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Accelerated Oxygen Mass Transfer in Copper and Vanadium Oxide-Based MIEC-Redox Membrane

  • Valery V. BelousovEmail author
  • Sergey V. Fedorov
Article
  • 32 Downloads

Abstract

Mixed ionic-electronic conducting (MIEC) membranes have a great potential for use in gas separation technology in the production of pure oxygen for metallurgy, micro- and nanoelectronics, biotechnology, pharmaceutics, etc. Before this happens, an important issue has to be addressed. This issue involves the design of novel MIEC membranes with enhanced oxygen transport. Recently, a concept of thick two-layer solid/liquid composite MIEC-Redox membranes with accelerated diffusion-bubbling oxygen transfer was proposed (see Belousov and Fedorov in ACS Appl Mater Interfaces 10:21794–21798, 2018). These diffusion-bubbling membranes could serve for efficient oxygen separation from air. However, there is no enough fundamental understanding of the mass transport processes involved. This understanding is important for evaluating the potential of MIEC-Redox membranes for practical application. The presented article gives a theory of oxygen mass transfer in two-layer copper and vanadium oxide-based MIEC-Redox membranes. The theory describes both the transport of oxygen ions in the outer layer of the membrane and the nucleation, growth, and transport of oxygen gas bubbles in the inner layer of the membrane. Kinetic regularities of oxygen mass transfer are established. The ways to enhance the productivity of MIEC-Redox membranes are outlined.

Nomenclature

A

Bubble/liquid interface area (m2)

C

Gas concentration (mol m−3)

Cf

Final gas concentrations (mol m−3)

Ci

Initial gas concentration (mol m−3)

c

Concentration of mobile oxygen ions (mol m−3)

D

Diffusion coefficient of oxygen gas (m2 s−1)

Di

Diffusion coefficient of oxygen ions (m2 s−1)

Def

Effective diffusion coefficient (m2 s−1)

d

Average distance between neighboring gas molecules (m)

F

Faraday’s constant, (C mol−1)

\( \Delta F^{*} \)

Free energy change (J)

g

Gravity (m s−2)

\( j_{{{\text{O}}_{2} }} \)

Oxygen flux (m3 m−2 s−1)

\( j_{{{\text{O}}_{2} }}^{\varvec{*}} \)

Oxygen permeability (m3 m−1 s−1)

k

Boltzmann constant (J K−1)

ks

Surface exchange coefficient (cm s−1)

L

Membrane thickness (m)

Lc

Membrane characteristic thickness (m)

Ld

Diffusion envelope thickness (m)

M

Molar mass (kg mol−1)

N

Structure unit number

Nb

Bubble density (m−3)

n

Gas molecule number in bubble

nb

Bubble number per unit surface (m−2)

ng

Nucleus density (m−3)

Pb

Pressure inside bubble (Pa)

Pe

Peclet number

Pf

Final pressure (Pa)

Pi

Initial pressure (Pa)

Pl

Liquid pressure (Pa)

\( P^{\prime}_{{{\text{O}}_{2} }} \)

Oxygen partial pressure at outer side of membrane (Pa)

\( P^{\prime\prime}_{{{\text{O}}_{2} }} \)

Oxygen partial pressure at inner side of membrane (Pa)

R

Universal gas constant (J K−1 mol−1)

Rb

Bubble radius (m)

\( \bar{R}_{\text{b}} \)

Average bubble radius (m)

Rbc

Critical bubble radius (m)

Re

Reynolds number

r

Radial coordinate

T

Absolute temperature (K)

t

Time (s)

τi

Oxygen ion transference number

\( u \)

Oxygen ion mobility (m2 V−1 s−1)

Vb

Bubble volume (m3)

\( \bar{V}_{\text{b}} \)

Average bubble volume (m3)

VD

Volume fraction of diffusion envelopes

Vg

Gas molecule volume (m3)

φ

Volume fraction of liquid

γlg

Liquid/gas interface tension (J m−2)

γsg

Solid/gas interface tension (J m−2)

γsl

Solid/liquid interface tension (J m−2)

ηg

Gas viscosity (Pa s)

ηl

Liquid viscosity (Pa s)

θ

Contact angle

μg

Chemical potential of oxygen in bubble (J)

μl

Chemical potential of oxygen in liquid (J)

ρg

Gas density inside bubble (kg m−3)

ρl

Liquid density (kg m−3)

σ

Conductivity (S m−1)

σef

Effective conductivity (S m−1)

vb

Bubble motion rate (m s−1)

\( \bar{v}_{\text{b}} \)

Average bubble motion rate (m s−1)

vD

Volume of the diffusion envelope (m3)

ψ

Geometric term

ω

Bubble nucleation rate (s−1)

Notes

Acknowledgment

We are grateful to the Russian Science Foundation (RSF) for supporting this work (Project No. 16-19-10608).

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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  1. 1.Laboratory of Functional Ceramics, A.A. Baikov Institute of Metallurgy and Materials ScienceRussian Academy of SciencesMoscowRussia

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