Page 258 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Electrode Polarisations 23 5

decreases with decreasing temperature. In general, the qbnc is not a very strong
function of temperature.
As stated earlier, the process of gaseous transport through porous electrodes is
not describable by first order kinetics: nevertheless a characteristic time constant
can be approximated by:

For a typical anode-supported cell, 1, is 0.5 to 1 mm, and D,(eff) is -0.1 to -0.5
cm2/sec. Thus, the corresponding characteristic time is on the order of several
milliseconds to a few tenths of a second. The estimated tortuosity factors, based
on cell performance measurements, range between -5 or 6 to as high as 15 to
20. The estimated tortuosity factor based on geometrical path a molecule
traverses is typically less than 5 or 6. High values of the tortuosity factors
estimated from cell performance data thus cannot be described solely on the basis
of geometric considerations: other effects such as Knudsen diffusion, adsorption
and surface diffusion probably also play a role. It is to be emphasised, however,
that very high tortuosity factors have indeed been measured in many other cases
involving gaseous transport through porous bodies with low porosities and smali
pore sizes [7]. Despite the fact that a high tortuosity factor cannot be justified on
geometric arguments alone, it still is a useful parameter for describing
concentration polarisation.
Concentration polarisation at the cathode similarly is related to the transport
of O2 and N2 through the porous cathode. The net flux of O2 from the oxidant
stream, through the cathode to the cathode/electrolyte interface. is linearly
proportional to the net current density. In this case aIso, gaseous transport is a
function of the fundamental binary diffusivity, Do2-~*, and cathode
microstructure. The physical ‘resistance’ to the transport of gaseous species
through the cathode is reflected as an ‘electrical voltage’ loss. This polarisation
loss is known as cathodic concentration polarisation, q:onc, and is given as

T&,,,~ = f(Do2-x2, Microstructure, Partial Pressures, Current Density) (12)

The q& increases with increasing current density, but not in a linear fashion.
The time constant or response time must be a function of diffusivity and a
characteristic diffusion distance, and thus the response time is finite, non-zero.
Similar to the anode, a characteristic time for the cathode may be given by:

where DCce,) is the effective diffusivity through the cathode, and IC is the cathode
thickness. For an anode-supported cell, for a cathode thickness of -200 microns,
and effective cathode diffusivity, Dc(ef,) of -0.05 cm2/s, the characteristic time is
-8 milliseconds; that is, in the millisecond range. In terms of physically