The thesis investigates the flow of non-Newtonian fluids in porous media using network modeling. Non-Newtonian fluids occur in diverse natural and synthetic forms and have many important applications including in the oil industry. They show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent in which strain rate solely depends on the instantaneous stress, time-dependent in which strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency.The methodology followed in this investigation is pore-scale network modeling. Two three-dimensional topologically-disordered networks representing a sand pack and Berea sandstone were used. The networks are built from topologicallyequivalent three-dimensional voxel images of the pore space with the pore sizes, shapes and connectivity reflecting the real medium. Pores and throats are modeled as having triangular, square or circular cross-section by assigning a shape factor, which is the ratio of the area to the perimeter squared and is obtained from the pore space description. An iterative numerical technique is used to solve the pressure field and obtain the total volumetric flow rate and apparent viscosity. In some cases, analytical expressions for the volumetric flow rate in a single tube are derived and implemented in each throat to simulate the flow in the pore space. The time-independent category of the non-Newtonian fluids is investigated using two time-independent fluid models: Ellis and Herschel-Bulkley. Thorough comparison between the two random networks and the uniform bundle-of-tubes model i is presented. The analysis confirmed the reliability of the non-Newtonian network model used in this study. Good results are obtained, especially for the Ellis model, when comparing the network model results to experimental data sets found in the literature. The yield-stress phenomenon is also investigated and several numerical algorithms were developed and implemented to predict threshold yield pressure of the network. An extensive literature survey and investigation were carried out to understand the phenomenon of viscoelasticity and clearly identify its characteristic features, with special attention paid to flow in porous media. The extensional flow and viscosity and converging-diverging geometry were thoroughly examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shear-thinning, elasticity and thixotropic timedependency, was identified as a promising candidate for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm that employs this model to simu...

We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi-compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi-compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N-compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting 'reduced' Darcy formulation leads to a dramatic reduction in algebraic-system size and is therefore computationally cheaper to solve than the full multi-compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject-specific model of the left ventricle.

The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010

The `no-slip' is a fundamental assumption and generally-accepted boundary condition in rheology, tribology and fluid mechanics with strong experimental support. The violations of this condition, however, are widely recognized in many situations, especially in the flow of non-Newtonian fluids. Wall slip could lead to large errors and flow instabilities, such as sharkskin formation and spurt flow, and hence complicates the analysis of fluid systems and introduces serious practical difficulties. In this article, we discuss slip at fluid-solid interface in an attempt to highlight the main issues related to this diverse complex phenomenon and its implications.Comment: 69 page

In this paper, analytical expressions correlating the volumetric flow rate to In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.

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A method to extract myocardial coronary permeabilities appropriate to parameterise a continuum porous perfusion model using the underlying anatomical vascular network is developed. Canine and porcine whole-heart discrete arterial models were extracted from high-resolution cryomicrotome vessel image stacks. Five parameterisation methods were considered that are primarily distinguished by the level of anatomical data used in the definition of the permeability and pressure-coupling fields. Continuum multi-compartment porous perfusion model pressure results derived using these parameterisation methods were compared quantitatively via a root-mean-square metric to the Poiseuille pressure solved on the discrete arterial vasculature. The use of anatomical detail to parameterise the porous medium significantly improved the continuum pressure results. The majority of this improvement was attributed to the use of anatomically-derived pressure-coupling fields. It was found that the best results were most reliably obtained by using porosity-scaled isotropic permeabilities and anatomically-derived pressure-coupling fields. This paper presents the first continuum perfusion model where all parameters were derived from the underlying anatomical vascular network.

Dedicated to the Fritz Haber Institute, Berlin, on the occasion of its 100th anniversary Metals and metal oxides anchored to porous support materials are widely used as heterogeneous catalysts in a number of important industrial chemical processes. These catalysts owe their activity to the formation of unique metal/metal oxide support interactions, typically resulting in highly dispersed actives stabilized in a particular electronic or coordination state. [1][2][3] They are employed in fixed-bed reactors as extruded or pelletized millimeter-sized "catalyst bodies" minimizing pressure drops along the length of the reactor. Since the efficiency of the whole catalytic system depends on the behavior and efficiency of the catalyst body per se, its design has very great importance. Crucial to this design is an understanding of the factors which influence the distribution and nature of the active phase during preparation. The type of desired distribution is very much dependant on catalytic process and required products; for example, an egg-shell distribution (as opposed to uniform, egg-white, or egg-yolk), where the active phase is located at the edges of the catalyst body, can be favored if the product forms readily. [4,5] Herein, we study catalyst bodies of nickel supported on gAl 2 O 3 . These catalysts are widely employed for hydrogenation. [1][2][3]6] They are often prepared using highly soluble nickel nitrate or chloride precursor salts, which allow for the preparation of catalysts with high metal loadings in a single impregnation step. Two problems are commonly encountered with the preparation of these catalysts: the formation of unwanted metal aluminate (spinel) phases and poor metal dispersion within the catalyst body. The dispersion of the metal ions within the alumina can be controlled by the addition of complexing agents to the impregnation solution, thereby changing the molecular structure of the precursor (through ligand exchange) as well as the interactions of the precursor with the support. Additionally, the presence of chelating ligands in the precursor increases both the metal oxide reducibility and dispersion. [7][8][9][10] In recent times, absorption, spectroscopic, and scattering techniques have been developed to obtain spatial information on the distribution of chemical species in catalyst bodies, which allows the phenomena taking place during their preparation to be monitored. [7] These techniques include Raman, IR, and UV/Vis microspectroscopy; magnetic resonance imaging (MRI); tomographic energy dispersive diffraction imaging (TEDDI); and micro-computed tomography (mCT). [11][12][13][14][15][16][17] Importantly, both MRI and TEDDI are able to probe in a non-invasive manner in two dimensions, thus providing time-resolved information on both the impregnation and calcination/activation processes. Whilst the former is limited to the study of paramagnetic species and is therefore almost exclusively limited to probing the impregnation stage, TEDDI provides detailed information regarding elemental and ...