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In this study we construct a data-driven model describing Lithium plating in a battery cell, which is a key process contributing to degradation of such cells. Starting from the fundamental Doyle-Fuller-Newman (DFN) model, we use asymptotic…
In this article the Butler-Volmer equation used in describing Lithium-ion (Li-ion) batteries is discussed. First, a complete mathematical model based on a macro-homogeneous approach developed by Neuman is presented. Two common mistakes…
Ultrahigh rate performance of active particles used in lithium-ion battery electrodes has been revealed by single-particle measurements, which indicates a huge potential for developing high-power batteries. However, the charging/discharging…
This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of…
The Butler-Volmer (BV) equation links the current flux crossing an electrochemical interface to the electric potential drop across it with the assumption of Arrhenius kinetics and the Boltzmann factor. Applying the semilogarithmic Tafel…
We reformulate and extend porous electrode theory for non-ideal active materials, including those capable of phase transformations. Using principles of non-equilibrium thermodynamics, we relate the cell voltage, ionic fluxes, and Faradaic…
We build a transient multidimensional multiphysical model based on continuum theories, involving the coupled mechanical, thermal and electrochemical phenomena occurring simultaneously in the discharge or charge of lithium-ion batteries. The…
The unified 3D phase-field model for the description of the lithium-ion cell as a whole is developed. The model takes into account the realistic distribution of particles in porous electrodes, percolative transport of ions, and the…
The microscopic theory of chemical reactions is based on transition state theory, where atoms or ions transfer classically over an energy barrier, as electrons maintain their ground state. Electron transfer is fundamentally different and…
In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis…
We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse…
In this article we investigate a model for the temperature within a Lithium-Ion battery. The model takes the form of a parabolic PDE for the temperature coupled with two elliptic PDE's for the electric potential within the solid and…
We present a porous electrode model for lithium-ion batteries using Butler--Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic…
Essential to various practical applications of lithium-ion batteries is the availability of accurate equivalent circuit models. This paper presents a new coupled electro-thermal model for batteries and studies how to extract it from data.…
Many intercalation compounds possess layered structures or inter-penetrating lattices that enable phase separation into three or more stable phases, or "stages," driven by competing intra-layer and inter-layer forces. While these structures…
We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion cells. We establish…
Lithium-bismuth bimetallic cells are amongst the best explored liquid metal batteries. A simple and fast quasi-one-dimensional cell voltage model for such devices is presented. The equilibrium cell potential is obtained from a complex…
Accurate parameter dependent electro-chemical numerical models for lithium-ion batteries are essential in industrial application. The exact parameters of each battery cell are unknown and a process of estimation is necessary to infer them.…
Lithium-ion batteries are pivotal to technological advancements in transportation, electronics, and clean energy storage. The optimal operation and safety of these batteries require proper and reliable estimation of battery capacities to…
A nonequilibrium thermodynamic model is presented for the nonisothermal lithium-ion battery cell. Coupling coefficients, all significant for transport of heat, mass, charge and chemical reaction, were used to model profiles of temperature,…