Mass Balance Principles Research Articles

Upscaling geochemical reaction rates using pore-scale network modeling

Geochemical reaction rate laws are often measured using crushed minerals in well-mixed laboratory systems that are designed to eliminate mass transport limitations. Such rate laws are often used directly in reactive transport models to predict the reaction and transport of chemical species in consolidated porous media found in subsurface environments. Due to the inherent heterogeneities of porous media, such use of lab-measured rate laws may introduce errors, leading to a need to develop methods for upscaling reaction rates. In this work, we present a methodology for using pore-scale network modeling to investigate scaling effects in geochemical reaction rates. The reactive transport processes are simulated at the pore scale, accounting for heterogeneities of both physical and mineral properties. Mass balance principles are then used to calculate reaction rates at the continuum scale. To examine the scaling behavior of reaction kinetics, these continuum-scale rates from the network model are compared to the rates calculated by directly using laboratory-measured reaction rate laws and ignoring pore-scale heterogeneities. In this work, this methodology is demonstrated by upscaling anorthite and kaolinite reaction rates under simulation conditions relevant to geological CO 2 sequestration. Simulation results show that under conditions with CO 2 present at high concentrations, pore-scale concentrations of reactive species and reaction rates vary spatially by orders of magnitude, and the scaling effect is significant. With a much smaller CO 2 concentration, the scaling effect is relatively small. These results indicate that the increased acidity associated with geological sequestration can generate conditions for which proper scaling tools are yet to be developed. This work demonstrates the use of pore-scale network modeling as a valuable research tool for examining upscaling of geochemical kinetics. The pore-scale model allows the effects of pore-scale heterogeneities to be integrated into system behavior at multiple scales, thereby identifying important factors that contribute to the scaling effect.

Compartmental modeling to quantify α-linolenic acid conversion after longer term intake of multiple tracer boluses

To estimate in vivo alpha-linolenic acid (ALA; C18:3n-3) conversion, 29 healthy subjects consumed for 28 days a diet providing 7% of energy from linoleic acid (C18:2n-6) and 0.4% from ALA. On day 19, subjects received a single bolus of 30 mg of uniformly labeled [(13)C]ALA and for the next 8 days 10 mg twice daily. Fasting plasma phospholipid concentrations of (12)C- and (13)C-labeled ALA, eicosapentaenoic acid (EPA; C20:5n-3), docosapentaenoic acid (DPA; C22:5n-3), and docosahexaenoic acid (DHA; C22:6n-3) were determined on days 19, 21, 23, 26, 27, and 28. To estimate hepatic conversion of n-3 fatty acids, a tracer model was developed based on the averaged (13)C data of the participants. A similar tracee model was solved using the averaged (12)C values, the kinetic parameters derived from the tracer model, and mean ALA consumption. ALA incorporation into plasma phospholipids was estimated by solving both models simultaneously. It was found that nearly 7% of dietary ALA was incorporated into plasma phospholipids. From this pool, 99.8% was converted into EPA and 1% was converted into DPA and subsequently into DHA. The limited incorporation of dietary ALA into the hepatic phospholipid pool contributes to the low hepatic conversion of ALA into EPA. A low conversion of ALA-derived EPA into DPA might be an additional obstacle for DHA synthesis.

Using a 1-D mixing model to simulate the vertical flux of heat and oxygen in a lake subject to episodic mixing

A one-dimensional, two-layer lake model is used to simulate the daily temperature and oxygen profile of an English Lake in response to changes in wind, air temperature and radiation. The thermal model component derives from the TEMIX lake model originally developed by the Institute of Limnology in St. Petersburg [Mironov, D.V., Golosov, S.D., Zilitinkevitch, S.S., Kreiman, K.D., Terzhevik, A.Y., 1991. Seasonal changes of temperature and mixing conditions in a lake. In: Zilitinkevitch, S.S. (Ed.), Modelling Air–Lake Interactions. Springer-Verlag, pp. 74–90]. This paper describes the model's adaptation and its extension to incorporate dissolved oxygen to simulate periods of anoxia of short duration during summer stratification. The new oxygen model component, which is based on mass-balance principles, divides the lake into two layers in a similar way to the thermal model. Its primary purpose is to model periods of anoxia for use in studies of fish survival. The model has been tested over a 10-year period from 1991 to 1999 using daily weather data and fortnightly observations of chlorophyll a and secchi depth. Ten years of fortnightly oxygen measurements, together with 2 years of more detailed (hourly) oxygen data, indicate that simulated and observed oxygen levels are in reasonable agreement considering the sparseness of the chlorophyll observations. The balance between the relative effects of temperature and BOD on oxygen depletion is of particular importance to model accuracy.

ABUSING THE FICK PRINCIPLE

Dear Editor-in-Chief: We wish to take umbrage with the data, analysis, and conclusions regarding the interrelationships among cardiac output 𝑄̇, V̇O2max, and O2 extraction presented in the recent paper by LePretre and colleagues (7). The authors utilized the eponymous Fick principle, which is based on simple mass balance considerations and states that can be calculated from simultaneous measurement of V̇O2, and the arterial (CaO2) and mixed venous (CV̇vO2) blood O2 contents (i.e., O2 extraction): Following the landmark publication in 1870, Adolf Fick’s principle has formed a fundamental cornerstone of cardiovascular physiology and medicine (2). For example, in the late 1800s it was used to measure 𝑄̇ in dogs (4) and horses (13), and following the first successful heart catheterization by Werner Forssman in 1929, in man (3,6). Today, with multiple invasive and noninvasive techniques to measure 𝑄̇, the Fick principle is often used to determine O2 extraction: and it is using this form that LePretre et al. supposedly derived their O2 extraction data depicted in Figure 5 and Table 3 of their publication. As evident from equations 1 and 2 above, it is impossible for O2 extraction (CaO2 − CV̄O2) to be changing while both 𝑄̇ and V̇O2 are constant. However, their Figure 5 demonstrates an approximately 30% decrease in CaO2 − CV̄2 at constant rates of 𝑄̇ and V̄O2 (see their Fig. 4) during heavy/severe exercise. Moreover, the mean values for O2max and 𝑄̇max presented in their Table 3 are not consistent with the maximal O2 extraction data in that table. Specifically, the values presented are 13.2, 13.1, and 13.3 mL O2·100 mL−1 blood, whereas those calculated from their data are 20–40% higher (i.e., 15.7, 17.9, and 16.9 mL O2·100 mL−1 blood, respectively). In conclusion, the data presented by LePretre et al. (7) appear to be inconsistent with basic principles of mass balance as delineated by the Fick principle. Moreover, investigations that have measured O2 extraction directly either across the body or exercising limbs at heavy/severe exercise intensities (1,5,9–11) do not demonstrate either a temporal or intensity-related reduction in O2 extraction as depicted by LePretre et al. Indeed, from the relationship established between 𝑄̇ and O2 for dynamic exercise, O2 extraction must increase as a hyperbolic function of muscle(s) and pulmonary O2 (8,12). Thus, it may be appropriate to hold in question the fidelity of the data presented by LePretre et al. and their conclusions based upon that data. Danielle J. Padilla Timothy I. Musch David C. Poole Departments of Anatomy and Physiology and Kinesiology, Kansas State University, Manhattan, KS

GIS를 이용한 토사이송 및 퇴적분포 예측기법 개발

본 연구에서는 분포형 모형과 셀의 유입, 유출 및 저류량에 대한 질량보존의 법칙을 이용하여 토사의 이송 및 퇴적분포예측기법을 개발하였다. 모형은 (a) 토사침식 예측 (b) 흐름방향 및 유출량 산정 그리고 (c) 토사에 대한 질량보존의 법칙에 따른 셀별 토사이동량 산정의 세 단계로 구성되었다. 토양침식은 범용토양손실공식(USLE)을 활용하였으며 분포형 모형에서의 경사장(L) 산정은 일방향(SF)과 다방향 흐름 알고리즘(MF)을 사용하였다. 경사(S) 산정을 위해서는 Maximum Downhill Slope Method (MDS) and the Neighborhood Method (NBH) 기법을 활용하였고 셀별 토양의 이동은 Ferro등(1998)과 Swift (2000)의 토사전달률(DR)개념을 적용하였다. 개발된 모형은 시험유역의 실측 토사량과의 비교검토를 통하여 검증하였다. 3개의 농업용 저수지 유역에 적용한 결과, Ferro의 토사전달률 산정공식과 MDS, MF 기법을 이용한 해석이 저수지의 운영기록과 가장 유사한 결과를 제시한다는 사실을 확인할 수 있었다. In this study, a two-dimensional model for identifying areas of erosion and deposition over a basin was developed based on the mass balance principle in a distributed model. The program consists of three steps: (a) estimation of soil erosion; (b) determination of flow amount and direction; and (c) estimation of mass balance. Soil erosion was estimated with USLE. A single-direction (SF) and a multi-direction flow algorithm (MF) were applied to estimate slope length (L). The Maximum Downhill Slope Method (MDS) and the Neighborhood Method (NBH) were used to estimate the slope degree (S). Sediment transport resulting from eroded soil was estimated using Ferro's (1998) and Swift's (2000) sediment delivery ratio (DR). The model was validated by comparing the predicted sediment yields for three basins with measured data. The developed algorithm showed that Ferro's DR method combined with the MDS and MF produced the best agreement with the dredging records of three agricultural reservoir basins in Korea.

Dynamic simulation and analysis of a water chiller refrigeration system

In this paper, a lumped-parameter dynamic model of a water chiller refrigeration system based on mass and energy balance principles is developed. First the component models for an evaporator, compressor, condenser and a thermostatic expansion valve (TEV) were derived. These models were integrated to develop an overall model of a water chiller system. A control-oriented approach to model development was taken and the effect of control inputs such as compressor operational frequency and TEV opening fraction on the output performance of the system was investigated. The transient response characteristics show that the thermal system responses are much slower than pressure and mass flow rate responses revealing a two time-scale property of the system. Steady state performance of the system is also analyzed and graphical relationships between refrigerant mass flow rate, suction vapor superheat temperature, operation frequency and thermostatic expansion valve opening fraction are presented.

Dosimetric Adjustments for Interspecies Extrapolation of Inhaled Poorly Soluble Particles (PSP)

Direct calculation of delivered dose in the species of interest potentially affects the magnitude of an uncertainty factor needed to address extrapolation of laboratory animal data to equivalent human exposure scenarios, thereby improving the accuracy of human health risk estimates. Development of an inhalation reference concentration (RfC) typically involves extrapolation of an effect level observed in a laboratory animal exposure study to a level of exposure in humans that is not expected to result in an appreciable health risk. The default dose metric used for respiratory effects is the average deposited dose normalized by regional surface area. However, the most relevant dose metric is generally one that is most closely associated with the mode of action leading to the response. Critical factors in determining the best dose metric to characterize the dose-response relationship include the following: the nature of the biological response being examined; the magnitude, duration, and frequency of the intended exposure scenario; and the mechanisms by which the toxicants exert their effects.Dosimetry models provide mechanistic descriptions of these critical factors and can compute species-specific dose metrics. In this article, various dose metrics are postulated based on potential modes of action for poorly soluble particles (PSP). Dosimetry models are used to extrapolate the internal dose metric across species and to estimate the human equivalent concentration (HEC). Dosimetry models for the lower respiratory tract (LRT) of humans and rats are used to calculate deposition and retention using the principle of particle mass balance in the lower respiratory tract. Realistic asymmetric lung geometries using detailed morphometric measurements of the tracheobronchial (TB) airways in rats and humans are employed in model calculations. Various dose metrics are considered for the TB and pulmonary (P) regions. Because time is an explicit parameter incorporated in species-specific constants such as mucociliary clearance rates used in the models, the impact of the application of optimal model structures to refine adjustments and assumptions used in default risk assessment approaches to address exposure duration are discussed.HEC estimates were found for particles ranging in sizes that corresponded to existing toxicity studies of PSP (0.3 to 5μm). A dose metric expressed as number of particles per biologically motivated normalization factors (e.g., number of ventilatory units, number of alveoli, and number of macrophages) was lower than the current default of mass normalized to regional surface area for either deposited or retained dose estimates. Retained dose estimates were lower than deposited dose estimates across all particle sizes evaluated. Dose metrics based on the deposited mass per unit area in small and large airways of the TB region indicate HECs of 1 to 5 times those of rats: that is, an equivalent exposure to humans which would achieve the same internal dose as in the rat would be 1 to 5 times greater. HEC estimates in the TB region increase with an increase in particle size for particles from 0.3 to ≤ 2μm, then decrease with an increase in particle size for particles >2 μm in the small airways and >3 μm in the large airways. The HEC decreases with increase in particle size in the P region across all particle sizes studied, and the decrease has a more significant slope for those particles >2 μm due to the limited inhalability of particles this size in rats relative to humans.Our modeling results elucidate a number of important issues to be considered in assessing current default approaches to dosimetry adjustment for inhaled PSP. Simulation of realistic, polydisperse particle distributions for the human exposure scenario results in reduced HEC estimates compared to estimates derived with the experimental particle distribution used in the laboratory animal study. Consideration should be given also to replacing the default dose metric of normalized deposited dose in the P region with normalized retained dose. Chronic effects are more likely due to retained dose and estimates calculated using retained versus deposited mass are shown to be lower across all particle sizes. Because dose metrics based on normalized particle number rather than normalized mass result in lower HEC estimates, use of inhaled mass as the default should also be revisited, if the pathogenesis suggests particle number determines the mode of action. Based on demonstrated age differences, future work should pursue the construction of “lifetime” estimates calculated by sequentially appending simulations for each specific age span.

Kinetic modelling of continuous submerged fermentation of cheese whey for single cell protein production

A mathematical model describing the kinetics of continuous production of single cell protein from cheese whey using Kluyveromyces fragilis was developed from the basic principles of mass balance. The model takes into account the substrate utilization for growth and maintenance and the effect of substrate concentration and cell death rate on the net cell growth and substrate utilization during the fermentation process. A lactose concentration below 1.91 g/L limited growth of yeast cells whereas a lactose concentration above 75 g/L inhibited the growth of the yeast. The model was tested using experimental data obtained from a continuous system operated at various retention times (12, 18 and 24 h), mixing speeds (200, 400 and 600 rpm) and air flow rates (1 and 3 vvm). The model was capable of predicting the effluent cell and substrate concentrations with R 2 ranging from 0.95 to 0.99. The viable cell mass and lactose consumption ranged from 1.3 to 34.3 g/L and from 74.31% to 99.02%, respectively. A cell yield of 0.74 g cell/g lactose (close to the stoichiometric value of 0.79 g cell/g lactose) was achieved at the 12 h retention time—3 vvm air flow rate—600 rpm mixing speed combination. The total biomass output (viable and dead cells) at this combination was 37 g/L.

Modeling Flow and Pollutant Removal of Wet Detention Pond Treating Stormwater Runoff

A mathematical model of pollutant removal by wet ponds was developed based on the mass balance principle and the release–storage equation. The release–storage equation can be linear or nonlinear depending on the wet pond shape and the spillway crest features. If the exponent index of the storage relationship (d) is equal to the index of the outflow equation (b), the wet pond hydrological routing model is linear. Otherwise, the model is nonlinear. Substituting the release–storage equation into the continuity equation produces a nonlinear ordinary differential equation (ODE). A Runge–Kutta method was used to solve the resulting nonlinear ODE. When the ratio of indexes d/b=2/3, the hydrologic wet pond model reduces to a special case that leads to an implicit analytical solution. The pollutant removal and flow routing models were tested with data obtained from an actual wet pond for treating highway runoff. The predicted flow discharges and pollutant concentrations compared well with the observed data.

Asymptotic stability of a nonisothermal plug flow reactor infinite-dimensional model

The asymptotic stability property is studied for a nonisothermal plug flow tubular reactor model, which is described by semi-linear partial differential equations (PDE's) derived from mass and energy balance principles. It is reported that, under some condition on the model parameters, any constant temperature equilibrium profile is an asymptotically stable equilibrium of such model. The analysis is based on an asymptotic stability criterion for a class of infinitedimensional (distributed parameter) semi-linear Banach state space systems and the concept of strictly m-dissipative operator.

A new interpretation of the Keller-Segel model based on multiphase modelling

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.

Residence time, groundwater age, and solute output in steady-state groundwater systems

The total travel distance and the hydraulic conductivity in steady-state groundwater flow systems are modeled with asymmetric gamma distribution functions. The ratio of the total travel distance over the hydraulic conductivity, scaled by a factor involving the hydraulic gradient and the aquifer porosity, equals the residence time of groundwater. The residence time measures the period elapsed between recharge and discharge of groundwater from an aquifer flow system. The residence time is a random variable whose probability density function (p.d.f.) is determined by those of the total travel distance and the hydraulic conductivity. The p.d.f. of the residence time was derived and from that, applying basic mass-balance considerations, followed that of the groundwater age. The age is the time elapsed since the recharge of groundwater in transit through an aquifer flow system. It is shown that the p.d.f.s of the residence time and the groundwater age are related by a first-order, linear, differential equation. The cumulative distribution functions of the residence time and the groundwater age and their first and second moments are also derived, and so is the output concentration of a solute that enters a steady-state groundwater flow system dissolved in recharge. A computational example illustrates the advantage of treating the residence time and the groundwater age statistically and constraining them with Darcy's law and mass-balance principles. Solute output shows a complex structure with stable and radioactive solutes in deceptively simple steady-state groundwater flow regimes.

CARBON SEQUESTRATION IN ECOSYSTEMS: THE ROLE OF STOICHIOMETRY

The fate of carbon (C) in organisms, food webs, and ecosystems is to a major extent regulated by mass-balance principles and the availability of other key nutrient elements. In relative terms, nutrient limitation implies excess C, yet the fate of this C may be quite different in autotrophs and heterotrophs. For autotrophs nutrient limitation means less fixation of inorganic C or excretion of organic C, while for heterotrophs nutrient limitation means that more of ingested C will “go to waste” in the form of egestion or respiration. There is in general a mismatch between autotrophs and decomposers that have flexible but generally high C:element ratios, and consumers that have lower C:element ratios and tighter stoichiometric regulation. Thus, C-use efficiency in food webs may be governed by the element ratios in autotroph biomass and tend to increase when C:element ratios in food approach those of consumers. This tendency has a strong bearing on the sequestration of C in ecosystems, since more C will be diverted to detritus entering soils or sediments when C-use efficiency is low due to stoichiometric imbalance. There will be a strong evolutionary pressure to utilize such excess C for structural and metabolic purposes. This article explores how these basic principles may regulate C sequestration on different scales in aquatic and terrestrial ecosystems.

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface.

Reaction Kinetics of Ozone in Variably Saturated Porous Media

A kinetic model based on the mass balance principle with equilibrium partitioning of gaseous ozone into pore water was developed to delineate the reactions of ozone in variably saturated porous media contaminated with phenanthrene. Dimensionless fraction factors were used in the kinetic model to account for the reactions of ozone with soil organic matter ~SOM!, metal oxide ~MO!, and phenanthrene as a function of water saturation. The enhanced removal of phenanthrene resulting from heterogeneous catalytic reactions between ozone and soil organic matter and metal oxide was incorporated as lumped parameters in the reaction rate coefficients of gaseous and dissolved ozone with phenanthrene. Laboratory experiments employing 5 cm long mini column reactor systems were conducted to estimate the reaction constants for three porous medium types ~glass beads, baked field soil, and field soil ! at various water-saturation levels. Water saturation and SOM were found to significantly affect the decomposition of gaseous ozone in both uncontaminated and contaminated porous media. It was found that water saturation over 75% completely eliminates gas-to-solid interfacial ozone reactions with SOM and MO. The kinetic model, with the reaction parameters estimated in this study, predicted reasonably well the experimental data obtained from both the mini column reactor and 20 cm long columns packed with field soil, suggesting that the kinetic model would be suitable for describing the fate and reactions of ozone in variably saturated porous media for soil types and experimental conditions similar to those tested in this study.

An Algorithm for Pseudocompound Delumping and Lumping into Homologous Groups

An algorithm for pseudocompound delumping and lumping into homologous groups is developed. This algorithm is useful for modeling refineries when using commercial simulators and detailed reactor models. Generally, commercial simulators represent petroleum fractions using pseudocompounds; however, reactor models and their kinetics are based on known compounds. This algorithm delumps the pseudocompounds into homologous groups that are represented by model compounds, which are then used by a detailed reactor model. After the reaction, the outlet stream is lumped again to pseudocompounds that are used in the remaining operations of the commercial simulator. The lumping operations are based on mass balance principles and fundamental properties of the hydrocarbon mixture. This algorithm is applied to the modeling of a hydrotreatment unit that belongs to the Mexican System of Refineries which uses a detailed three phase trickle bed reactor. The problem is to delump and lump the pseudocompounds, which represent light gas oil, into paraffins, naphthenes, and mono and polyaromatics. Results show a good agreement with industrial data.

A systems analysis tool for construction and demolition wastes management

Managing construction and demolition (C&D) wastes has challenged many municipalities with diminishing waste disposal capacity. Facing such challenges, the Massachusetts Department of Environmental Protection proposed a policy restricting the landfill disposal of certain C&D waste materials, if unprocessed. This research is to study the potential economic impact of such restriction on construction contractors and C&D waste processors. A spreadsheet-based systems analysis model has been developed to assist the cost-benefit evaluation for various C&D waste management scenarios. The model, developed based on the mass balance principle, is designed to track a C&D waste stream through the various stages of a waste management system, i.e. generation, source separation, processing, recycling, and final disposal. This model, by incorporating the material flow data with the cost/revenue data associated with each management activity, can then provide an economic analysis for a proposed C&D waste management scenario. A case study illustrating the application of this model for Massachusetts is also presented.

Geoid determination using adapted reference field, seismic Moho depths and variable density contrast

The traditional remove-restore technique for geoid computation suffers from two main drawbacks. The first is the assumption of an isostatic hypothesis to compute the compensation masses. The second is the double consideration of the effect of the topographic–isostatic masses within the data window through removing the reference field and the terrain reduction process. To overcome the first disadvantage, the seismic Moho depths, representing, more or less, the actual compensating masses, have been used with variable density anomalies computed by employing the topographic–isostatic mass balance principle. In order to avoid the double consideration of the effect of the topographic–isostatic masses within the data window, the effect of these masses for the used fixed data window, in terms of potential coefficients, has been subtracted from the reference field, yielding an adapted reference field. This adapted reference field has been used for the remove–restore technique. The necessary harmonic analysis of the topographic–isostatic potential using seismic Moho depths with variable density anomalies is given. A wide comparison among geoids computed by the adapted reference field with both the Airy–Heiskanen isostatic model and seismic Moho depths with variable density anomaly and a geoid computed by the traditional remove–restore technique is made. The results show that using seismic Moho depths with variable density anomaly along with the adapted reference field gives the best relative geoid accuracy compared to the GPS/levelling geoid.

Mathematical Modeling and Applications for Concrete Carbonation

A new concept, carbon dioxide (CO2) transport in concrete, is proposed in this paper to describe solute-transport processes. Using this concept, a new one-dimensional mathematical model was developed to describe the transport phenomena of carbon dioxide in concrete structures. By treating transport phenomena as a concrete carbonation process, a one-dimensional linear partial differential equation was derived based on the principle of mass balance and convective-dispersive equation and was found the analytical solution by the separation of variables and the Laplace transform methods combined with some substitution approaches. The concrete carbonation numerical results were determined using parameters, such as the diffusion coefficient, CO2 concentration, carbonation depth and time, occurring in concrete structures. The numerical results are presented to illustrate the practical applications of this model. These results are shown clearly that the proposed model may actually describe the concrete carbonation process chemically and physically. It is suggested that experiment should be performed to select suitable parameters for numerical simulations.

Concentration of solutes in the renal inner medulla: interstitial hyaluronan as a mechano-osmotic transducer

Although the concentrating process in the renal outer medulla is well understood, the concentrating mechanism in the renal inner medulla remains an enigma. The purposes of this review are fourfold. 1) We summarize a theoretical basis for classifying all possible steady-state inner medullary countercurrent concentrating mechanisms based on mass balance principles. 2) We review the major hypotheses that have been proposed to explain the axial osmolality gradient in the interstitium of the renal inner medulla. 3) We summarize and expand on the Schmidt-Nielsen hypothesis that the contractions of the renal pelvocalyceal wall may provide an important energy source for concentration in the inner medulla. 4) We discuss the special properties of hyaluronan, a glycosaminoglycan that is the chief component of a gel-like renal inner medullary interstitial matrix, which may allow it to function as a mechano-osmotic transducer, converting energy from the contractions of the pelvic wall to an axial osmolality gradient in the medulla. These considerations set the stage for renewed experimental investigation of the urinary concentrating process and a new generation of mathematical models of the renal concentrating mechanism, which treat the inner medullary interstitium as a viscoelastic system rather than a purely hydraulic system.