A new approach to model the spatiotemporal development of biofilm phase in porous media

Bacteria can exist within biofilms that are attached to the solid matrix of a porous medium. Under certain conditions, the biomass can fully occupy the pore space leading to reduced hydraulic conductivity and mass transport. Here, by treating biofilm as a growing, high-viscosity phase, a novel macroscopic approach to model biofilm spatial expansion and its corresponding effects on porous medium hydraulic properties is presented. The separate yet coupled flow of the water and biofilm phases is handled by using relative permeability curves that allow for biofilm movement within the porous medium and bioclogging effects. Fluid flow is governed by Darcy's law and component transport is set by the convection-diffusion equation reaction terms for each component. Here, the system of governing equations is solved by using a commercial multiphase flow reservoir simulator, which is used to validate the model against published laboratory experiments. A comparison of the model and experimental observations reveal that the model provides a reasonable means to predict biomass development in the porous medium. The results reveal that coupled flow of water and movement of biofilm, as described by relative permeability curves, is complex and has a large impact on the development of biomass and consequent bioclogging in the porous medium.     

Biofilm development and the dynamics of preferential flow paths in porous media

A two-dimensional pore-scale numerical model was developed to evaluate the dynamics of preferential flow paths in porous media caused by bioclogging. The liquid flow and solute transport through the pore network were coupled with a biofilm model including biomass attachment, growth, decay, lysis, and detachment. Blocking of all but one flow path was obtained under constant liquid inlet flow rate and biomass detachment caused by shear forces only. The stable flow path formed when biofilm detachment balances growth, even with biomass weakened by decay. However, shear forces combined with biomass lysis upon starvation could produce an intermittently shifting location of flow channels. Dynamic flow pathways may also occur when combined liquid shear and pressure forces act on the biofilm. In spite of repeated clogging and unclogging of interconnected pore spaces, the average permeability reached a quasi-constant value. Oscillations in the medium permeability were more pronounced for weaker biofilms.     

Pore‐network modeling of biofilm evolution in porous media

The influence of bacterial biomass on hydraulic properties of porous media (bioclogging) has been explored as a viable means for optimizing subsurface bioremediation and microbial enhanced oil recovery. In this study, we present a pore network simulator for modeling biofilm evolution in porous media including hydrodynamics and nutrient transport based on coupling of advection transport with Fickian diffusion and a reaction term to account for nutrient consumption. Biofilm has non‐zero permeability permitting liquid flow and transport through the biofilm itself. To handle simultaneous mass transfer in both liquid and biofilm in a pore element, a dual‐diffusion mass transfer model is introduced. The influence of nutrient limitation on predicted results is explored. Nutrient concentration in the network is affected by diffusion coefficient for nutrient transfer across biofilm (compared to water/water diffusion coefficient) under advection dominated transport, represented by mass transport Péclet number >1. The model correctly predicts a dependence of rate of biomass accumulation on inlet concentration. Poor network connectivity shows a significantly large reduction of permeability, for a small biomass pore volume. Biotechnol. Bioeng. 2011;108: 2413–2423. © 2011 Wiley Periodicals, Inc.     

Xanthan degragation by biofilm in porous media

Biological activity in oil reservoirs can cause significant problems such as souring and plugging. This study focuses on the problem of polymer degradation and permeability reduction due to biofilm formation during polymer injection for improved oil recovery. Polymers are included in injection fluids to increase their viscosity. Results relating biological processes and polymer degradation to fluid‐dynamic conditions in a laboratory model porous medium are presented.

A transparent flow cell with an etched two‐dimensional network of pores served as a model porous medium. A sterile xanthan polymer and natural sea water solution were continuously injected into the porous medium. A bacterial culture capable of xanthan degradation was introduced into the cell by a single injection. Some of the cells from this culture attached to the pore walls forming an immobile bacterial culture, termed biofilm. The development of this biofilm, its xanthan degradation and its effect on permeability were measured.

The effects of injection rate and rate transitions were analyzed. Injection fluid viscosity was reduced by 30% after 5 min flow through the porous medium at the maximum steady state degradation rate observed. Permeability was significantly reduced by the xanthan degrading biofilm, causing an increase in pressure drop through the porous medium of up to 80%. Polymer injection in oil reservoirs may, therefore, have negative effects on oil recovery, unless efficient biofouling control is applied. The methodology presented may serve as a tool in the development of biofouling control measures in porous media.     

Three-dimensional modeling of the brain's ECS by minimum configurational energy packing of fluid vesicles

The extracellular space of the brain is the heterogeneous porous medium formed by the spaces between the brain cells. Diffusion in this interstitial space is the mechanism by which glucose and oxygen are delivered to the brain cells from the vascular system. It is also a medium for the transport of certain informational substances between the cells (called volume transmission), and for drug delivery. This work involves three-dimensional modeling of the extracellular space as void space in close-packed arrays of fluid membrane vesicles. These packings are generated by minimizing the configurational energy using a Monte Carlo procedure. Both regular and random packs of vesicles are considered. A random walk algorithm is then used to compute the geometric tortuosities, and the results are compared with published experimental data. For the random packings, it is found that although the absolute values for the tortuosities differ, the dependence of the tortuosity on pore volume fraction is very similar to that observed in experiment. The tortuosities we measure are larger than those computed in previous studies of packings of convex polytopes, and modeling improvements, which require higher resolution studies and an improved modeling of brain cell shapes and mechanical properties, could help resolve remaining discrepancies between model simulations and experiment. It is also shown that the specular reflection scheme is the appropriate technique for implementing zero-flux boundary conditions in random walk simulations commonly encountered in diffusion problems.     

Restricted diffusion of molecules in porous affinity chromatography adsorbents.

A restricted diffusion model is constructed and solved in order to study the permeability of large adsorbate molecules in the pores of affinity chromatography media, when the adsorbate molecules are adsorbed onto immobilized ligands. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size distribution, pore connectivity of the adsorbent, molecular size of adsorbate and ligand, and the fractional saturation of adsorption sites (ligands), are considered. Affinity adsorbents with dilute and high ligand concentrations are examined, and the permeability of the adsorbate in porous networks of connectivity nT is studied by means of effective medium approximation (EMA) numerical solutions. As expected, the permeability of the adsorbate decreases as the size of the adsorbate and/or ligand molecule increases. The permeability also decreases when the fractional saturation of the ligands increases, as well as when the pore connectivity of the network decreases. The dependence of the permeability on the pore connectivity tends to be less marked in adsorbents with concentrated ligand than in porous media with dilute ligand concentration. The conditions are also presented for which the percolation threshold is attained in a number of different systems. The restricted diffusion model and results of this work may be of importance in studies involving the modeling, prediction of the dynamic behavior, design, and control of affinity chromatography (biospecific adsorption) systems employing porous adsorbents. The theoretical results may also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix, so that the adsorbate of interest can be efficiently separated from a given solution. Furthermore, with appropriate modifications this restricted diffusion model may be used in studies involving the immobilization of ligands or enzymes in porous solids.     

Pore-scale investigation of biomass plug development and propagation in porous media.

Biomass plugging of porous media finds application in enhanced oil recovery and bioremediation. An understanding of biomass plugging of porous media was sought by using a porous glass micromodel through which biomass and nutrient were passed. This study describes the pore-scale physics of biomass plug propagation of Leuconostoc mesenteroides under nutrient-rich conditions. It was found that, as the nutrient flowed through the micromodel, the initial biomass plug occurred at the nutrient-inoculum interface due to growth in the larger pore throats. As growth proceeded, biomass filled and closed these larger pore throats, until only isolated groupings of pore throats with smaller radii remained empty. As nutrient flow continued, a maximum pressure drop was reached. At the maximum pressure drop, the biomass yielded in a manner similar to a Bingham plastic to form a breakthrough channel consisting of a path of interconnected pore throats. The channel incorporated the isolated groupings of empty pore throats that had been present before breakthrough. As the nutrient flow continued, subsequent plugs developed as breakthrough channels refilled with biomass and in situ growth was stimulated in the region just downstream of the previous plug. The downstream plugs had a higher fraction of isolated groupings of empty pore throats, which can be attributed to depletion of nutrient downstream. When the next breakthrough channel formed, it incorporated these isolated groupings, causing the breakthrough channels to be branched. It was observed that the newly formed plug could be less stable with this higher fraction of empty pore throats and that the location of breakthrough channels changed in subsequent plugs. This change in breakthrough channel location could be attributed to the redistribution of nutrient flow and the changes in flowrate in the pore throats.     

Transport diffusivities of fluids in nanopores by non-equilibrium molecular dynamics simulation

We present a method to study fluid transport through nanoporous materials using highly efficient non-equilibrium molecular dynamics simulations. A steady flow is induced by applying an external field to the fluid particles within a small slab of the simulation cell. The external field generates a density gradient between both sides of the porous material, which in turn triggers a convective flux through the porous medium. The heat dissipated by the fluid flow is released by a Gaussian thermostat applied to the wall particles. This method is effective for studying diffusivities in a slit pore as well as more natural, complex wall geometries. The dependence of the diffusive flux on the external field sheds light on the transport diffusivities and allows a direct calculation of effective diffusivities. Both pore and fluid particle interactions are represented by coarse-grained molecular models in order to present a proof-of-concept and to retain computational efficiency in the simulations. The application of the method is demonstrated in two different scenarios, namely the effective mass transport through a slit pore and the calculation of the effective self-diffusion through this system. The method allows for a distinction between diffusive and convective contributions of the mass transport.     

A New Proposal for the Action of Vasopressin, Based on Studies of a Complex Synthetic Membrane

The total osmotic flow of water across cell membranes generally exceeds diffusional flow measured with labeled water. The ratio of osmotic to diffusional flow has been widely used as a basis for the calculation of the radius of pores in the membrane, assuming Poiseuille flow of water through the pores. An important assumption underlying this calculation is that both osmotic and diffusional flow are rate-limited by the same barrier in the membrane. Studies employing a complex synthetic membrane show, however, that osmotic flow can be limited by one barrier (thin, dense barrier), and the rate of diffusion of isotopic water by a second (thick, porous) barrier in series with the first. Calculation of a pore radius is meaningless under these conditions, greatly overestimating the size of the pores determining osmotic flow. On the basis of these results, the estimation of pore radius in biological membranes is reassessed. It is proposed that vasopressin acts by greatly increasing the rate of diffusion of water across an outer barrier of the membrane, with little or no accompanying increase in pore size.     

Interstitial flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells

Interstitial flow through the tunica media of an artery wall in the presence of the internal elastic lamina (IEL), which separates it from the subendothelial intima, has been studied numerically. A two-dimensional analysis applying the Brinkman model as the governing equation for the porous media flow field was performed. In the numerical simulation, the IEL was modeled as an impermeable barrier to water flux, except for the fenestral pores, which were uniformly distributed over the IEL. The tunica media was modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells (SMCs) embedded in a fiber matrix simulating the interstitial proteoglycan and collagen fibers. A series of calculations was conducted by varying the physical parameters describing the problem: the area fraction of the fenestral pore (0. 001-0.036), the diameter of the fenestral pore (0.4-4.0 microm), and the distance between the IEL and the nearest SMC (0.2-0.8 microm). The results indicate that the value of the average shear stress around the circumference of the SMC in the immediate vicinity of the fenestral pore could be as much as 100 times greater than that around an SMC in the fully developed interstitial flow region away from the IEL. These high shear stresses can affect SMC physiological function.     

Prediction of the micro-fluid dynamic environment imposed to three-dimensional engineered cell systems in bioreactors

Bioreactors allowing culture medium perfusion overcome diffusion limitations associated with static culturing and provide flow-mediated mechanical stimuli. The hydrodynamic stress imposed to cells will depend not only on the culture medium flow rate, but also on the scaffold three-dimensional (3D) micro-architecture. We developed a CFD model of the flow of culture medium through a 3D scaffold of homogeneous geometry, with the aim of predicting the shear stress acting on cells as a function of parameters that can be controlled during the scaffold fabrication process, such as the scaffold porosity and the pore size, and during the cell culture, such as the medium flow rate and the diameter of the perfused scaffold section. We built three groups of models corresponding to three pore sizes: 50, 100 and 150 microm. Each group was made of four models corresponding to 59%, 65%, 77%, and 89% porosity. A commercial finite-element code was used to set up and solve the problem and to analyze the results. The mode value of shear stress varied between 2 and 5 mPa, and was obtained for a circular scaffold of 15.5 mm diameter, perfused by a flow rate of 0.5 ml/min. The simulations showed that the pore size is a variable strongly influencing the predicted shear stress level, whereas the porosity is a variable strongly affecting the statistical distribution of the shear stresses, but not their magnitude. Our results provide a basis for the completion of more exhaustive quantitative studies to further assess the relationship between perfusion, at known micro-fluid dynamic conditions, and tissue growth in vitro.     

Computational structure characterisation tools in application to ordered and disordered porous materials

In this article, we present a set of computational tools for systematic characterisation of ordered and disordered porous materials. These tools include calculation of the accessible surface area and geometric pore size distribution, analysis of the structure connectivity and percolation analysis of the porous space. We briefly discuss the algorithms behind these calculations. To demonstrate the capabilities of the tools and the type of insights that can be gained from their application, we consider a series of case studies. These case studies include small molecular fragments, several crystalline metal-organic materials, and variants of these materials with induced defects and disorder in their structure. The simulation package is available upon request.     

Real time monitoring of biofilm development under flow conditions in porous media

Biofilm growth can impact the effectiveness of industrial processes that involve porous media. To better understand and characterize how biofilms develop and affect hydraulic properties in porous media, both spatial and temporal development of biofilms under flow conditions was investigated in a translucent porous medium by using Pseudomonas fluorescens HK44, a bacterial strain genetically engineered to luminesce in the presence of an induction agent. Real-time visualization of luminescent biofilm growth patterns under constant pressure conditions was captured using a CCD camera. Images obtained over 8 days revealed that variations in bioluminescence intensity could be correlated to biofilm cell density and hydraulic conductivity. These results were used to develop a real-time imaging method to study the dynamic behavior of biofilm evolution in a porous medium, thereby providing a new tool to investigate the impact of biological fouling in porous media under flow conditions.     

Boundary Layer Flow Past a Stretching Surface in a Porous Medium Saturated by a Nanofluid: Brinkman-Forchheimer Model

In this study, the steady forced convection flow and heat transfer due to an impermeable stretching surface in a porous medium saturated with a nanofluid are investigated numerically. The Brinkman-Forchheimer model is used for the momentum equations (porous medium), whereas, Bongiorno’s model is used for the nanofluid. Uniform temperature and nanofluid volume fraction are assumed at the surface. The boundary layer equations are transformed to ordinary differential equations in terms of the governing parameters including Prandtl and Lewis numbers, viscosity ratio, porous medium, Brownian motion and thermophoresis parameters. Numerical results for the velocity, temperature and concentration profiles, as well as for the reduced Nusselt and Sherwood numbers are obtained and presented graphically.     

A porous elastic model for bacterial biofilms: application to the simulation of deformation of bacterial biofilms under microfluidic jet impingement

The presence of bacterial biofilms is detrimental in a wide range of healthcare situations especially wound healing. Physical debridement of biofilms is a method widely used to remove them. This study evaluates the use of microfluidic jet impingement to debride biofilms. In this case, a biofilm is treated as a saturated porous medium also having linear elastic properties. A numerical modeling approach is used to calculate the von Mises stress distribution within a porous medium under fluid-structure interaction (FSI) loading to determine the initial rupture of the biofilm structure. The segregated model first simulates the flow field to obtain the FSI interface loading along the fluid-solid interface and body force loading within the porous medium. A stress-strain model is consequently used to calculate the von Mises stress distribution to obtain the biofilm deformation. Under a vertical jet, 60% of the deformation of the porous medium can be accounted for by treating the medium as if it was an impermeable solid. However, the maximum deformation in the porous medium corresponds to the point of maximum shear stress which is a different position in the porous medium than that of the maximum normal stress in an impermeable solid. The study shows that a jet nozzle of 500 μm internal diameter (ID) with flow of Reynolds number (Re) of 200 can remove the majority of biofilm species.     

Permeability analysis of scaffolds for bone tissue engineering

Porous artificial bone substitutes, especially bone scaffolds coupled with osteobiologics, have been developed as an alternative to the traditional bone grafts. The bone scaffold should have a set of properties to provide mechanical support and simultaneously promote tissue regeneration. Among these properties, scaffold permeability is a determinant factor as it plays a major role in the ability for cells to penetrate the porous media and for nutrients to diffuse. Thus, the aim of this work is to characterize the permeability of the scaffold microstructure, using both computational and experimental methods. Computationally, permeability was estimated by homogenization methods applied to the problem of a fluid flow through a porous media. These homogenized permeability properties are compared with those obtained experimentally. For this purpose a simple experimental setup was used to test scaffolds built using Solid Free Form techniques. The obtained results show a linear correlation between the computational and the experimental permeability. Also, this study showed that permeability encompasses the influence of both porosity and pore size on mass transport, thus indicating its importance as a design parameter. This work indicates that the mathematical approach used to determine permeability may be useful as a scaffold design tool.     

Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.     

Hydromagnetic Flow and Heat Transfer over a Porous Oscillating Stretching Surface in a Viscoelastic Fluid with Porous Medium

An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.     

Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls

This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.