Dispersion controlled by permeable surfaces: surface properties and scaling

2016 ◽  
Vol 801 ◽  
pp. 13-42 ◽  
Author(s):  
Bowen Ling ◽  
Alexandre M. Tartakovsky ◽  
Ilenia Battiato
Keyword(s):  
Mass Transport ◽  
Solute Transport ◽  
Surface Properties ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Operating Conditions ◽  
Péclet Number ◽  
Porosity And Permeability ◽  
Matrix Porosity ◽  
The Impact

Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.

A Mass Transport Model for CVD Coating of Optical Fibers

2003 ◽  
Author(s):  
Wei Huang ◽  
Wilson K. S. Chiu
Keyword(s):  
Mass Transport ◽  
Diffusion Model ◽  
Optical Fibers ◽  
Peclet Number ◽  
Flow Reactor ◽  
Transport Model ◽  
Gas Diffusion ◽  
Transfer Model ◽  
Continuous Stirred Tank Reactor ◽  
Péclet Number

Carbon coated optical fibers are produced by the chemical vapor deposition process which includes multi-species mass transport with chemical reactions. A proper numerical model of this process will help elucidate the basic mechanisms and optimize the process to improve coating quality. A heat transfer model has been developed in our research group. We are now developing an applicable chemical kinetics model to include mass transport with gas phase and surface reactions. Several different chemical reactor models have been tried, including a continuous-stirred tank reactor (CSTR) model, a plug flow reactor (PFR) model and a multi-component diffusion model with the Maxwell-Stefan approximations. We found that in reactor conditions with well-mixed or large mass Peclet number, the CSTR and PFR models validate well with experimental results. But a multi-component gas diffusion model is needed for low mass Peclet number conditions. The model has been extended to a wider range of temperatures necessary for this optical fiber coating process.

scholarly journals The Effect of Cell Compression and Cathode Pressure on Hydrogen Crossover in PEM Water Electrolysis

2021 ◽  
Author(s):  
Agate Martin ◽  
Patrick Trinke ◽  
Markus Stähler ◽  
Andrea Stähler ◽  
Fabian Scheepers ◽  
...  
Keyword(s):  
Mass Transport ◽  
Cell Voltage ◽  
Water Electrolysis ◽  
Material Design ◽  
Operating Conditions ◽  
Cell Performance ◽  
Membrane Electrode ◽  
Current Densities ◽  
Hydrogen Crossover ◽  
The Impact

Abstract Hydrogen crossover poses a crucial issue for polymer electrolyte membrane (PEM) water electrolysers in terms of safe operation and efficiency losses, especially at increased hydrogen pressures. Besides the impact of external operating conditions, the structural properties of the materials also influence the mass transport within the cell. In this study, we provide an analysis of the effect of elevated cathode pressures (up to 15 bar) in addition to increased compression of the membrane electrode assembly on hydrogen crossover and the cell performance, using thin Nafion 212 membranes and current densities up to 3.6 A cm-2. It is shown that a higher compression leads to increased mass transport overpotentials, although the overall cell performance is improved due to the decreased ohmic losses. The mass transport limitations also become visible in enhanced anodic hydrogen contents with increasing compression at high current densities. Moreover, increases in cathode pressure are amplifying the compression effect on hydrogen crossover and mass transport losses. The results indicate that the cell voltage should not be the only criterion for optimizing the system design, but that the material design has to be considered for the reduction of hydrogen crossover in PEM water electrolysis.

scholarly journals DETERMINATION OF TRANSPORT PARAMETERS FOR SOLUTES IN SALT-TREATED SOIL COLUMNS

2017 ◽  
Vol 48 (1) ◽  
Author(s):  
Bahia & Naser
Keyword(s):  
Sodium Chloride ◽  
Calcium Chloride ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Transport Parameters ◽  
Péclet Number ◽  
Mixed Salts ◽  
Sodium And Potassium

A laboratory experiment was carried out at the Department of Soil Sciences and Water Resources, College of Agriculture, University of Baghdad. Silty clay soil was treated with three salt solutions (NaCl, CaCl2 and mixed NaCl–CaCl2). Homogeneously packed soil columns (10 cm, 40 cm) were leached six times using tap water. Effluent samples were collected to determine ion concentration Cl-, Ca++, Na+, K+ and Mg++. Breakthrough curves were used to estimate solute transport parameters (retardation factor, peclet number) using an analytical solution of convection-dispersion equation (CDE) by CXTFIT program. The results showed that relative concentration of chloride was increased rapidly with calcium chloride, which increased sodium leaching rate at starting of breakthrough curve. Sodium chloride increased water requirements for calcium displacement. Results indicated a good fitting of convection-dispersion equation with breakthrough curves data. The best-fit were used to calculate peclet number, retardation factor and dispersion coefficient. When soil was treated with calcium chloride, Peclet number of chloride was increased from 3.13 to 6.48, while it has been decreased for calcium, sodium and potassium. Sodium chloride decreased peclet numbers of chloride, calcium and sodium. Also mixed salts increased sodium peclet number from 1.01 to 9.02. Results showed, calcium chloride decreased retardation factor of chloride from 1.59 to 0.50, while it has been increased from 1.39, 1.58 to 175.00, 493.36 for each of sodium and potassium, respectively. Retardation factor of calcium was decreased when soil was treated with sodium chloride or mixed salts. Dispersion coefficient was decreased for chloride, and increased for calcium and magnesium. When soil was treated with calcium chloride, dispersion coefficients have been increased from 24.29, 25.56 to 40.51, 40.89 cm2hr-1 for sodium and potassium, respectively.

Small Péclet-number mass transport to a finite strip: An advection–diffusion–reaction model of surface-based biosensors

2019 ◽  
Vol 31 (5) ◽  
pp. 763-781
Author(s):  
EHUD YARIV
Keyword(s):  
Shear Flow ◽  
Mass Transport ◽  
Sherwood Number ◽  
Peclet Number ◽  
Outer Region ◽  
Diffusion Reaction ◽  
Background Concentration ◽  
Leading Order ◽  
Péclet Number ◽  
Inner Region

AbstractWe consider two-dimensional mass transport to a finite absorbing strip in a uniform shear flow as a model of surface-based biosensors. The quantity of interest is the Sherwood number Sh, namely the dimensionless net flux onto the strip. Considering early-time absorption, it is a function of the Péclet number Pe and the Damköhler number Da, which, respectively, represent the characteristic magnitude of advection and reaction relative to diffusion. With a view towards modelling nanoscale biosensors, we consider the limit Pe«1. This singular limit is handled using matched asymptotic expansions, with an inner region on the scale of the strip, where mass transport is diffusively dominated, and an outer region at distances that scale as Pe-1/2, where advection enters the dominant balance. At the inner region, the mass concentration possesses a point-sink behaviour at large distances, proportional to Sh. A rescaled concentration, normalised using that number, thus possesses a universal logarithmic divergence; its leading-order correction represents a uniform background concentration. At the outer region, where advection by the shear flow enters the leading-order balance, the strip appears as a point singularity. Asymptotic matching with the concentration field in that region provides the Sherwood number as $${\rm{Sh}} = {\pi \over {\ln (2/{\rm{P}}{{\rm{e}}^{1/2}}) + 1.0559 + \beta }},$$ wherein β is the background concentration. The latter is determined by the solution of the canonical problem governing the rescaled inner concentration, and is accordingly a function of Da alone. Using elliptic-cylinder coordinates, we have obtained an exact solution of the canonical problem, valid for arbitrary values of Da. It is supplemented by approximate solutions for both small and large Da values, representing the respective limits of reaction- and transport-limited conditions.

Characterization of stationary mixing patterns in a three-dimensional open Stokes flow: spectral properties, localization and mixing regimes

2009 ◽  
Vol 639 ◽  
pp. 291-341 ◽  
Author(s):  
M. GIONA ◽  
S. CERBELLI ◽  
F. GAROFALO
Keyword(s):  
Finite Length ◽  
Peclet Number ◽  
Scaling Laws ◽  
Eigenvalue Problems ◽  
Operating Conditions ◽  
Creeping Flow ◽  
Scaling Analysis ◽  
Dominant Eigenvalue ◽  
Péclet Number ◽  
The Real

This article analyses stationary scalar mixing downstream an open flow Couette device operating in the creeping flow regime. The device consists of two coaxial cylinders of finite length Lz, and radii κ R and R (κ < 1), which can rotate independently. At relatively large values of the aspect ratio α = Lz/R ≫ 1, and of the Péclet number Pe, the stationary response of the system can be accurately described by enforcing the simplifying assumption of negligible axial diffusion. With this approximation, homogenization along the device axis can be described by a family of generalized one-dimensional eigenvalue problems with the radial coordinate as independent variable. A variety of mixing regimes can be observed by varying the geometric and operating parameters. These regimes are characterized by different localization properties of the eigenfunctions and by different scaling laws of the real part of the eigenvalues with the Péclet number. The analysis of this model flow reveals the occurrence of sharp transitions between mixing regimes, e.g. controlled by the geometric parameter κ. The eigenvalue scalings can be theoretically predicted by enforcing eigenfunction localization and simple functional equalities relating the behaviour of the eigenvalues to the functional form of the associated eigenfunctions. Several flow protocols corresponding to different geometric and operating conditions are considered. Among these protocols, the case where the inner and the outer cylinders counter-rotate exhibits a peculiar intermediate scaling regime where the real part of the dominant eigenvalue is independent of Pe over more than two decades of Pe. This case is thoroughly analysed by means of scaling analysis. The practical relevance of the results deriving from spectral analysis for fluid mixing problems in finite-length Couette devices is addressed in detail.

scholarly journals From “Black Box” to a Real Description of Overall Mass Transport through Membrane and Boundary Layers

Membranes ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 18
Author(s):  
Endre Nagy ◽  
Márta Vitai
Keyword(s):  
Mass Transport ◽  
Peclet Number ◽  
Porous Membrane ◽  
Black Box ◽  
Box Model ◽  
Transmembrane Pressure ◽  
Transport Parameters ◽  
Characteristic Parameters ◽  
Péclet Number ◽  
Dense Membrane

The “black box” model defines the enhancement, the polarization modulus, and the intrinsic enhancement, without knowing the transport mechanism in the membrane. This study expresses the above-mentioned characteristic parameters, simultaneously taking into account the mass transport expressions developed for both the polarization and the membrane layers. Two membrane models are studied here, namely a solution-diffusion model characterizing solute transport through a dense membrane and a solution-diffusion plus convection model characterizing transport through a porous membrane due to transmembrane pressure difference. It is shown that the characteristic parameters of the “black box” model (E, or ) can be expressed as a function of the transport parameters and independently from each other using two-layer models. Thus, membrane performance could be predicted by means of the transport parameters. Several figures show how enhancement and the polarization modulus varied as a function of the membrane Peclet number and the solubility coefficient. Enhancement strongly increased up to its maximum value when H > 1, in the case of transport through a porous membrane, whereas its change remained before unity in the case of a dense membrane. When the value of H < 1, the value of E gradually decreased with increasing values of the membrane Peclet number.

Impact of Reservoir Permeability on Flowing Sandface Temperatures: Dimensionless Analysis

SPE Journal ◽  
2013 ◽  
Vol 18 (04) ◽  
pp. 685-694 ◽  
Author(s):  
J.F.. F. App ◽  
K.. Yoshioka
Keyword(s):  
Heat Transfer ◽  
Temperature Change ◽  
Expansion Coefficient ◽  
Peclet Number ◽  
Maximum Temperature ◽  
Péclet Number ◽  
Dimensionless Analysis ◽  
Reservoir Permeability ◽  
Layer Flow ◽  
The Impact

Summary Layer flow contributions are increasingly being quantified through the analysis of measured sandface flowing temperatures. It is commonly known that the maximum temperature change is affected by the magnitude of the drawdown and the Joule-Thomson expansion coefficient of the fluid. Another parameter that strongly impacts layer sandface flowing temperatures is the layer permeability. Aside from determining the drawdown, the layer permeability also affects the ratio of heat transfer by convection to conduction within a reservoir. The impact of permeability can be represented by the Péclet number, which is a dimensionless quantity representing the ratio of heat transfer by convection to conduction. The Péclet number is directly proportional to reservoir permeability. Through dimensionless analysis, it will be shown that for a given drawdown (based on a dimensionless Joule-Thomson expansion coefficient JTD) the temperature change diminishes at low Péclet numbers and increases at high Péclet numbers. This implies that for low-permeability reservoirs such as shale gas or tight oil, the temperature changes will be minimal (less than 0.1ºF) despite the large drawdowns in many instances. Dimensionless analysis is performed for both steady-state and transient thermal models. Results from multilayer transient simulations illustrate the ability to identify contrasting permeability layers on the basis of the Péclet number effect.

scholarly journals Phoretic self-propulsion at finite Péclet numbers

2014 ◽  
Vol 747 ◽  
pp. 572-604 ◽  
Author(s):  
Sébastien Michelin ◽  
Eric Lauga
Keyword(s):  
Particle Size ◽  
Theoretical Analysis ◽  
Peclet Number ◽  
Chemical Interaction ◽  
Computational Results ◽  
Parallel Study ◽  
Péclet Number ◽  
Interaction Layer ◽  
Small Scales ◽  
The Impact

AbstractPhoretic self-propulsion is a unique example of force- and torque-free motion on small scales. The classical framework describing the flow field around a particle swimming by self-diffusiophoresis neglects the advection of the solute field by the flow and assumes that the chemical interaction layer is thin compared to the particle size. In this paper we quantify and characterize the effect of solute advection on the phoretic swimming of a sphere. We first rigorously derive the regime of validity of the thin-interaction-layer assumption at finite values of the Péclet number (${Pe}$). Under this assumption, we solve computationally the flow around Janus phoretic particles and examine the impact of solute advection on propulsion and the flow created by the particle. We demonstrate that although advection always leads to a decrease of the swimming speed and flow stresslet at high values of the Péclet number, an increase can be obtained at intermediate values of ${Pe}$. This possible enhancement of swimming depends critically on the nature of the chemical interactions between the solute and the surface. We then derive an asymptotic analysis of the problem at small ${Pe}$ which allows us to rationalize our computational results. Our computational and theoretical analysis is accompanied by a parallel study of the influence of reactive effects at the surface of the particle (Damköhler number) on swimming.

Shear Dispersion in a Rough-Walled Fracture

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1669-1688 ◽  
Author(s):  
Morteza Dejam ◽  
Hassan Hassanzadeh ◽  
Zhangxin Chen
Keyword(s):  
Peclet Number ◽  
Dispersion Coefficient ◽  
Coupled System ◽  
Fracture Aperture ◽  
Maximum Height ◽  
Fracture Roughness ◽  
Péclet Number ◽  
Relative Roughness ◽  
Shear Dispersion ◽  
Porous Walls

Summary An expression is analytically presented for the shear dispersion, or Taylor (1953) and Aris (1956) dispersion, of a solute transporting in a coupled system, which consists of a matrix and a rough-walled fracture. To derive a shear-dispersion coefficient in a fracture with rough and porous walls, the continuities of solute concentrations and their fluxes are imposed at the fracture walls. The dispersion coefficient for the coupled system is obtained as a function of the Péclet number and relative roughness, where the latter parameter is defined as the ratio of the maximum height of the roughness to the minimum half-aperture of the fracture. Several models for fracture-roughness geometry, including periodically and randomly shaped roughness models, are applied to study the effect of fracture-aperture variation on dispersion. The dispersion coefficient for all rough-walled fractures identifies three different regions in terms of the degree of relative roughness. The results show that for small values of the relative roughness (0&lt;ε≤0.1), the dispersion coefficient is at maximum for bell-shaped geometry and at minimum for triangular-shaped and randomly shaped geometries. When the relative roughness is within 0.1&lt;ε&lt;10, the dispersion is observed to be at maximum for rectangular-walled and at minimum for triangular-walled fractures. The results also reveal that for high values of the relative roughness (ε≥10), the dispersion is higher for bell-shaped roughness, whereas the triangular-walled fracture results in the lowest dispersion. It is found that for all roughness geometries an increase in either the Péclet number or relative roughness leads to an increase in the dispersion.

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