A Numerical Model for Studying the Effect of Plasma Layer on the Process of Blood Oxygenation in the Pulmonary Capillaries

1990 ◽  
Vol 112 (4) ◽  
pp. 457-463 ◽  
Author(s):  
Maithili Sharan ◽  
M. P. Singh ◽  
A. Aminataei
Keyword(s):  
Molecular Diffusion ◽  
Plasma Layer ◽  
Nonlinear Partial Differential Equations ◽  
Homogeneous Model ◽  
Blood Oxygenation ◽  
Facilitated Diffusion ◽  
Heterogeneous Model ◽  
The Core ◽  
Pulmonary Capillaries ◽  
Diffusion Convection

A two layer model for the blood oxygenation in pulmonary capillaries is proposed. The model consists of a core of erythrocytes surrounded by a symmetrically placed plasma layer. The governing equations in the core describe the free molecular diffusion, convection, and facilitated diffusion due to the presence of haemoglobin. The corresponding equations in the plasma layer are based on the free molecular diffusion and the convective effect of the blood. According to the axial train model for the blood flow proposed by Whitmore (1967), the core will move with a uniform velocity whereas flow in the plasma layer will be fully developed. The resulting system of nonlinear partial differential equations is solved numerically. A fixed point iterative technique is used to deal with the nonlinearities. The distance traversed by the blood before getting fully oxygenated is computed. It is shown that the concentration of O2 increases continuously along the length of the capillary for a given ratio of core radius to capillary radius. It is found that the rate of oxygenation increases as the core to capillary ratio decreases. The equilibration length increases with a heterogeneous model in comparison to that in a homogeneous model. The effect of capillary diameters and core radii on the rate of oxygenation has also been examined.

Capillary network structure does not affect theoretical analysis of glomerular size selectivity

1995 ◽  
Vol 268 (5) ◽  
pp. F972-F979
Author(s):  
A. Remuzzi ◽  
B. Ene-Iordache
Keyword(s):  
Pressure Drop ◽  
Homogeneous Model ◽  
Wistar Rat ◽  
Size Selectivity ◽  
Membrane Pore ◽  
Heterogeneous Model ◽  
Glomerular Size ◽  
The Difference ◽  
Membrane Pore Size ◽  
Log Normal

Anatomical studies have demonstrated that the glomerular capillaries are complex and heterogeneous networks. Conventional models of glomerular size selectivity, however, are based on the assumption of simplified geometries. We developed a theoretical model of glomerular size-selective function based on the geometric data obtained in a previous reconstruction of a glomerular network from a normal Munich-Wistar rat. This heterogeneous model was compared with the homogeneous model conventionally used to calculate membrane selective parameters from the fractional clearance of two test solutes, neutral dextran and Ficoll. For both models we assumed a hypothetical log-normal distribution of pore sizes and calculated optimal membrane pore-size parameters using previously published values of fractional clearances. The difference between the sieving coefficients calculated with the two models was negligible, never exceeding 5.5%. Since the homogeneous model does not consider the pressure drop along the glomerular capillary, we also computed fractional clearances with the homogeneous model, assuming the same pressure drop as in the heterogeneous one. The differences in computed fractional clearances using the homogeneous model with and without a pressure drop were less than 1.2%. We concluded that models based on identical capillary networks can therefore be used for interpreting sieving coefficients for macromolecules.

Heat Transfer in Fixed Bed Elliptic Cylindrical Reactor via Two-Phase Model

2020 ◽  
Vol 400 ◽  
pp. 45-50
Author(s):  
Antonildo Santos Pereira ◽  
Rodrigo Moura da Silva ◽  
Maria Conceição Nóbrega Machado ◽  
Luan Pedro Melo Azerêdo ◽  
Anderson Ferreira Vilela ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Solid Phase ◽  
Homogeneous Model ◽  
Fixed Bed ◽  
Fluid Phase ◽  
Packed Bed ◽  
Two Phase ◽  
Heterogeneous Model ◽  
Fully Implicit ◽  
Cylindrical Reactor

The study of heat transfer in fixed bed tubular reactors of heated or cooled walls has presented great interest by the academy and industry. The adequate and safe design of such equipment requires the use of reliable and realistic mathematical. Unfortunately several studies are restrict to homogeneous model applied to circular and elliptic cylindrical reactors. Then, the objective of this work was to predict heat transfer in packed-bed elliptic cylindrical reactor, by using a proposed heterogeneous model. The mathematical model is composed for one solid phase and another fluid phase, in which the balance equation for each constituent is applied separately. The finite volume method was utilized to solve the partial differential equations using the WUDS scheme for interpolation of the convective and diffusive terms, and the fully implicit formulation. Results of the temperature distribution of the fluid and solid phases along the reactor are presented and analyzed. It was verified that the highest temperature gradients of the phases are located close to the wall and inlet of the reactor.

scholarly journals Study on Pulse Characteristic of Produced Crude Composition in CO2 Flooding Pilot Test

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Pengxiang Diwu ◽  
Tongjing Liu ◽  
Zhenjiang You ◽  
Ganggang Hou ◽  
Runwei Qiao ◽  
...  
Keyword(s):  
Carbon Number ◽  
Pilot Test ◽  
Co2 Flooding ◽  
Pulse Characteristic ◽  
Heterogeneous Model ◽  
Injection Volume ◽  
The Core ◽  
Reservoir Models ◽  
Nonmonotonic Function ◽  
Nonmonotonic Variation

It has been observed in many laboratory tests that the carbon number of the maximum concentration components (CNMCC) of produced oil varies monotonically with CO2 injection volume at the core scale. However, in CO2 flooding pilot test at the field scale, we find that the CNMCC is usually nonmonotonic function of CO2 injection volume, which is called “pulse characteristic” of CNMCC. To investigate the mechanism of this phenomenon, we analyze the physical process of CO2 flooding in heterogeneous reservoir and explain the reason of the pulse characteristic of CNMCC. Moreover, two 3D reservoir models with 35 nonaqueous components are proposed for numerical simulation to validate the conjecture. The simulation results show that pulse characteristic of CNMCC only occurs in the heterogeneous model, confirming that the pulse characteristic results from the channeling path between wells, which yields nonmonotonic variation of oil-CO2 mixing degree. Based on it, a new method can be developed to identify and quantify the reservoir heterogeneity.

Analysis of Equilibrium Shifting by Inter-Stage Reactant Feeding in a Series of Isothermal Reactors

2014 ◽  
Vol 12 (1) ◽  
pp. 163-179
Author(s):  
Florent Allain ◽  
Jean-François Portha ◽  
Laurent Falk
Keyword(s):  
Flow Reactor ◽  
Homogeneous Model ◽  
Plug Flow ◽  
Volumetric Flow Rate ◽  
Continuous Reactor ◽  
Two Stage ◽  
Heterogeneous Model ◽  
Number Systems ◽  
Reversible Reactions ◽  
The Impact

Abstract This paper focuses on the impact of reactant staging on conversion for one single reversible reaction in a two-stage, isothermal, continuous reactor. The analytical expression of global conversion has been derived for a series of two continuously stirred-tank reactors. Improvements in the overall conversion and yield by staging can be obtained for low Damköhler number systems leading to low conversions, when the volumetric flow rate of the staged reactant has a higher value than that of the other one. The example of triolein transesterification involving three reversible reactions in a two-stage plug flow reactor is also studied as a concrete example of a consecutive/parallel reversible reactions system. Results are obtained by using a pseudo-homogeneous model and are compared with those obtained with a heterogeneous model from a previous study.

scholarly journals Stress and damage in concrete induced by pipe cooling at mesoscopic scale

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769050 ◽  
Author(s):  
Yongrong Qiu ◽  
Guoxin Zhang
Keyword(s):  
Temperature Difference ◽  
Homogeneous Model ◽  
Cooling Water ◽  
Second Phase ◽  
Mass Concrete ◽  
Cooling Mode ◽  
Heterogeneous Model ◽  
Research Results ◽  
Advantages And Disadvantages ◽  
Induced Stress

Pipe cooling is one of the most important measures of mass concrete temperature control, but pipe cooling has its advantages and disadvantages. Inappropriate pipe-cooling water temperature may result in excessive stress and crack. Considering the fact that concrete is a type of three-phase composite material and the sizes of cooling pipe and aggregate are basically on the same scale, the mesoscopic heterogeneity of concrete may have a great effect on the stress field surrounding the pipe. This article computes the pipe cooling–induced stress and damage and analyzes the differences between the homogeneous model and heterogeneous model based on mesoscopic mechanics. In this study, both linear elastic analysis and nonlinear damage analysis are performed; elastic modulus and creep are used as a function of concrete age; and several factors such as temperature difference, multistep cooling mode, and earlier cooling are also studied. The research results show that due to the mesoscopic heterogeneity characteristics of concrete, there is a great deal of difference between homogeneous model and heterogeneous model; pipe cooling can lead to large residual stress around the aggregate and produce a large range of damage, and previous homogeneous model indeed underestimates the effect of cooling-induced stress; using multistep cooling and early cooling mode can reduce this damage; the cooling-induced damage has significant influence on the anti-crack performance of concrete. In the final, based on the research results, the temperature difference between the concrete and pipe water of the second-phase cooling was recommended to be controlled at approximately 5°C.

scholarly journals Tracer test modeling for local scale residence time distribution characterization in an artificial recharge site

2016 ◽  
Author(s):  
Cristina Valhondo ◽  
Lurdes Martínez-Landa ◽  
Jesús Carrera ◽  
Juan J. Hidalgo ◽  
Isabel Tubau ◽  
...  
Keyword(s):  
Water Quality ◽  
Artificial Recharge ◽  
Groundwater Resources ◽  
Homogeneous Model ◽  
Tracer Test ◽  
Flow Conditions ◽  
Transport Parameters ◽  
Complex Flow ◽  
Concentration Data ◽  
Heterogeneous Model

Abstract. Artificial recharge of aquifers is a technique for improving water quality and increasing groundwater resources. Understanding the fate of a potential contaminant requires knowledge of the residence times distribution (RTD) of the water beneath the artificial recharge infrastructure. A simple way to obtain the RTDs is to perform a tracer test. We performed a pulse injection tracer test in an artificial recharge system through an infiltration basin to obtain the breakthrough curves, which yield directly the RTDs. These were very broad and we used a numerical model to interpret them, and to extend the characterization to other flow conditions. The model comprised nine layers at the site scaled to emulate the layering of aquifer deposits. Two types of hypotheses were considered: homogeneous (all flow and transport parameters identical for every layer) and heterogeneous (diverse parameters for each layer). The parameters were calibrated against the head and concentration data in both model types, which were validated quite satisfactory against 1,1,2-Trichloroethane and electrical conductivity data collected over a long period of time with highly varying flow conditions. We found that the broad RTDs were caused by both the complex flow structure generated under the basin (the homogeneous model produced broad RTDs) and the heterogeneity of the media (the heterogeneous model yielded much better fits). We conclude that acknowledging heterogeneity is required to properly assess mixing and broad RTDs, which are required to explain the water quality improvement of artificial recharge basins.

scholarly journals Effects of Collagen Heterogeneity on Myocardial Infarct Mechanics in a Multiscale Fiber Network Model

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Christopher E. Korenczuk ◽  
Victor H. Barocas ◽  
William J. Richardson
Keyword(s):  
Myocardial Infarction ◽  
Finite Element ◽  
Homogeneous Model ◽  
Mechanical Anisotropy ◽  
Local Alignment ◽  
Fiber Density ◽  
Heterogeneous Model ◽  
Fiber Alignment ◽  
Sample Shape ◽  
Homogeneous Models

The scar that forms after a myocardial infarction is often characterized by a highly disordered architecture but generally exhibits some degree of collagen fiber orientation, with a resulting mechanical anisotropy. When viewed in finer detail, however, the heterogeneity of the sample is clear, with different subregions exhibiting different fiber orientations. In this work, we used a multiscale finite element model to explore the consequences of the heterogeneity in terms of mechanical behavior. To do so, we used previously obtained fiber alignment maps of rat myocardial scar slices (n = 15) to generate scar-specific finite element meshes that were populated with fiber models based on the local alignment state. These models were then compared to isotropic models with the same sample shape and fiber density, and to homogeneous models with the same sample shape, fiber density, and average fiber alignment as the scar-specific models. All simulations involved equibiaxial extension of the sample with free motion in the third dimension. We found that heterogeneity led to a lower degree of mechanical anisotropy and a higher level of local stress concentration than the corresponding homogeneous model, and also that fibers failed in the heterogeneous model at much lower macroscopic strains than in the isotropic and homogeneous models. Taken together, these results suggest that scar heterogeneity may impair myocardial mechanical function both in terms of anisotropy and strength, and that individual variations in scar heterogeneity could be an important consideration for understanding scar remodeling and designing therapeutic interventions for patients after myocardial infarction.

scholarly journals Impact of Host Heterogeneity on the Efficacy of Interventions to ReduceStaphylococcus aureusCarriage

2015 ◽  
Vol 37 (2) ◽  
pp. 197-204 ◽  
Author(s):  
Qiuzhi Chang ◽  
Marc Lipsitch ◽  
William P. Hanage
Keyword(s):  
Bacterial Infections ◽  
Homogeneous Model ◽  
Healthcare Setting ◽  
Host Population ◽  
Intervention Strategies ◽  
Control Measures ◽  
Heterogeneous Model ◽  
The Impact ◽  
Carriage Prevalence ◽  
Host Heterogeneity

BACKGROUNDStaphylococcus aureusis a common cause of bacterial infections worldwide. It is most commonly carried in and transmitted from the anterior nares. Hosts are known to vary in their proclivity forS. aureusnasal carriage and may be divided into persistent carriers, intermittent carriers, and noncarriers, depending on duration of carriage. Mathematical models ofS. aureusto predict outcomes of interventions have, however, typically assumed that all individuals are equally susceptible to colonization.OBJECTIVETo characterize biases created by assuming a homogeneous host population in estimating efficacy of control interventions.DESIGNMathematical model.METHODSWe developed a model ofS. aureuscarriage in the healthcare setting under the homogeneous assumption as well as a heterogeneous model to account for the 3 types ofS. aureuscarriers. In both models, we calculated the equilibrium carriage prevalence to predict the impact of control measures (reducing contact and decolonization).RESULTSThe homogeneous model almost always underestimatesS. aureustransmissibility and overestimates the impact of intervention strategies in lowering carriage prevalence compared to the heterogeneous model. This finding is generally consistent regardless of changes in model setting that vary the proportions of various carriers in the population and the duration of carriage for these carrier types.CONCLUSIONSNot accounting for host heterogeneity leads to systematic and substantial biases in predictions of the effects of intervention strategies. Further understanding of the clinical impacts of heterogeneity through modeling can help to target control measures and allocate resources more efficiently.Infect. Control Hosp. Epidemiol.2016;37(2):197–204

The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow

1979 ◽  
Vol 91 (2) ◽  
pp. 337-355 ◽  
Author(s):  
P. C. Chatwin ◽  
Paul J. Sullivan
Keyword(s):  
Molecular Diffusion ◽  
Practical Interest ◽  
Core Region ◽  
Real Case ◽  
Centre Of Mass ◽  
The Real ◽  
The Core ◽  
Relative Diffusion ◽  
Molecular Diffusivity ◽  
The Way

A problem of major practical interest is the variation with x and t of the statistical properties of Γ(x, t), the distribution of concentration of a contaminant in a cloud containing a finite quantity Q of contaminant, released in a specified way at t = 0 over a volume of order L30. Of particular relevance is the case of relative diffusion (when x is measured throughout each realization relative to the centre of mass of the cloud), when important properties are L(t), the linear dimension of the cloud, C(x, t), the ensemble mean concentration, $\overline{c^2}({\bf x}, t)$, the variance of the concentration, and p(y, t), the distance-neighbour function. Much fundamental work has led to a knowledge of the way L varies with t, but not of the way the other properties vary. Hitherto therefore, prediction of such variation has normally used unjustifiable empirical concepts such as eddy diffusivities, but this is ultimately unsatisfactory, practically as well as theoretically. Hence the exact equations have been used to obtain a quite new description of the structure of a dispersing cloud, which it is hoped will serve as a basis for future practical work.When κ = 0 (where κ is the molecular diffusivity) the magnitude of p(y, t) is of order Q/L3 for most y, but of order Q/L30 when |y| is very small. By a variety of arguments it is shown that these facts can be explained (for many, if not all, flows) only if the distributions of C and $\overline{c^2}$, as well as that of p, have a core-bulk structure. In the bulk of the cloud C and $\overline{c^2}$ have magnitudes of order Q/L3 and Q2/L30L3 respectively, but there is a core region of thickness decreasing to zero surrounding the centre of mass within which they have much greater magnitudes. In one case, examined in some detail, the magnitudes in the core are of order Q/L30 and Q2/L60.It is then shown that the core and bulk exist even in the real case when κ ≠ 0. In the real case the core thickness no longer tends to zero but to a constant of order λc, the conduction cut-off length. As a consequence almost entirely of molecular diffusion acting in the core region, the magnitudes of C and $\overline{c^2}$ in both the core and the bulk decay to zero in a way which depends on the details of the fine-scale structure of the velocity field. Several examples of the decay are discussed.

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