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New local measurements of hydrodynamics in porous media

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Abstract

In this paper, a measurement system is used to carry out local hydrodynamic measurements at the pore scale of a fixed-bed reactor. It consists of four microelectrodes placed on the inner wall of four spheres mounted in tetrahedral form, thus constituting a pore of the fixed bed. Three flow regimes (laminar, inertial and turbulent-like) are identified by the analysis of the signal fluctuations (velocity gradient). The flow structures are characterised by means of the correlation (auto- and cross-) function analysis, and a closure equation required in modelling and simulation is suggested.

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Abbreviations

A e :

effective area of electrode, m2

C L :

concentration, mol/m3

C xx :

auto-correlation function of signal x

d ip :

distance between two probes, m

d′m :

average structure dimension, m

d′M :

maximum structure size, m

D :

diffusion coefficient, m2/s

d e :

electrode diameter, m

f :

frequency, s−1

F :

Faraday constant, 96,500 C/equi

F D(L–S) :

liquid–solid momentum exchange term, kg/m2/s2

g :

gravity, 9.81 m/s2

H :

transfer function

I :

limiting current, A

L :

liquid flow rate, kg/m2/s

P :

static pressure, Pa

P xx :

Power spectral density of signal x

Re p :

\( = \frac{{\rho _{{\text{L}}} u_{0} d_{{\text{p}}} }} {\mu } \), particle Reynolds number

S :

velocity gradient, s−1

t :

time, s

T c :

integral coherence time, s

u L :

liquid phase velocity, m/s

u′L :

fluctuation of liquid phase velocity, m/s

α L :

fluid volume fraction

ε :

porosity

μ :

liquid kinematic viscosity, Pa s

ν e :

number of electrons involved in the electrochemical reaction

ρ L :

liquid phase specific gravity, kg/m3

ρ 0 :

local liquid phase specific gravity, kg/m3

θ :

time lag (in correlation functions), s

θ c :

coherence time, s

τ :

tortuosity

ω :

dimensionless frequency

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Authors and Affiliations

  1. Laboratoire des Sciences du Génie Chimique, CNRS-ENSIC, 1 rue Grandville, B.P. 451, 54001, Nancy, Cedex, France

    F. Lesage, N. Midoux & M. A. Latifi

Authors
  1. F. Lesage
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  2. N. Midoux
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  3. M. A. Latifi
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Correspondence to M. A. Latifi.

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Lesage, F., Midoux, N. & Latifi, M.A. New local measurements of hydrodynamics in porous media. Exp Fluids 37, 257–262 (2004). https://doi.org/10.1007/s00348-004-0811-5

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  • DOI: https://doi.org/10.1007/s00348-004-0811-5

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