Modeling tree water flow as an unsaturated flow through a porous medium

The electric circuit analogy has had a profound influence on how tree physiologists measure, model and think about tree water flow. For example, previous models that attempt to account for changes in saturation use the electric circuit analogy to define capacitance as the change in saturation per change in pressure. Given that capacitance is constant, this relationship implies that subjecting a block of wood to a pressure of -2.5 MPa for 2 min results in the same change in saturation as subjecting the same block to the same pressure for 2 days. Given the definition of capacitance, it is unclear how the electric circuit analogy could be used to predict changes in saturation separately from changes in pressure. The inadequacies in the electric circuit analogy discussed in this paper necessitate a new theory of tree water flow that recognizes the sapwood as being a porous medium and explicitly deals with the full implications of the unsaturated flow occurring in the sapwood. The theory proposed in this paper combines the Cohesion theory with a mathematical theory of multiphase flow through porous media. Based on this theory, both saturated and unsaturated tree water flow models are presented. Previous partial differential equation models of tree water flow based on the electric circuit analogy are shown to be mathematically equivalent to the model of saturated porous flow. The unsaturated model of tree water flow explicitly models the pressure profile and the rates of change in saturation and specific interfacial area (a measure of how the water in the unsaturated sapwood is partitioned between mobile and immobile components). The unsaturated model highlights the differences between saturated and unsaturated flow and the need to measure the variables governing tree water flow at higher spatial and temporal resolutions.     

Immobilized enzymes: electrokinetic effects on reaction rates in a porous medium

The effect of the internal diffusion and electrical surface charge on the overall rate of a reaction catalyzed by an enzyme immobilized on a porous medium are examined. Effectiveness factors have been calculated which compare the global reaction rate to that existing in the absence of the internal diffusion and/or the electrical field. The surface charge, assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme, generates an electrical double layer at the pore surface. The double-layer potential is governed by the Poisson-Boltzmann equation. It is shown that the diffusion potential can be characterized by a modulus which depends upon the surface reaction rate, the charges and diffusivities of the substrate and products, the ionic strength, and the pore dimensions. The flux of a charged species in the pore occurs under the influences of the concentration gradient and the electrical potential gradient. The governing equations are solved by an iterative numerical method. The effects of pH, enzyme concentration, and substrate concentration on the rates of two different hydrolysis reactions catalyzed by immobilized papain are examined. The release of H(+) in one of the reactions causes the lowering of internal pH, and also a constancy of the internal pH when the external pH in creases beyond a certain value. The latter reaction also shows a maximum in the reaction rate with respect to enzyme concentration. The reaction not involving H(+) as a product shows a maximum in the reaction rate with respect to external pH, but a monotonic increase in the reaction rate as the enzyme concentration increases.     

Modeling biofilm accumulation and mass transport in a porous medium under high substrate loading

A packed bed biofilm reactor inoculated with pure culture Pseudomonas aeruginosa was run under high substrate loading and constant flow rate conditions. The 3.1-cm-diameter cylindrical reactor was 5 cm in length and packed with 1-mm glass beads. Daily observations of biofilm thickness, influent and effluent glucose substrate concentration, and effluent dissolved and total organic carbon were made during the 13-day experiment. Biofilm thickness appeared to rech quasi-steady-state condition after 10 days. A published biofilm process simulation program (AQUASIM) was used to analyze experimental data. Comparison of observed and simulated variables revealed three distinct phases of biofilm accumulation during the experiment: an initial phase, a growth phase, and a mature biofilm phase. Different combinations of biofilm and mass transport process variables were found to be important during each phase. Biofilm detachment was highly correlated with shear at the biofilm surface during all three phases of biofilm development. (c) 1995 John Wiley & Sons, Inc.     

Planktonic replication is essential for biofilm formation by Legionella pneumophila in a complex medium under static and dynamic flow conditions

Legionella pneumophila persists for a long time in aquatic habitats, where the bacteria associate with biofilms and replicate within protozoan predators. While L. pneumophila serves as a paradigm for intracellular growth within protozoa, it is less clear whether the bacteria form or replicate within biofilms in the absence of protozoa. In this study, we analyzed surface adherence of and biofilm formation by L. pneumophila in a rich medium that supported axenic replication. Biofilm formation by the virulent L. pneumophila strain JR32 and by clinical and environmental isolates was analyzed by confocal microscopy and crystal violet staining. Strain JR32 formed biofilms on glass surfaces and upright polystyrene wells, as well as on pins of "inverse" microtiter plates, indicating that biofilm formation was not simply due to sedimentation of the bacteria. Biofilm formation by an L. pneumophila fliA mutant lacking the alternative sigma factor sigma(28) was reduced, which demonstrated that bacterial factors are required. Accumulation of biomass coincided with an increase in the optical density at 600 nm and ceased when the bacteria reached the stationary growth phase. L. pneumophila neither grew nor formed biofilms in the inverse system if the medium was exchanged twice a day. However, after addition of Acanthamoeba castellanii, the bacteria proliferated and adhered to surfaces. Sessile (surface-attached) and planktonic (free-swimming) L. pneumophila expressed beta-galactosidase activity to similar extents, and therefore, the observed lack of proliferation of surface-attached bacteria was not due to impaired protein synthesis or metabolic activity. Cocultivation of green fluorescent protein (GFP)- and DsRed-labeled L. pneumophila led to randomly interspersed cells on the substratum and in aggregates, and no sizeable patches of clonally growing bacteria were observed. Our findings indicate that biofilm formation by L. pneumophila in a rich medium is due to growth of planktonic bacteria rather than to growth of sessile bacteria. In agreement with this conclusion, GFP-labeled L. pneumophila initially adhered in a continuous-flow chamber system but detached over time; the detachment correlated with the flow rate, and there was no accumulation of biomass. Under these conditions, L. pneumophila persisted in biofilms formed by Empedobacter breve or Microbacterium sp. but not in biofilms formed by Klebsiella pneumoniae or other environmental bacteria, suggesting that specific interactions between the bacteria modulate adherence.     

Design methodology accounting for the effects of porous medium heterogeneity on hydraulic residence time and biodegradation in horizontal subsurface flow constructed wetlands

Horizontal flow constructed wetlands are engineered systems capable of eliminating a wide range of pollutants from the aquatic environment. Nevertheless, poor hydrodynamic behavior is commonly found resulting in preferential pathways and variations in both (i) the hydraulic residence time distribution (HRTD) and, consequently, (ii) the wetland's treatment efficiency. The aim of this work was to outline a methodology for wetland design that accounts for the effect of heterogeneous hydraulic properties of the porous substrate on the HRTD and treatment efficiency. Biodegradation of benzene was used to illustrate the influence of hydraulic conductivity heterogeneity on wetland efficiency. Random, spatially correlated hydraulic conductivity fields following a log-normal distribution were generated and then introduced in a subsurface flow numerical model. The results showed that the variance of the distribution and the correlation length in the longitudinal direction are key indicators of the extent of heterogeneity. A reduction of the mean hydraulic residence time was observed as the extent of heterogeneity increased, while the HRTD became broader with increased skewness. At the same time, substrate heterogeneity induced preferential flow paths within the wetland bed resulting in variations of the benzene treatment efficiency. Further to this it was observed that the distribution of biomass within the porous bed became heterogeneous, rising questions on the representativeness of sampling. It was concluded that traditional methods for wetland design based on assumptions such as a homogeneous porous medium and plug flow are not reliable. The alternative design methodology presented here is based on the incorporation of heterogeneity directly during the design phase. The same methodology can also be used to optimize existing systems, where the HRTD has been characterized with tracer experiments.     

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.     

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.     

A porous agar medium for improving the growth of plants under sterile conditions

Porous nutrient agar was prepared under sterile conditions by drawing molten 3.5% (w/v) nutrient agar into a plastic syringe, allowing it to set, extruding it into a test tube and giving the tube a firm flick. Simple colorimetric tests showed that gaseous diffusion was substantially faster through 3.5% (w/v) porous agar than through the 1% (w/v) non-porous agar frequently used for growing plants under sterile conditions. Root systems ofTrifolium subterraneum grew 80–90% larger in porous than in non-porous agar.     

Analysis of lung parenchyma as a parametric porous medium.

The dynamic behavior of the lung in health and disease depends on its viscoelastic properties. To better understand these properties, several mathematical models have been utilized by many investigators. In the present work, we present a new approach that characterizes the dynamics of gas flow into a viscoelastic porous medium that models the lung structure. This problem is considered in terms of the lung input impedance on a macro level and parenchymal tissue impedance on the level of an alveolar wall. We start from a basic theoretical analysis in which macroscopic tissue deformations are represented in accordance with the linearized Navier-Stokes equations. This approach has strong theoretical underpinnings in other situations but has not been applied to analyze the impedance of the inflated lung. Our analysis provides a theoretical basis for analyzing the interaction between flow into the lungs as a biophysical diffusion process and parenchymal viscoelasticity described phenomenologically, within the frameworks of standard viscoelasticity and structural damping. This lung impedance incorporates parameters of porosity, permeability, and viscoelasticity on micro and macro levels of parenchymal tissue. The analysis shows the theoretical basis of the transformation from the impedance of alveolar walls or isolated tissue strips to that of the intact parenchyma. We also show how the loading impedance at the lung boundary may have a significant impact on the dynamic behavior of whole lung viscoelasticity. Our analysis may be useful in directing specific tests of different models and for analyzing experimental measurements of viscoelastic parameters of lung material under normal and pathological conditions.     

Comparison of bioclogging effects in saturated porous media within one- and two-dimensional flow systems

The accumulation of microbial biomass in a porous medium can lead to a reduction of pore space and an associated decrease in the hydraulic conductivity of the medium – an effect called bioclogging. This phenomenon may occur in several natural and engineered subsurface systems and can be relevant in fields ranging from contaminant hydrology to civil and environmental engineering, as well as for enhanced oil recovery. During the last decades bioclogging has been studied in various laboratory and theoretical studies. Most of these studies considered only one-dimensional flow fields inside a porous medium. Although these studies provided valuable information on bioclogging and factors controlling it, recent studies showed that an extrapolation of these results to multi-dimensional flow fields is not straight forward. This paper reviews the experimental results obtained for one- and two-dimensional flow fields and compares the modeling results obtained using different conceptualizations of the pore space.     

Modeling of the co-transport of cryoprotective agents in a porous medium as a model tissue

Cryopreservation is likely the choice for long-term preservation of natural and engineered tissues, and high concentration multiple cryoprotective agents (CPAs) are usually used in such a process. To achieve high cell viability after cryopreservation, cells at all locations within the tissue must be protected properly by the CPAs during freezing. It is hence essential to know the distribution and concentration of CPAs within the tissue during multiple-CPA addition, to maximize cell survival and minimize tissue damage. In this work, a model to describe the CPA transport during multiple-CPA addition in a one-dimensional porous medium, as a simplified model of living tissue, was developed on the basis of the Maxwell-Stefan (M-S) equations. The UNIFAC and UNIQUAC models were used to evaluate the activity coefficients, and the Siddiqi-Lucas correlation was used for estimation of Maxwell-Stefan diffusivities. Simulations were carried out to examine the effect of temperature, tissue property, CPA type and the interactions between solutes on the CPA transport within construct during the CPA addition. It was found that these parameters, especially the interactions between the different CPA molecules, which was neglected before, significantly affect the transport of each individual CPA component. It is hence concluded that the traditional single-component analysis on the CPA diffusion is not adequate to quantify the multiple-CPA distribution in the tissue, particularly when the CPA concentrations are relatively high.     

Effect of couple stresses on the unsteady convective diffusion in fluid flow through a channel

A generalized dispersion model is used to obtain exact solution for unsteady convective diffusion in the presence of couple stresses. The effect of the couple stress parameter 'a' on the most dominant dispersion coefficient is clearly depicted. The dimensionless mean concentration distribution is obtained as a function of dimensionless axial distance, time and 'a'. The results for 'pure convection' are also reported. It is shown that the effect of couple stress is predominant only for small values of 'a' and when a----infinity the flow characteristics tend to their equivalents in Newtonian theory. The results of Taylor's dispersion model are recovered as a particular case in the limit tau----infinity.     

Biomass evolution in porous media and its effects on permeability under starvation conditions

The purpose of this study was to understand bacteria profile modification and its applications in subsurface biological operations such as biobarrier formation, in situ bioremediation, and microbial-enhanced oil recovery. Biomass accumulation and evolution in porous media were investigated both experimentally and theoretically. To study both nutrient-rich and carbon-source-depleted conditions, Leuconostoc mesenteroides was chosen because of its rapid growth rate and exopolymer production rate. Porous micromodels were used to study the effects of biomass evolution on the permeability of a porous medium. Bacterial starvation was initiated by switching the feed from a nutrient solution to a buffer solution in order to examine biofilm stability under nutrient-poor conditions. Four different evolution patterns were identified during the nutrient-rich and nutrient-depleted conditions used in the micromodel experiments. In phase I, the permeability of the porous micromodel decreased as a result of biomass accumulation in pore bodies and pore throats. In phase II, starvation conditions were initiated. The depletion of nutrient in the phase II resulted in slower growth of the biofilm causing the permeability to reach a minimum as all the remaining nutrients were consumed. In phase III, permeability began to increase due to biofilm sloughing caused by shear stress. In phase IV, shear stress remained below the critical shear stress for sloughing and the biofilm remained stable for long periods of time during starvation. The critical shear stress for biofilm sloughing provided an indication of biofilm strength. Shear removal of biofilms occurred when shear stress exceeded critical shear stress. A network model was used to describe the biofilm formation phenomenon and the existence of a critical shear stress. Simulations were in qualitative agreement with the experimental results, and demonstrate the existence of a critical shear stress.     

Adaptation of Delftia acidovorans for degradation of 2,4-dichlorophenoxyacetate in a microfluidic porous medium

Delftia acidovorans MC1071 can productively degrade R-2-(2,4-dichlorophenoxy)propionate (R-2,4-DP) but not 2,4-dichlorophenoxyacetate (2,4-D) herbicides. This work demonstrates adaptation of MC1071 to degrade 2,4-D in a model two-dimensional porous medium (referred to here as a micromodel). Adaptation for 2,4-D degradation in the 2 cm-long micromodel occurred within 35 days of exposure to 2,4-D, as documented by substrate removal. The amount of 2,4-D degradation in the adapted cultures in two replicate micromodels (~10 and 20 % over 142 days) was higher than a theoretical maximum (4 %) predicted using published numerical simulation methods, assuming instantaneous biodegradation and a transverse dispersion coefficient obtained for the same pore structure without biomass present. This suggests that the presence of biomass enhances substrate mixing. Additional evidence for adaptation was provided by operation without R-2,4-DP, where degradation of 2,4-D slowly decreased over 20 days, but was restored almost immediately when R-2,4-DP was again provided. Compared to suspended growth systems, the micromodel system retained the ability to degrade 2,4-D longer in the absence of R-2,4-DP, suggesting slower responses and greater resilience to fluctuations in substrates might be expected in the soil environment than in a chemostat.     

Theoretical investigation of the first-shell mechanism of acetylene hydration catalyzed by a biomimetic tungsten complex

The reaction mechanism of the hydration of acetylene to acetaldehyde catalyzed by [W^IVO(mnt)₂]²⁻ (where mnt²⁻ is 1,2-dicyanoethylenedithiolate) is studied using density functional theory. Both the uncatalyzed and the catalyzed reaction are considered to find out the origin of the catalysis. Three different models are investigated, in which an aquo, a hydroxo, or an oxo coordinates to the tungsten center. A first-shell mechanism is suggested, similarly to recent calculations on tungsten-dependent acetylene hydratase. The acetylene substrate first coordinates to the tungsten center in an η² fashion. Then, the tungsten-bound hydroxide activates a water molecule to perform a nucleophilic attack on the acetylene, resulting in the formation of a vinyl anion and a tungsten-bound water molecule. This is followed by proton transfer from the tungsten-bound water molecule to the newly formed vinyl anion intermediate. Tungsten is directly involved in the reaction by binding and activating acetylene and providing electrostatic stabilization to the transition states and intermediates. Three other mechanisms are also considered, but the associated energetic barriers were found to be very high, ruling out those possibilities.     

Evolutionary responses of tree phenology to the combined effects of assortative mating,gene flow and divergent selection

The timing of bud burst (TBB) in temperate trees is a key adaptive trait, the expression of which is triggered by temperature gradients across the landscape. TBB is strongly correlated with flowering time and is therefore probably mediated by assortative mating. We derived theoretical predictions and realized numerical simulations of evolutionary changes in TBB in response to divergent selection and gene flow in a metapopulation. We showed that the combination of the environmental gradient of TBB and assortative mating creates contrasting genetic clines, depending on the direction of divergent selection. If divergent selection acts in the same direction as the environmental gradient (cogradient settings), genetic clines are established and inflated by assortative mating. Conversely, under divergent selection of the same strength but acting in the opposite direction (countergradient selection), genetic clines are slightly constrained. We explored the consequences of these dynamics for population maladaptation, by monitoring pollen swamping. Depending on the direction of divergent selection with respect to the environmental gradient, pollen filtering owing to assortative mating either facilitates or impedes adaptation in peripheral populations.