Transport of Neutral Solute Across Articular Cartilage: The Role of Zonal Diffusivities

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
V. Arbabi ◽  
B. Pouran ◽  
H. Weinans ◽  
A. A. Zadpoor
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Equilibrium Concentration ◽  
Cartilage Tissue ◽  
Zone Model ◽  
Superficial Zone ◽  
Time Curve ◽  
Order Of Magnitude ◽  
Multizone Model

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute (Iodixanol) into cartilage was monitored using calibrated microcomputed tomography (micro-CT) images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

The mutual diffusion coefficient of ethanol–water mixtures: determination by a rapid, new method

1974 ◽  
Vol 336 (1606) ◽  
pp. 393-406 ◽  
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Laminar Flow ◽  
Diffusion Coefficients ◽  
Entire Range ◽  
Liquid Mixtures ◽  
Mutual Diffusion ◽  
Mutual Diffusion Coefficient ◽  
Mechanical Theory ◽  
Statistical Mechanical

Mutual diffusion coefficients for liquid mixtures of ethanol and water have been measured over the entire range of composition and for temperatures from 25 to 65 °C at a pressure of 1 bar (10 5 Pa). At the lowest temperature, the results establish the validity of a new experimental method based upon Taylor’s analysis of solute dispersion in laminar flow. The method offers advantages of simplicity and speed over other techniques, and allows direct measurement of diffusion coefficients at well-defined mixture compositions. The experimental data have an estimated uncertainty of ±2.5% . The results have been utilized to evaluate friction coefficients arising in the statistical mechanical theory of transport in liquid mixtures.

Determination of concentration-dependent diffusion coefficient of seven solvents in polystyrene systems using FTIR-ATR technique: experimental and mathematical studies

RSC Advances ◽  
2016 ◽  
Vol 6 (11) ◽  
pp. 9013-9022 ◽  
Author(s):  
Mohammad Karimi ◽  
Akbar Asadi Tashvigh ◽  
Fateme Asadi ◽  
Farzin Zokaee Ashtiani
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Solvent Concentration ◽  
Solvent Systems

In the present study a new mathematical model's outcome based on experimental data is considered to determine the diffusion coefficients in polystyrene/solvent systems as a function of solvent concentration.

Combined Edge and Anisotropy Effects on Fickian Mass Diffusion in Polymer Composites

2004 ◽  
Vol 126 (4) ◽  
pp. 427-435 ◽  
Author(s):  
Levent Aktas ◽  
Youssef K. Hamidi ◽  
M. Cengiz Altan
Keyword(s):  
Experimental Data ◽  
Diffusion Equation ◽  
Polymer Composites ◽  
Diffusion Coefficients ◽  
Anisotropic Diffusion ◽  
Rectangular Domain ◽  
Least Square ◽  
Fickian Diffusion ◽  
Finite Sample ◽  
Time Curve

The common methods used to determine the diffusion coefficients of polymer composites are based on the solution of Fickian diffusion equation in one-dimensional (1D) rectangular domain. However, these diffusivities usually involve errors primarily due to finite sample dimensions and anisotropy introduced by fiber reinforcements. In this study, the solution of transient, three-dimensional (3D) anisotropic Fickian diffusion equation is nondimensionalized using six parameters. The solution is then used to analyze the combined contribution of finite sample dimensions and anisotropy to the errors involved in diffusion constants calculated by 1D methods. The small time solution of the Fickian diffusion equation in 3D domain is used to analyze the slope used in diffusivity calculations. It is shown that the diffusion coefficient calculated by the 1D approach is exact only if the correct slope of percent mass gain versus root square time curve at t=0 is used. However, it has also been shown that depending on the part geometry and degree of anisotropy, there might be considerable differences between the measured slope from the experimental data and the actual slope at t=0. The mismatch between the slopes results in as much as 50% errors in estimates of diffusion coefficients. Using the 3D solution in nondimensional form, the magnitudes of these errors are studied. A least-square curve-fit method, which yields accurate anisotropic diffusion coefficients, is proposed. The method is demonstrated on artificially generated experimental data for a polymer composite containing 50% unidirectional reinforcement. The anisotropic diffusion coefficients used to generate the data are recovered with less than 1% error.

Diffusion of Curatives. I

1982 ◽  
Vol 55 (5) ◽  
pp. 1482-1498 ◽  
Author(s):  
D. A. Lederer ◽  
K. E. Kear ◽  
G. H. Kuhls
Keyword(s):  
Experimental Data ◽  
Molecular Weight ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Test Procedure ◽  
Mathematical Techniques ◽  
Increasing Temperature ◽  
Storage Temperatures ◽  
Rubber Article ◽  
Diffusion Profiles

Abstract Curatives will readily migrate across a rubber-to-rubber interface following the classical laws of diffusion. The rate of diffusion increases with increasing temperature. The absolute change in curative concentration diminishes with increasing distance from the interface and increases with time. A test procedure using conventional analytical methods can be used to accurately determine the diffusion coefficients of curatives at various storage temperatures in standard rubber formulations. Diffusion profiles and coefficients are dependent on the curative type. There appears to be a general correlation with molecular weight, with the rate of diffusion decreasing with increasing molecular weight. There is a small, rationalizable effect of concentration on the diffusion coefficient. The diffusion of curatives can cause a significant change in the cure system at or near the interface of a plied rubber article. Diffusion profiles for a particular rubber formulation can be predicted from experimental data using relatively simple analytical and mathematical techniques.

scholarly journals INVESTIGATION OF ELECTRONS DIFFUSION COEFFICIENT DEPENDENCE ON TEMPERATURE IN PLASMA GAS CO2, N2, HE AND MIXTURES

2020 ◽  
pp. 31-41
Author(s):  
Nisaan Saud ORAIBI
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Energy Distribution ◽  
Cross Section ◽  
Diffusion Coefficients ◽  
Equation Solution ◽  
Different Temperatures ◽  
Momentum Transfer Cross Section

The evolution of the μNth value at different temperatures was achieved through the drift velocity of electron. The results were show when the temperature was increased, the number of the electrons will be decreased because using the momentum transfer cross section for CO2 molecules through collisions. The calculation of the diffusion coefficient was used to deduce the μNth values of CO2 electrons at temperature between 288 to 573 k by utilization numerically the Boltzmann equation solution. The results were appearing the agreement with the theoretical and experimental data. Keywords: Diffusion Coefficients, Boltzmann Equation, Swarms Parameters, Energy Distribution Function.

scholarly journals The calculation of desalination of mineralized porous ice at thawing

2016 ◽  
Vol 56 (4) ◽  
pp. 545-554
Author(s):  
A. V. Sosnovsky ◽  
I. I. Kontorovich
Keyword(s):  
Diffusion Coefficient ◽  
Chemical Composition ◽  
Diffusion Coefficients ◽  
Drainage Water ◽  
Model Calculations ◽  
Ion Concentrations ◽  
Salt Ions ◽  
Mineralized Water ◽  
Mobility Of Ions ◽  
Order Of Magnitude

The results obtained in this work demonstrate that dynamics of desalination of porous ice depends on a mobility of ions of salts, and the mobility is determined by the diffusion coefficient. The ice was made by freezing of mineralized water of different chemical composition. Model calculations of average mineralization of the porous ice at its thawing were made, and the ion concentrations of different salts were defined. Values of the diffusion coefficients of the salt ions in the film of brine ice pellets were obtained by means of comparison of results of measurements and calculations of dynamics of content of the salt ions in a porous ice at its thawing. The diffusion coefficient of ions Na+, Cl−, SO4 2− is by order of magnitude larger than that of Ca2+ and by two orders of magnitudethan HCO3 −. This results in that the content of ions Na+, Cl−, SO42− decreases in porous ice at its thawing 3 times faster than the content of the ions Ca2+. Basing on analysis of chemical composition of drainage water in some regions in Russia a possibility to desalinate the porous ice formed during the winter sprinkling is demonstrated.

An Investigation of Concentration Dependency of Mass Diffusion Coefficients in Multi-Component Diffusion

2010 ◽  
Author(s):  
Atsuki Komiya ◽  
Juan F. Torres ◽  
Junnosuke Okajima ◽  
Shuichi Moriya ◽  
Shigenao Maruyama ◽  
...  
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Superposition Principle ◽  
Mass Diffusion ◽  
Diffusion Field ◽  
Transient Diffusion ◽  
Concentration Dependency ◽  
The Difference

In this paper the concentration dependency of mass diffusion coefficients in binary system was investigated. We have developed a novel and accurate visualization system using a small area of transient diffusion fields by adopting a phase shifting technique. Through accurate visualization of the transient diffusion field, it is possible to determine the mass diffusion coefficient. Unlike a conventional interferometer, the proposed system provides high spatial resolution profiles of concentration even though the target area is less than 1.0 mm. This allows the measurement of local transient diffusion field with a high accuracy. The determination of mass diffusion coefficient of each component in multi-component system was also conducted. For the accurate and reliable measurement of mass diffusion coefficient, the experimental error should be taken into account. The experimental data usually contains unexpected accidental error and inherent errors of the measurement system. In this study, an optimization technique using conjugate gradient method is developed for the precise determination of the mass diffusion coefficients. The difference between the experimental and numerical concentration distribution is set as the objective function for the optimization method. The conjugate gradient method searches the optimal value by minimizing the objective function. For the concentration dependency evaluation, sodium chloride (NaCl) in pure water was selected as solute. For determination of each mass diffusion coefficient in multi-component system, NaCl and lysozyme in buffer solution was selected. The experiments were performed under isothermal conditions. The proposed measurement method was validated by comparing the measured data with those available in the literature. The results indicated that the concentration dependency was successfully investigated from the experimental data. The mass diffusion coefficient of each component also could be determined from the experimental data as evidenced by good agreement with the published data. The difference between the reference and determined value of mass diffusion coefficient was less than 10%. It can be said that the diffusion of each solute inside the cell progresses independently within the dilute concentration ranges and the superposition principle of concentration of NaCl and lysozyme was satisfied. The influence of concentration of solution on the diffusion process and allowable concentration range of the superposition principle are determined and discussed.

scholarly journals A New Method for the Measurement of the Diffusion Coefficient of Adsorbed Vapors in Thin Zeolite Films, Based on Magnetoelastic Sensors

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3251
Author(s):  
Dimitris Kouzoudis ◽  
Theodoros Baimpos ◽  
Georgios Samourgkanidis
Keyword(s):  
Diffusion Coefficient ◽  
Organic Compound ◽  
Diffusion Coefficients ◽  
Volatile Organic ◽  
Adsorption Data ◽  
Order Of Magnitude ◽  
Type Zeolite ◽  
Magnetoelastic Sensors ◽  
Zeolite Films ◽  
First Time

In the current work an experimental method is used in order to calculate the diffusivity D (diffusion coefficient) of various vapors in thin zeolite films. The method is based on adsorption data from magnetoelastic sensors on top of which a zeolite layer was synthesized, and the diffusivity is extracted by fitting the data to Fick’s laws of diffusion. In particular, the method is demonstrated for two volatile organic compound (VOC) vapors on two different zeolites, the p-Xylene adsorption in Faujasite type zeolite with D = 1.89 × 10 − 13   m 2 / s at 120   ° C and the propene adsorption in Linde Type A type zeolite with D = 5.9 × 10 − 14   m 2 / s at 80   ° C , two diffusion coefficients which are extracted experimentally for first time. Our results are within the order of magnitude of other VOC/zeolite values reported in literature.

Assessments of Impurity Diffusion Coefficients of Selected Pure Metals in Fcc Fe

2014 ◽  
Vol 936 ◽  
pp. 545-551
Author(s):  
Xian Xian Hu ◽  
Xiao Gang Lu ◽  
Yan Lin He
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Impurity Diffusion ◽  
Mobility Database ◽  
Pure Metals

Abstract: The atomic mobilities for impurity diffusion of Al, Au, Co, Cu, Mn, Mo, Nb, Ni, Pt, Sn and Zn in fcc Fe have been critically assessed based on the experimental diffusion coefficient data available in the literature. The impurity diffusion coefficients calculated from the atomic mobilities agree reasonably well with the reliable experimental data. This work provides a helpful guidance for the establishment of a general Fe-based mobility database to design new Fe-based alloys for practical purposes.

Diagnostics of metal samples using the results of experimental and theoretical study of positively charged microparticles formed upon sample destruction

2018 ◽  
Vol 84 (10) ◽  
pp. 23-28
Author(s):  
D. A. Golentsov ◽  
A. G. Gulin ◽  
Vladimir A. Likhter ◽  
K. E. Ulybyshev
Keyword(s):  
Experimental Data ◽  
Early Stage ◽  
Experimental Studies ◽  
Material Model ◽  
Total Charge ◽  
Cross Sectional ◽  
Practical Applications ◽  
Mechanical And Electrical Properties ◽  
Order Of Magnitude ◽  
Using Data

Destruction of bodies is accompanied by formation of both large and microscopic fragments. Numerous experiments on the rupture of different samples show that those fragments carry a positive electric charge. his phenomenon is of interest from the viewpoint of its potential application to contactless diagnostics of the early stage of destruction of the elements in various technical devices. However, the lack of understanding the nature of this phenomenon restricts the possibility of its practical applications. Experimental studies were carried out using an apparatus that allowed direct measurements of the total charge of the microparticles formed upon sample rupture and determination of their size and quantity. The results of rupture tests of duralumin and electrical steel showed that the size of microparticles is several tens of microns, the particle charge per particle is on the order of 10–14 C, and their amount can be estimated as the ratio of the cross-sectional area of the sample at the point of discontinuity to the square of the microparticle size. A model of charge formation on the microparticles is developed proceeding from the experimental data and current concept of the electron gas in metals. The model makes it possible to determine the charge of the microparticle using data on the particle size and mechanical and electrical properties of the material. Model estimates of the total charge of particles show order-of-magnitude agreement with the experimental data.

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