and other reactive species (e.g., H2O2) at or near the rotating membrane surface. These highly oxidizing radials are also highly reactive with dissolved organic compounds and microorganisms so they will act to minimize biological and chemical fouling. Furthermore, the centrifugal instabilities and high shear created by the rotation of the cylindrical membrane significantly reduce concentration polarization and particle deposition at the membrane surface and also create optimal mass transfer conditions to promote high rates of photocatalytic reaction.

The project involves three principal research tasks: 1) synthesis of reactive membranes and construction of prototype reactive rotating membrane systems; 2) characterization and selection of an optimum reactive membrane system for particle filtration, organic degradation, micropollutant destruction, microbial disinfection, and fouling control based on model water tests; and 3) testing reactive membrane performance using real waters, with special attention to determining how disinfection byproduct formation potential is modified by treatment. By rigorously comparing the performance of the reactive membrane prototypes to reference systems reflecting the individual action of either photocatalysis or rotating filtration, we will determine under what conditions the coupling of photocatalysis and membrane filtration causes a deterioration in intrinsic properties. In this way, we will also determine the synergistic interactions that result in high removals of particles and microorganisms, oxidative transformation of organic compounds, and effective control of surface fouling. Model water tests will be used to select a set of reactive membrane prototypes for testing with real surface waters.

This research will have a profound impact on the growth of the low-pressure membrane industry and promote an expansion in its application beyond drinking water treatment to water reuse, advanced wastewater treatment, and industrial water processing. The advantages of the reactive membrane system over conventional membranes are reduced pre/post-treatment and cleaning requirements and greater production of higher quality filtrate. These advantages should offset any additional costs related to manufacturing and operating the system. The broader impact of this research is that it provides a technologically reliable way to use water having low organic and microbiological quality as a drinking water source, which is critical in many parts of the world and the U.S. where fresh water quality is seriously degraded. The research program integrates fluid mechanics, environmental chemistry, material synthesis, and photochemistry to provide a superb interdisciplinary research program for two doctoral candidates.

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).

The PI will spend the academic year 2009-2010 in the Climate Group in the Geophysical Sciences Department at the University of Chicago. Primary goals of the immersion year include (1) gaining a scientific overview of key physical components of the climate system, including how they interact, their characteristic temporal and spatial scales, and how they are modeled; (2) gaining experience with paleoclimate proxy data, including how they are obtained, how they are interpreted quantitively, their uncertainties and their quality; (3) developing research collaborations with climate scientists at the University of Chicago aimed at understanding the role of coupling and feedback in climate change. To ensure a broad overview of key components of the climate system, the PI has identified three research project areas that interface with the research activities of faculty and their students in the Geophysical Sciences Department at the University of Chicago. These projects concern (1) mathematical modeling of the ice component of the climate system, which is important to understand for predicting sea level rise due to global warming, (2) mechanisms of abrupt climate change in the last glacial cycle that are related to thermohaline circulation in the deep Atlantic, which would be constrained by new paleoclimate proxy records of North Atlantic sea-surface temperature and salinity changes, and (3) investigations of system level climate models of extreme glaciation events in earth's distant past including models of `Snowball Earth'.


Additional activities include (1) expanding the PI's participation in the Climate Group journal club, which she joined in January 2009, by leading some of the journal club discussions and proposing topics of investigation that relate to her mathematical expertise in dynamical systems and bifurcation theory, (2) attending weekly departmental seminars to gain a broad perspective on geophysical sciences research, (3) auditing graduate courses on `Climate Dynamics' and `Global Climate Models', and (4) attending a number of professional meetings and workshops related to climate science. Expected outcomes of the immersion year include (1) developing sustainable interdisciplinary research collaborations with leading climate scientists, (2) identifying relevant projects for applied mathematics Ph.D. research, and (3) developing a seminar course on `Challenges of Modeling the Climate and Climate Change' aimed at Northwestern University advanced undergraduate and graduate students.

Granular mixing and its interplay with segregation are complicated, since flow induces segregation by particle size or density. A canonical system for the study of granular flow is a partially filled rotating tumbler. Because, to a reasonable approximation, the dynamics in a tumbler take place in a thin flowing surface layer, a simple, compact, and extensible continuum model can be used to study the flow. However, a suitable general theoretical framework for mixing (and segregation) as well as appropriate mathematical tools to implement the theory are lacking. Full understanding requires an integrated effort consisting of new theory inspired by abstract mathematical concepts and supporting computational and experimental results. The theoretical work proposed here will focus on the application of Piecewise Isometries, Linked Twist Maps, and Lagrangian Coherent Structures. The ultimate objective of the research is to develop a theoretical framework using a dynamical systems approach that will lead to new mathematical tools to predict flow, mixing, segregation, and pattern formation for granular matter in 2d and 3d tumbler geometries with steady and time-periodic forcing. The approach is based on the geometry and symmetries of the 3d flow generated by the forcing (mixing protocols). Complementary experiments and simulations will be used to confirm the applicability of these theoretical approaches to real granular mixing and segregation problems.

The physics of the flow of granular matter is one of the big questions in science. Granular matter is a prototype of a complex system with collective behavior far from equilibrium. Yet many fundamental questions remain. At the same time, an understanding of granular flow has tremendous practical importance in situations ranging from landslides to food processing. Flowing granular systems are strongly disordered and yet display competition between chaos (mixing) and order (segregation). But inroads to date have been modest. Here, we introduce new dynamical systems approaches for the study of granular matter that are grounded in higher mathematics. Dynamical systems tools offer mathematical frameworks that can be exploited in the study of granular flow. Scientific progress here can have an immediate impact on technology and practice. Furthermore, the new mathematical approaches considered here have potential for broad-ranging impact on many physical systems, perhaps creating an entirely new paradigm much like the science of chaotic advection did for mixing of fluids in the 1990s.

Engineers and scientists generally think in terms of three means to mix fluids, which can be easily explained in terms of mixing cream in coffee. Diffusion disperses the cream in a cup of coffee via molecular collisions; chaotic advection, or stirring, generates thin layers of coffee and cream that merge; turbulence mixes the coffee and cream by strong agitation or vigorous stirring. However, the simple technique of cutting and shuffling, much like what takes place in shuffling a deck of cards or mixing the colors of a Rubik's cube, is also a means of mixing that is commonplace. However, it is not well understood in the context of engineering systems such as mixing powders and granules for pharmaceuticals, plastic resins, and chemicals. This award supports the development of a formal mathematical framework to predict mixing by cutting and shuffling that is validated by computational and experimental results. The theory is inspired by abstract mathematical concepts, but is motivated by systems for blending and mixing bulk particles or granules, a common process in the chemical and pharmaceutical industries. The research links fundamental mathematics and practical applications while training the next generation of scientists and engineers.

While molecular diffusion, chaotic advection, and turbulence as mixing mechanisms have long been studied, mixing by cutting and shuffling is not well explored or understood. This award centers on a relatively new mathematical approach that describes cutting and shuffling known as Piecewise Isometries (PWI). The idea is to apply PWI concepts to mixing as well as to connect PWI with traditional dynamical systems approaches. The objective is to develop and utilize PWI within a dynamical systems framework to predict mixing by cutting and shuffling in 2D and 3D geometries with eventual applications to practical mixing systems. The development of the 3D dynamical systems framework will be informed by the mixing of granular materials, leading to an integrated theory inspired by abstract mathematical concepts but connected to practical applications of cutting and shuffling. The mathematics of PWI will be integrated into the dynamical systems toolkit, while complementary experiments and simulations will be used to confirm the applicability of the theoretical approaches to a model granular mixing system. The merging of new mathematics, dynamical systems approaches, and physical applications could result in an entirely new paradigm for understanding and predicting mixing.

CBET - 1511450
PI: Umbanhowar, Paul

Granular materials such as sand, snow, and salt consist of large numbers of solid particles that interact with each other primarily through contact foces. Flowing granular materials occur in natural phenomena, such as landslides and avalanches, and in industrial processes, such as pharmaceutical manufacturing and ore processing. When the particles differ from each other in size, density, roughness or some other physical characteristic, they can segregate during flow, which complicates processing and diminishes product quality. The goal of this project is to discover ways to avoid or reduce segregation and improve mixing in unsteady granular flows, i.e. flows that vary in time. The project involves experiments to determine how flow modulation can best control segregation and mixing for materials consisting of particles of various sizes. The experiments will be complemented by modeling and computer simulation that can help interpret the results and predict optimal modulation methods for controlling segregation. Results will generate useful processing methods and modeling tools for industrial practitioners. The project team will comprise a diverse group of researchers and students, including students from underrepresented groups and local high schools.

The project will examine the interplay between unsteady kinematics and segregation to develop a continuum-based framework to predict spatial particle segregation distributions for polydisperse particles in bounded heap flow and rotating tumbler flow. The results will be used to demonstrate how flow modulations, such as feed rate variations in heap flow or rotational speed variations in tumbler flow, can inhibit segregation and improve mixing. Findings from the project will guide industrial granular materials processes and systems by providing methodologies that apply over a wide range of operating conditions and that are supported by a continuum-based model. The model will account for unsteady flow, segregation, and collisional diffusion, all of which are important elements in a broad array of granular processes. The combination of experiments and simulations will provide an expanded and improved understanding of flow, segregation, mixing and pattern formation in granular systems.

Granular flows are common in industry. Billions of tons of ores, grains, powders, and plastic resin are handled each year in the US. When particles differ in size or density, flowing granular materials tend to segregate, or de-mix, which can cause severe problems in particle and powder processing in industries where a uniform mixture is usually desired. Although the understanding of segregation and mixing in granular flows has advanced over the last two decades based on an array of experimental, computational, and theoretical approaches, current models of segregation at the particle level are simplistic and empirical. The objective of this GOALI project is to develop a particle-level model based on fundamental physics that can accurately predict segregation from the size and density of the specific particles that are flowing. This particle-level model can then be implemented in large-scale models of granular flows that are used to predict granular flow and segregation in a wide range of particle handling processes. The results of this research, which will be carried out in collaboration with researchers from Procter and Gamble and Dow, will provide practical approaches to enhance mixing (or segregation) of granular materials, which can be utilized to improve and enhance industrial processes in diverse applications ranging from chemicals to pharmaceuticals to foodstuffs to consumer products. The research team will engage students at graduate and undergraduate levels, especially those from underrepresented groups, and provide them with opportunities for research training in collaboration with their industrial counterparts.

Until recently, processing approaches to prevent segregation of granular materials have been ad hoc, often resulting in operating conditions that are inefficient. An advection-diffusion-segregation model with a shear rate-based segregation flux model developed by the research team has made it possible to rationally design systems to overcome many of these problems. However, the key particle-based parameter for the segregation flux model is not well understood, not easily predicted for particles of varying size or density, and not based on first principles. This project focuses on developing a predictive framework for particle-level segregation to: (1) Understand the fundamental physical mechanisms of segregation at the particle level; and (2) Develop a predictive segregation model that includes the effects of both particle size and density. Discrete element method (DEM) simulations will be used in which the flow and segregation conditions can be manipulated, sometimes in ways that are not possible experimentally, along with theoretical modeling to connect macroscale continuum models with segregation forces on individual particles. This project moves beyond previous research by considering segregation flux for combined size and density, a much more difficult problem than either one alone. The approaches and tools developed in the project will play an important role in the design of particle processing systems to enhance mixing and prevent segregation of granular materials.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

A major problem in processing granular materials such as particles, beads, and powders is that small particles fall between larger ones and de-mix, or “segregate,” as the particles flow. Although methods to predict and prevent the segregation of mixtures of large and “small” particles have been developed over the past decade, the segregation behavior changes dramatically when small particles are replaced by “fine” particles, which are so small that they can easily fall between large particles even when the large particles are stationary. Avoiding de-mixing in chemical or pharmaceutical processing is essential for product quality (uniform distributions of ingredients in pharmaceutical tablets), reducing waste (segregated fine particles are often discarded), mitigating safety concerns (airborne fine particles are an explosion hazard), minimizing health risks (inhalation of fine particles), and preventing fouled equipment (fine particles coat surfaces of equipment and sensors). In geophysical flows, fine particles can increase landslide hazards by acting as friction-reducing ball bearings or becoming airborne (billowing clouds in rock avalanches). Currently, however, the physics of fine particle de-mixing is poorly understood. The goal of this award is to develop a fundamental understanding of how fine particles segregate using computer simulations, which could lead to an accurate and widely applicable model for such granular flows.

Discrete Element Method (DEM) computer simulations, validated with experiments, will be used to develop a fundamental understanding of fine particle flow and segregation. At the flow level, the size and spatial distributions of interstices between large particles through which fine particles transit will be characterized for a variety of flow conditions and particle size ratios leading to a relation for the dependence of the fine particle percolation velocity on the shear rate, particle size ratio, and species concentration. At the individual particle level, particle contact forces, ballistic interactions, and free sifting percolation kinematics will be characterized. The goal is to develop a predictive model for segregating fine particles much like the advection-diffusion-segregation continuum model that has been successfully implemented to predict the segregation of particles with small size ratios (less than 3). This award will transform the understanding, prediction, and control of the segregation and mixing of large and fine particles from ad hoc approaches to a physics-based model. It may also result in new insights into dry lubrication and geophysical flows where particle sizes vary by orders of magnitude.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.