On the impact of free surfaces on the measurement of diffusion coefficients in metallic binary alloys using shear cells

2015 ◽  
Vol 81 ◽  
pp. 602-617 ◽  
Author(s):  
Xavier Ruiz ◽  
Nuria Sáez ◽  
Josefina Gavaldà ◽  
Jordi Pallarès
Keyword(s):  
Diffusion Coefficients ◽  
Binary Alloys ◽  
Free Surfaces ◽  
Shear Cells ◽  
The Impact

Diffusion-Based Modeling of Gas Transport in Organic-Rich Ultratight Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-26
Author(s):  
Zizhong Liu ◽  
Hamid Emami-Meybodi
Keyword(s):  
Diffusion Coefficient ◽  
Adsorption Capacity ◽  
Surface Diffusion ◽  
Diffusion Coefficients ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Hydrocarbon Transport ◽  
The Impact ◽  
And Storage

Summary The complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-actingorganic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

scholarly journals Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites

2020 ◽  
Vol 117 (23) ◽  
pp. 12700-12706
Author(s):  
Young Ki Lee ◽  
Xiaoguai Li ◽  
Paris Perdikaris ◽  
John C. Crocker ◽  
Celia Reina ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Diffusion Coefficients ◽  
Particle Shape ◽  
Colloidal Crystals ◽  
Principal Component ◽  
Nucleation And Growth ◽  
Spherically Symmetric ◽  
Dynamical Models ◽  
Micrometer Scale ◽  
The Impact

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Role of Variable Conductance on Heat and Mass Transport Mechanism Using Generalized Theory

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Imran Haider Qureshi ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem ◽  
M. Nawaz
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Chemical Reaction ◽  
Diffusion Coefficients ◽  
Mass Diffusion ◽  
Memory Effects ◽  
Temperature Dependent ◽  
Newton's Law ◽  
Newton’S Law ◽  
The Impact

Abstract Fourier law of heat conduction, its analog Fick's first law, and Newton's law of viscosity are classical laws that are not capable of exhibiting memory effects. Conservation laws based on these classical laws do not give predictions about memory effects on the transport phenomena. Recently, proposed novel laws are called Cattaneo–Christov heat flux. Models are based on the generalization of classical laws of heat conduction, mass diffusion, and Newton's law of viscosity. This investigation considers this generalized theory to model the impact of relaxation phenomenon on the transport of momentum, heat, and mass in Maxwell fluid (viscoelastic fluid) of temperature-dependent viscosity and thermal conductivity in the presence of temperature-dependent mass diffusion coefficients. It is observed from the simulations that memory effects play a key role in controlling momentum, thermal and concentration boundary layer thicknesses. It is also noted that the rate of diffusion of heat and mass has shown an increasing trend when thermal conductivity and mass diffusion coefficients are increased via rise in temperature of the fluid. The generative chemical reaction on the transport of specie relative to the impact on the transport of specie when it is compared with the impact of destructive chemical reaction on the transport of specie.

NUMERICAL ANALYSIS OF THE IMPACT OF ATHEROSCLEROTIC PLAQUE AND DIFFERENT STENT SPACING ON DRUG DEPOSITION

2015 ◽  
Vol 15 (01) ◽  
pp. 1550011
Author(s):  
DONG RUIQI ◽  
JIANG WENTAO ◽  
YAN FEI ◽  
ZHENG TINGHUI ◽  
FAN YUBO
Keyword(s):  
Diffusion Coefficient ◽  
Atherosclerotic Plaque ◽  
Drug Concentration ◽  
Diffusion Coefficients ◽  
Drug Eluting Stent ◽  
Artery Wall ◽  
Obvious Effect ◽  
Drug Deposition ◽  
Curved Artery ◽  
The Impact

Objectives: To investigate the influence of atherosclerotic plaque and different drug-eluting stent (DES) spacing on drug deposition in the curved artery wall. Methods: Based on the computational fluid dynamics (CFD) method, the numerical investigation on distributions of drug concentration in the artery wall was carried out considering three different interstrut distances and five values of the plaque diffusion coefficients. The results were compared with those of the model without plaque. Results: Under the same stent spacing, drug deposition weakly increased with the increasing plaque diffusion coefficient. When the same diffusion coefficient value was taken, drug deposition presented steady growth with the expansion of stent spacing. When the stent spacing was of 1-strut length or the diffusion coefficient of plaque was much smaller than the diffusion coefficient of tissue (an order of magnitude or more), the drug deposition would be evidently reduced. Conclusions: In a curved artery, the stent spacing is still an important factor in drug deposition. The diffusion coefficients of plaque have little influence on the average drug concentration, but they show a relatively obvious effect on drug distributions.

scholarly journals Mathematical modeling of groundwater contamination with varying velocity field

2017 ◽  
Vol 65 (2) ◽  
pp. 192-204 ◽  
Author(s):  
Pintu Das ◽  
Sultana Begam ◽  
Mritunjay Kumar Singh
Keyword(s):  
Groundwater Contamination ◽  
Analytical Solutions ◽  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Time Dependent ◽  
Analytical Models ◽  
Retardation Factor ◽  
Hydrodynamic Dispersion ◽  
The Impact

Abstract In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).

scholarly journals Numerical simulation of reacting flow in the combustion chamber and study of the impact of turbulent diffusion coefficients

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402095497
Author(s):  
Evgenij Strokach ◽  
Igor Borovik ◽  
Fang Chen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Chemical Reactions ◽  
Turbulence Model ◽  
Turbulent Diffusion ◽  
Diffusion Coefficients ◽  
Radiation Heat Transfer ◽  
Mixing Efficiency ◽  
Radiation Heat ◽  
The Impact

A methodology for combustion modeling with complex mixing and thermodynamic conditions, especially in thrusters, is still under development. The resulting flow and propulsion parameters strongly depend on the models used, especially on the turbulence model as it determines the mixing efficiency. In this paper, the effect of the sigma-type turbulent diffusion coefficients arriving in the diffusion term of the turbulence model is studied. This study was performed using complex modeling, considering the conjugate effect of several physical phenomena such as turbulence, chemical reactions, and radiation heat transfer. To consider the varying turbulent Prandtl, an algebraic model was implemented. An adiabatic steady diffusion Flamelet approach was used to model chemical reactions. The P1 differential model with a WSGG spectral model was used for radiation heat transfer. The gaseous oxygen (GOX) and methane (GCH4) operating thruster developed at the Chair of turbomachinery and Flight propulsion of the Technical University of Munich (TUM) is taken as a test case. The studies use the 3D RANS approach using the 60° sector as the modeling domain. The normalized and absolute pressures, the integral and segment averaged heat flux are compared to numerical results. The wall heat fluxes and pressure distributions show good agreement with the experimental data, while the turbulent diffusion coefficients mostly influence the heat flux.

Impact of a falling jet

2010 ◽  
Vol 657 ◽  
pp. 22-35 ◽  
Author(s):  
PAUL CHRISTODOULIDES ◽  
FRÉDÉRIC DIAS
Keyword(s):  
Galerkin Method ◽  
Froude Number ◽  
Steady Flow ◽  
Maximum Pressure ◽  
Horizontal Plate ◽  
Vertical Pipe ◽  
Simplified Models ◽  
Free Surfaces ◽  
Bernoulli’S Equation ◽  
The Impact

Given the complexity of the problem of the impact of a mass of liquid on a solid structure, various simplified models have been introduced in order to obtain some insight on particular aspects of the problem. Here the steady flow of a jet falling from a vertical pipe, hitting a horizontal plate and flowing sideways is considered. Depending on the elevation H of the pipe relative to the horizontal plate and the Froude number F, the flow can either leave the pipe tangentially or detach from the edge of the pipe. When the flow leaves tangentially, it can either be diverted immediately by the plate or experience squeezing before being diverted. First, the problem is reformulated using conformal mappings. The resulting problem is then solved by a collocation Galerkin method; a particular form is assumed for the solution, and certain coefficients in that representation are then found numerically by satisfying Bernoulli's equation on the free surfaces at certain discrete points. The resulting equations are solved by Newton's method, yielding various configurations of the solution based on the values of F and H. The pressure exerted on the plate is computed and discussed. For a fixed value of F, the maximum pressure along the plate goes through a minimum as H increases from small to large values. Results are presented for the three possible configurations: (i) tangential departure from the pipe and no squeezing, (ii) tangential departure from the pipe followed by squeezing of the liquid and (iii) detachment of the liquid from the pipe (with subsequent squeezing).

Effects of Diffusion Coefficients and Struts Apposition Using Numerical Simulations for Drug Eluting Coronary Stents

2007 ◽  
Vol 129 (5) ◽  
pp. 733-742 ◽  
Author(s):  
Rosaire Mongrain ◽  
Isam Faik ◽  
Richard L. Leask ◽  
Josep Rodés-Cabau ◽  
Éric Larose ◽  
...  
Keyword(s):  
Blood Flow ◽  
Diffusion Coefficients ◽  
Concentration Distribution ◽  
Polymer Coating ◽  
Numerical Models ◽  
Vascular Wall ◽  
Therapeutic Window ◽  
Wall Region ◽  
Drug Eluting ◽  
The Impact

In the context of drug eluting stent, we present two-dimensional numerical models of mass transport of the drug in the wall and in the lumen to study the effect of the drug diffusion coefficients in the three principal media (blood, vascular wall, and polymer coating treated as a three-compartment problem) and the impact of different strut apposition configurations (fully embedded, half embedded, and not embedded). The different conditions were analyzed in terms of their consequence on the drug concentration distribution in the arterial wall. We apply the concept of the therapeutic window to the targeted vascular wall region and derive simple metrics to assess the efficiency of the various stent configurations. Although most of the drug is dispersed in the lumen, variations in the blood flow rate within the physiological range of coronary blood flow and the diffusivity of the drug molecule in the blood were shown to have a negligible effect on the amount of drug in the wall. Our results reveal that the amount of drug cumulated in the wall depends essentially on the relative values of the diffusion coefficients in the polymer coating and in the wall. Concerning the strut apposition, it is shown that the fully embedded strut configuration would provide a better concentration distribution.

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