989 research outputs found
A hierarchy of models for simulating experimental results from a 3D heterogeneous porous medium
In this work we examine the dispersion of conservative tracers (bromide and
fluorescein) in an experimentally-constructed three-dimensional dual-porosity
porous medium. The medium is highly heterogeneous (), and
consists of spherical, low-hydraulic-conductivity inclusions embedded in a
high-hydraulic-conductivity matrix. The bi-modal medium was saturated with
tracers, and then flushed with tracer-free fluid while the effluent
breakthrough curves were measured. The focus for this work is to examine a
hierarchy of four models (in the absence of adjustable parameters) with
decreasing complexity to assess their ability to accurately represent the
measured breakthrough curves. The most information-rich model was (1) a direct
numerical simulation of the system in which the geometry, boundary and initial
conditions, and medium properties were fully independently characterized
experimentally with high fidelity. The reduced models included; (2) a
simplified numerical model identical to the fully-resolved direct numerical
simulation (DNS) model, but using a domain that was one-tenth the size; (3) an
upscaled mobile-immobile model that allowed for a time-dependent mass-transfer
coefficient; and, (4) an upscaled mobile-immobile model that assumed a
space-time constant mass-transfer coefficient. The results illustrated that all
four models provided accurate representations of the experimental breakthrough
curves as measured by global RMS error. The primary component of error induced
in the upscaled models appeared to arise from the neglect of convection within
the inclusions. Interestingly, these results suggested that the conventional
convection-dispersion equation, when applied in a way that resolves the
heterogeneities, yields models with high fidelity without requiring the
imposition of a more complex non-Fickian model.Comment: 27 pages, 9 Figure
A mathematical model for mechanically-induced deterioration of the binder in lithium-ion electrodes
This study is concerned with modeling detrimental deformations of the binder
phase within lithium-ion batteries that occur during cell assembly and usage. A
two-dimensional poroviscoelastic model for the mechanical behavior of porous
electrodes is formulated and posed on a geometry corresponding to a thin
rectangular electrode, with a regular square array of microscopic circular
electrode particles, stuck to a rigid base formed by the current collector.
Deformation is forced both by (i) electrolyte absorption driven binder
swelling, and; (ii) cyclic growth and shrinkage of electrode particles as the
battery is charged and discharged. The governing equations are upscaled in
order to obtain macroscopic effective-medium equations. A solution to these
equations is obtained, in the asymptotic limit that the height of the
rectangular electrode is much smaller than its width, that shows the
macroscopic deformation is one-dimensional. The confinement of macroscopic
deformations to one dimension is used to obtain boundary conditions on the
microscopic problem for the deformations in a 'unit cell' centered on a single
electrode particle. The resulting microscale problem is solved using numerical
(finite element) techniques. The two different forcing mechanisms are found to
cause distinctly different patterns of deformation within the microstructure.
Swelling of the binder induces stresses that tend to lead to binder
delamination from the electrode particle surfaces in a direction parallel to
the current collector, whilst cycling causes stresses that tend to lead to
delamination orthogonal to that caused by swelling. The differences between the
cycling-induced damage in both: (i) anodes and cathodes, and; (ii) fast and
slow cycling are discussed. Finally, the model predictions are compared to
microscopy images of nickel manganese cobalt oxide cathodes and a qualitative
agreement is found.Comment: 25 pages, 11 figure
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