Three-dimensional fluid pressure mapping in porous media using magnetic resonance imaging with gas-filled liposomes

This paper presents and demonstrates a method for using magnetic resonance imaging to measure local pressure of a fluid saturating a porous medium. The method is tested both in a static system of packed silica gel and in saturated sintered glass cylinders experiencing fluid flow. The fluid used contains 3% gas in the form of 3-μm average diameter gas filled 1,2-distearoyl-sn-glycero-3-phosphocholine (C18:0, MW: 790.16) liposomes suspended in 5% glycerol and 0.5% Methyl cellulose with water. Preliminary studies at 2.35 T demonstrate relative magnetic resonance signal changes of 20% per bar in bulk fluid for an echo time TE=40 ms, and 6-10% in consolidated porous media for TE=10 ms, over the range 0.8-1.8 bar for a spatial resolution of 0.1 mm3 and a temporal resolution of 30 s. The stability of this solution with relation to applied pressure and methods for improving sensitivity are discussed. © 2007 Elsevier Inc. All rights reserved.

A three dimensional numerical investigation of hillslope flow processes

Physically based distributed models of catchment hydrology are likely to be made available as engineering tools in the near future. Although these models are based on theoretically acceptable equations of continuity, there are still limitations in the present modelling strategy. Of interest to this thesis are the current modelling assumptions made concerning the effects of soil spatial variability, including formations producing distinct zones of preferential flow. The thesis contains a review of current physically based modelling strategies and a field based assessment of soil spatial variability. In order to investigate the effects of soil nonuniformity a fully three dimensional model of variability saturated flow in porous media is developed. The model is based on a Galerkin finite element approximation to Richards equation. Accessibility to a vector processor permits numerical solutions on grids containing several thousand node points. The model is applied to a single hillslope segment under various degrees of soil spatial variability. Such variability is introduced by generating random fields of saturated hydraulic conductivity using the turning bands method. Similar experiments are performed under conditions of preferred soil moisture movement. The results show that the influence of soil variability on subsurface flow may be less significant than suggested in the literature, due to the integrating effects of three dimensional flow. Under conditions of widespread infiltration excess runoff, the results indicate a greater significance of soil nonuniformity. The recognition of zones of preferential flow is also shown to be an important factor in accurate rainfall-runoff modelling. Using the results of various fields of soil variability, experiments are carried out to assess the validity of the commonly used concept of `effective parameters'. The results of these experiments suggest that such a concept may be valid in modelling subsurface flow. However, the effective parameter is observed to be event dependent when the dominating mechanism is infiltration excess runoff.

Coalescence of secondary dispersions

A study has been made of the coalescence of secondary dispersions in beds of woven meshes. The variables investigated were superficial velocity, bed depth, mesh geometry and fibre material; the effects of presoaking the bed in the dispersed phase before operation were also considered. Equipment was design~d to generate a 0.1% phase ratio toluene in water dispersion whose mean drop size was determined using a Coulter Counter. The coalesced drops were sized by photography and a novel holographic technique was developed to evaluate the mean diameter of the effluent secondary drops. Previous models describing single phase flow in porous media are reviewed and it was found that the experimental data obtained in this study is best represented by Keller's equation which is based on a physical model similar to the internal structure of the meshes. Statistical analysis of two phase data produced a correlation, for each mesh tested, relating the pressure drop to superficial velocity and bed depth. The flow parameter evaluated from the single phase model is incorporated into a theoretical comparison of drop capture mechanisms which indicated that direct and indirect interception are predominant. The resulting equation for drop capture efficiericy is used to predict the initial, local drop capture rate in a coalescer. A mathematical description of the saturation profiles was formulated and verified by average saturation data. Based 6n the Blake-Kozeny equation, an expression is derived analytically to predict the two phase pressure drop using the parameters which characterise the saturation profiles. By specifying the local saturation at the inlet face for a given velocity, good agreement between experimental pressure drop data and the model predictions was obtained.

Coalescence of secondary dispersions in packed beds

A study has been made of the coalescence of secondary dispersions in beds of monosized glass ballotini. The variables investigated were superficial velocity, bed depth, ballotini size and dispersed phase concentration. Equipment was designed to generate a toluene ln water dispersion with phase ratios from 0.1 - 1.0 v/v % and whose mean drop size was determined using a Coulter Counter. The coalesced drops were sized by photography and the mean diameter of the effluent drops was determined using a Malvern Particle Size Analyser. Previous models describing single phase flow in porous media are reviewed and it was found that the experimental data obtained in this study is best represented by the Carman-Kozeny equations. Relative permeability correlations were used to predict the saturation profiles across the bed from measured two phase pressure drop data. Theoretical comparison of drop capture mechanisms indicated that direct and indirect interception are predominant. The total capture efficiency for the bed can also be evaluated using Spielman and Fitzpatrick's correlation.The resulting equation is used to predict the initial, local drop capture rate in a coalescer. A mathematical description of the saturation profiles is formulated and verified by the saturation profiles obtained by relative permeability. Based on the Carman-Kozeny equation, an expression is derived analytically to .predict the two phase pressure drop using the parameters which characterise the saturation profiles. By specifying the local saturation at the inlet face for a given velocity and phase ratio, good agreement between experimental pressure drop data and the model predictions was obtained. An attempt to predict the exit drop size has been made using an analogy for flow through non cylindrical channels.

Atmospheric plasma treatment of porous polymer constructs for tissue engineering applications

Porous 3D polymer scaffolds prepared by TIPS from PLGA (53:47) and PS are intrinsically hydrophobic which prohibits the wetting of such porous media by water. This limits the application of these materials for the fabrication of scaffolds as supports for cell adhesion/spreading. Here we demonstrate that the interior surfaces of polymer scaffolds can be effectively modified using atmospheric air plasma (AP). Polymer films (2D) were also modified as control. The surface properties of wet 2D and 3D scaffolds were characterised using zeta-potential and wettability measurements. These techniques were used as the primary screening methods to assess surface chemistry and the wettability of wet polymer constructs prior and after the surface treatment. The surfaces of the original polymers are rather hydrophobic as highlighted but contain acidic functional groups. Increased exposure to AP improved the water wetting of the treated surfaces because of the formation of a variety of oxygen and nitrogen containing functions. The morphology and pore structure was assessed using SEM and a liquid displacement test. The PLGA and PS foam samples have central regions which are open porous interconnected networks with maximum pore diameters of 49 μm for PLGA and 73 μm for PS foams. (Figure Presented) © 2007 Wiley-VCH Verlag GmbH & Co. KGaA.

MRI pressure and stress measurement in novel homogeneous soft solids

This paper presents MRI measurements of a novel semi solid MR contrast agent to pressure. The agent is comprised of potassium chloride cross linked carageenan gum at a concentration of 2% w/v, with micron size lipid coated bubbles of air at a concentration of 3% v/v. The choice for an optimum suspending medium, the methods of production and the preliminary MRI results are presented herein. The carageenan gum is shown to be ideally elastic for compressions relating to volume changes less than 15%, in contrast to the inelastic gellan gum also tested. Although slightly lower than that of gellan gum, carageenan has a water diffusion coefficient of 1.72×10-9 m2.s-1 indicating its suitability to this purpose. RARE imaging is performed whilst simultaneously compressing test and control samples and a maximum sensitivity of 1.6% MR signal change per % volume change is found which is shown to be independent of proton density variations due to the presence of microbubbles and compression. This contrast agent could prove useful for numerous applications, and particularly in chemical engineering. More generally the method allows the user to non-invasively image with MRI any process that causes, within the solid, local changes either in bubble size or bubble shape. © 2008 American Institute of Physics.

The critical role of intracavity dynamics in high-power mode-locked fiber lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Intracavity dynamics in mode-locked lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile. © 2010 American Institute of Physics.

Intracavity dynamics for power and energy enhancement in mode-locked lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile.

Osmotic flow in porous membranes:effects of electric charge

The electrostatic model for osmotic flow across a porous membrane in our previous study (Akinaga et al. 2008)" was extended to include the streaming potential, for solutes and pores of like charge and fixed surface charge densities. The magnitude of the streaming potential was determined to satisfy zero current condition along the pore axis. It was found that the streaming potential affects the velocity profiles of the pressure driven flow as well as the osmotic flow through the pore, and decreases their flow rates, particularly in the case of large Debye length relative to the pore radius, whereas it has little effect on the reflection coefficients of spherical solutes through cylindrical pores.

Spray drier simulation and air flow pattern studies

The literature pertaining to the key stages of spray drying has been reviewed in the context of the mathematical modelling of drier performance. A critical review is also presented of previous spray drying models. A new mathematical model has been developed for prediction of spray drier performance. This is applicable to slurries of rigid, porous crust-forming materials to predict trajectories and drying profiles for droplets with a distribution of sizes sprayed from a centrifugal pressure nozzle. The model has been validated by comparing model predictions to experimental data from a pilot-scale counter-current drier and from a full-scale co-current drier. For the latter, the computed product moisture content was within 2%, and the computed air exit temperature within 10oC of experimental data. Air flow patterns have been investigated in a 1.2m diameter transparent countercurrent spray tower by flow visualisation. Smoke was introduced into various zones within the tower to trace the direction, and gauge the intensity, of the air flow. By means of a set of variable-angle air inlet nozzles, a variety of air entry configurations was investigated. The existence of a core of high rotational and axial velocity channelling up the axis of the tower was confirmed. The stability of flow within the core was found to be strongly dependent upon the air entry arrangement. A probe was developed for the measurement of air temperature and humidity profiles. This was employed for studying evaporation of pure water drops in a 1.2m diameter pilot-scale counter-current drier. A rapid approach to the exit air properties was detected within a 1m distance from the air entry ports. Measured radial profiles were found to be virtually flat but, from the axial profiles, the existence of plug-flow, well-mixed-flow and some degree of air short-circuiting can be inferred. The model and conclusions should assist in the improved design and optimum operation of industrial spray driers.

The steady performance of a porous and compliant aerostatic thrust bearing

Recent developments in aerostatic thrust bearings have included: (a) the porous aerostatic thrust bearing containing a porous pad and (b) the inherently compensated compliant surface aerostatic thrust bearing containing a thin elastomer layer. Both these developments have been reported to improve the bearing load capacity compared to conventional aerostatic thrust bearings with rigid surfaces. This development is carried one stage further in a porous and compliant aerostatic thrust bearing incorporating both a porous pad and an opposing compliant surface. The thin elastomer layer forming the compliant surface is bonded to a rigid backing and is of a soft rubber like material. Such a bearing is studied experimentally and theoretically under steady state operating conditions. A mathematical model is presented to predict the bearing performance. In this model is a simplified solution to the elasticity equations for deflections of the compliant surface. Account is also taken of deflections in the porous pad due to the pressure difference across its thickness. The lubrication equations for flow in the porous pad and bearing clearance are solved by numerical finite difference methods. An iteration procedure is used to couple deflections of the compliant surface and porous pad with solutions to the lubrication equations. Comparisons between experimental results and theoretically predicted bearing performance are in good agreement. However these results show that the porous and compliant aerostatic thrust bearing performance is lower than that of a porous aerostatic thrust bearing with a rigid surface in place of the compliant surface. This discovery is accounted to the recess formed in the bearing clearance by deflections of the compliant surface and its effect on flow through the porous pad.

A study of the micro-mechanics of granular media

The development of more realistic constitutive models for granular media, such as sand, requires ingredients which take into account the internal micro-mechanical response to deformation. Unfortunately, at present, very little is known about these mechanisms and therefore it is instructive to find out more about the internal nature of granular samples by conducting suitable tests. In contrast to physical testing the method of investigation used in this study employs the Distinct Element Method. This is a computer based, iterative, time-dependent technique that allows the deformation of granular assemblies to be numerically simulated. By making assumptions regarding contact stiffnesses each individual contact force can be measured and by resolution particle centroid forces can be calculated. Then by dividing particle forces by their respective mass, particle centroid velocities and displacements are obtained by numerical integration. The Distinct Element Method is incorporated into a computer program 'Ball'. This program is effectively a numerical apparatus which forms a logical housing for this method and allows data input and output, and also provides testing control. By using this numerical apparatus tests have been carried out on disc assemblies and many new interesting observations regarding the micromechanical behaviour are revealed. In order to relate the observed microscopic mechanisms of deformation to the flow of the granular system two separate approaches have been used. Firstly a constitutive model has been developed which describes the yield function, flow rule and translation rule for regular assemblies of spheres and discs when subjected to coaxial deformation. Secondly statistical analyses have been carried out using data which was extracted from the simulation tests. These analyses define and quantify granular structure and then show how the force and velocity distributions use the structure to produce the corresponding stress and strain-rate tensors.

Clogging in horizontal subsurface flow constructed wetlands

Horizontal Subsurface Flow Treatment Wetlands (HSSF TWs) are used by Severn Trent Water as a low-cost tertiary wastewater treatment for rural locations. Experience has shown that clogging is a major operational problem that reduces HSSF TW lifetime. Clogging is caused by an accumulation of secondary wastewater solids from upstream processes and decomposing leaf litter. Clogging occurs as a sludge layer where wastewater is loaded on the surface of the bed at the inlet. Severn Trent systems receive relatively high hydraulic loading rates, which causes overland flow and reduces the ability to mineralise surface sludge accumulations. A novel apparatus and method, the Aston Permeameter, was created to measure hydraulic conductivity in situ. Accuracy is ±30 %, which was considered adequate given that conductivity in clogged systems varies by several orders of magnitude. The Aston Permeameter was used to perform 20 separate tests on 13 different HSSF TWs in the UK and the US. The minimum conductivity measured was 0.03 m/d at Fenny Compton (compared with 5,000 m/d clean conductivity), which was caused by an accumulation of construction fines in one part of the bed. Most systems displayed a 2 to 3 order of magnitude variation in conductivity in each dimension. Statistically significant transverse variations in conductivity were found in 70% of the systems. Clogging at the inlet and outlet was generally highest where flow enters the influent distribution and exits the effluent collection system, respectively. Surface conductivity was lower in systems with dense vegetation because plant canopies reduce surface evapotranspiration and decelerate sludge mineralisation. An equation was derived to describe how the water table profile is influenced by overland flow, spatial variations in conductivity and clogging. The equation is calibrated using a single parameter, the Clog Factor (CF), which represents the equivalent loss of porosity that would reproduce measured conductivity according to the Kozeny-Carman Equation. The CF varies from 0 for ideal conditions to 1 for completely clogged conditions. Minimum CF was 0.54 for a system that had recently been refurbished, which represents the deviation from ideal conditions due to characteristics of non-ideal media such as particle size distribution and morphology. Maximum CF was 0.90 for a 15 year old system that exhibited sludge accumulation and overland flow across the majority of the bed. A Finite Element Model of a 15 m long HSSF TW was used to indicate how hydraulics and hydrodynamics vary as CF increases. It was found that as CF increases from 0.55 to 0.65 the subsurface wetted area increases, which causes mean hydraulic residence time to increase from 0.16 days to 0.18 days. As CF increases from 0.65 to 0.90, the extent of overland flow increases from 1.8 m to 13.1 m, which reduces hydraulic efficiency from 37 % to 12 % and reduces mean residence time to 0.08 days.

Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).