Mobility of Power-law and Carreau Fluids through Fibrous Media

The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied with a focus on developing relationships for evaluating the effective fluid mobility. Three different methods have been used here: i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than $\varepsilon\simeq0.65$, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers

Layer-by-layer functionalized nanotube arrays: A versatile microfluidic platform for biodetection

We demonstrate the layer-by-layer (LbL) assembly of polyelectrolyte multilayers (PEM) on three-dimensional nanofiber scaffolds. High porosity (99%) aligned carbon nanotube (CNT) arrays are photolithographically patterned into elements that act as textured scaffolds for the creation of functionally coated (nano)porous materials. Nanometer-scale bilayers of poly(allylamine hydrochloride)/poly(styrene sulfonate) (PAH/SPS) are formed conformally on the individual nanotubes by repeated deposition from aqueous solution in microfluidic channels. Computational and experimental results show that the LbL deposition is dominated by the diffusive transport of the polymeric constituents, and we use this understanding to demonstrate spatial tailoring on the patterned nanoporous elements. A proof-of-principle application, microfluidic bioparticle capture using N-hydroxysuccinimide-biotin binding for the isolation of prostate-specific antigen (PSA), is demonstrated.National Science Foundation (U.S.) (Award DMR-0819762

Combinatorial molecular optimization of cement hydrates

Despite its ubiquitous presence in the built environment, concrete’s molecular-level properties are only recently being explored using experimental and simulation studies. Increasing societal concerns about concrete’s environmental footprint have provided strong motivation to develop new concrete with greater specific stiffness or strength (for structures with less material). Herein, a combinatorial approach is described to optimize properties of cement hydrates. The method entails screening a computationally generated database of atomic structures of calcium-silicate-hydrate, the binding phase of concrete, against a set of three defect attributes: calcium-to-silicon ratio as compositional index and two correlation distances describing medium-range silicon-oxygen and calcium-oxygen environments. Although structural and mechanical properties correlate well with calcium-to-silicon ratio, the cross-correlation between all three defect attributes reveals an indentation modulus-to-hardness ratio extremum, analogous to identifying optimum network connectivity in glass rheology. We also comment on implications of the present findings for a novel route to optimize the nanoscale mechanical properties of cement hydrate.National Ready Mixed Concrete Association (Research sponsorship)Education Foundation (N.J.) (Research sponsorship)Portland Cement Association (Research sponsorship

Thermal analysis of air-cooled fuel cells

Temperature distribution in a fuel cell significantly affects the performance and efficiency of the fuel cell system. Particularly, in low temperature fuel cells, improvement of the system requires proper thermal management, which indicates the need for developing accurate thermal models. In this study, a 3D numerical thermal model is presented to analyze the heat transfer and predict the temperature distribution in air-cooled proton exchange membrane fuel cells (PEMFC). In the modeled fuel cell stack, forced air flow supplies oxidant as well as cooling. Conservation equations of mass, momentum, and energy are solved in the oxidant channel, while energy equation is solved in the entire domain, including the gas diffusion layers and separator plates, which play a significant role in heat transfer. Parametric studies are performed to investigate the effects of various properties and operating conditions on the maximum cell temperature. The present results are further validated with experiment. This model provides a theoretical foundation for thermal analysis of air-cooled PEMFC stacks, where temperature non-uniformity is high and thermal management and stack cooling is a significant challenge

Hydrodynamic interactions of complex fluids and fibrous media

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 171-183).Hydrodynamic interactions of fluids and fibers are encountered in many applications, from filtration processes to the development of novel materials such as nanofluids and nanocomposites, and even in biological systems such as transport of fluids in plants and tissues. It is therefore, valuable from both a scientific and engineering perspective, to understand and be able to predict the behavior of such systems. In this thesis, hydrodynamic effects arising from the presence of fibers in fluid flows are studied in two different scenarios: i) Newtonian and non-Newtonian fluids flowing through fixed arrays of fibers (fibrous media), and ii) fibers suspended in fluids and the rheological changes resulting from the fiber-fluid hydrodynamic interactions. First, the flow of Newtonian fluids through and at the interface of fibrous porous media is studied. The primary objective of this part of the thesis was the design and development of a microfluidic device incorporating fixed beds of carbon nanotubes for filtration of specific biomarkers from biological fluid samples. Therefore, the focus is centered on defining and evaluating an interception efficiency, which provides a measure of the fraction of fluid streamlines that intercept a porous collector. It is shown through numerical simulations, that in general, the effects of geometrical confinement as well as fluid inertia and porosity (as captured by the Reynolds number and Darcy number respectively) on the flow interception efficiency are interdependent; however, for most practical cases it is possible to decouple these effects (e.g. at Darcy numbers < 10-4). For the specific case of fibrous collectors consisting of carbon nanotubes, experimental studies are conducted to investigate the convection and diffusion of dilute polymer solutions through cylindrical paths of vertically aligned carbon nanotubes. The experiments demonstrate the ability to systematically control the thickness and uniformity of adsorbed polymers on the carbon nanotubes through variation in the geometrical confinement of the fibrous array. The studies of flow transverse to fibers are also extended to the case of non-Newtonian fluids. Emphasis is placed on theoretical development of general mobility functions for complex fluids flowing through fibrous media. This is one of the major contributions of this thesis, which yields generalized laws for predicting the pressure drop that an array of fibers induces on the steady flow of fluids with a yield-stress and a rate-dependent viscosity. The resulting formulation can be applied to various geometrical arrangements and a wide range of porosities. Based on this model, we construct a unified dimensionless criterion in the form of a modified Bingham number (or dimensionless yield stress) rescaled with a suitable porosity function, which incorporates all the rheological and pore-scale parameters that are required to determine the dominant viscoplastic regime. Finally, suspensions of fibers in a Newtonian liquid matrix are studied. In this case the fibers are allowed to be flexible and move within the suspending media in addition to having attractive potentials with each other. These degrees of freedom give the resulting fiber suspensions striking features such as viscoelasticity and ability to form a percolated gel network at volume fractions as low as ~ 3% for the system of interest, which consists of an aqueous suspension of nanocrystalline cellulose fibers (length 200nm, aspect ratio 20). The changes in the rheological behavior of these dispersed fibrous systems are investigated as the volume fraction of nanofibers are varied. Finally, the correlative technique of differential dynamic microscopy (DDM) is implemented to study the collective fiber dynamics and we demonstrate that this method can be used as a complementary technique to provide microrheological insight that extends the ability to rheologically characterize the steady and transient viscoelastic properties of complex heterogeneous fluids.by Setareh Shahsavari.Ph. D

Mobility and pore-scale fluid dynamics of rate-dependent yield-stress fluids flowing through fibrous porous media

The steady flow of viscoplastic fluids through fibrous porous media is studied numerically and theoretically. We consider fluids with a plastic yield stress and a rate-dependent viscosity that can be described by the Herschel-Bulkley model. We first investigate the pore-scale flow characteristics through numerical simulations for flow transverse to a square array of fibers with comprehensive parametric studies to independently analyze the effects of the rheological properties of the fluid and the geometrical characteristics of the fibrous medium. Our numerical simulations show that the critical Bingham number at which the flow transitions from a fully-yielded regime to locally unyielded regions depends on the medium porosity. We develop a scaling model for describing the bulk characteristics of the flow, taking into account the coupled effects of the medium porosity and the fluid rheology. This model enables us to accurately predict the pressure-drop–velocity relationship over a wide range of Bingham numbers, power-law indices, and porosities with a formulation that can be applied to a square or a hexagonal array of fibers. The ultimate result of our scaling analysis is a generalized form of Darcy's law for Herschel-Bulkley fluids with the mobility coefficient provided as a function of the system parameters. Based on this model, we construct a modified Bingham number rescaled with a suitable porosity function, which incorporates all the rheological and pore-scale parameters that are required to determine the dominant flow regime

Interception efficiency in two-dimensional flow past confined porous cylinders

The flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector, is an important parameter in applications such as particle capture, filtration, and sedimentation. In this work, flow permeation through a porous circular cylinder located symmetrically between two impermeable parallel plates is investigated numerically under different flow and geometrical conditions. A flow interception efficiency is defined and calculated based on the flow permeation rate for a wide range of system parameters. The dependencies on all physical variables can be captured in three dimensionless numbers: the Reynolds number, the Darcy number (ratio of permeability to the square of cylinder diameter), and the plate separation relative to the cylinder size. The flow interception efficiency is very low in the limit of unbounded cylinders but significantly increases by restricting the flow domain. The fluid permeation rate through the porous cylinder varies nonlinearly with the relative plate/cylinder spacing ratio, especially when the gap between the cylinder and the confining plates is small compared to the cylinder size. In general, the effects of the Reynolds number, the Darcy number, and confinement on the flow interception efficiency are coupled; however, for most practical cases it is possible to factorize these effects. For practical ranges of the Darcy number (Da<10[superscript −4], which means that the pore size is at least one order of magnitude smaller than the porous cylinder diameter), the interception efficiency varies linearly with Da, is independent of the Reynolds number at low Reynolds numbers (Re[subscript D]<10), and varies linearly with Reynolds number at higher flow rates. In addition to numerical solutions, theoretical expressions are developed for the flow interception efficiency in two limiting cases of confined and unbounded flow, based on modeling the system as a network of hydrodynamic resistances, which agree well with the numerical results. Furthermore, an expression for the drag coefficient on the porous cylinder is proposed as a function of the Darcy number which can be used in the limit of large plate/cylinder relative spacing.National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Award DMR-0819762)Massachusetts Institute of Technology. Department of Mechanical Engineering (Rohsenow Fellowship