Microsoft Word - PRES22_0064.docx
DOI: 10.3303/CET2294050
Paper Received: 01 April 2022; Revised: 13 April 2022; Accepted: 18 April 2022
Please cite this article as: Castro M.T., Del Rosario J.A.D., Ocon J.D., 2022, Energy Density Optimization in a Primary Alkaline Battery using
Multiphysics Modeling, Chemical Engineering Transactions, 94, 301-306 DOI:10.3303/CET2294050
A publication of
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 94, 2022 The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš, Sandro Nižetić
Copyright © 2022, AIDIC Servizi S.r.l.
ISBN 978-88-95608-93-8; ISSN 2283-9216
Energy Density Optimization in a Primary Alkaline Battery
using Multiphysics Modeling
Michael T. Castro, Julie Anne D. Del Rosario, Joey D. Ocon*
Laboratory of Electrochemical Engineering (LEE), Department of Chemical Engineering, University of the Philippines
Diliman, Quezon City 1101, Philippines
jdocon@up.edu.ph
Primary alkaline batteries have been widely used in portable electronics due to their low cost and safety. The
consumption and disposal of these batteries has prompted notable research on their recycling. Another
approach to reducing alkaline battery disposal is to extend their lifetime by increasing their energy density. In
this work, the energy density of an AA primary alkaline battery was maximized by determining the optimum
amount of electrode materials through multiphysics modeling. An electrochemical model of the alkaline battery
is developed in COMSOL Multiphysics® and validated with discharge curves (i.e., voltage vs. time) obtained
under constant resistance loads. The electrode thicknesses are then optimized to maximize the energy density
of the battery while maintaining its exterior dimensions. The sensitivity of the energy density with respect to the
electrode porosities and interfacial areas is then analyzed. The electrochemical model was able to replicate the
discharge curves obtained under a 250 mA constant current discharge. The energy density is maximized by
decreasing the thickness of the zinc anode. However, this results in anode dissolution near the current collectors
and could compromise the electrical continuity in the battery. Increasing the anode thickness prevents
dissolution at the current collectors but increases unused mass in the battery. The results of this study can be
used to develop longer-lasting alkaline batteries. Furthermore, the model can be improved by considering
thermal effects or modified to aid the development of rechargeable alkaline batteries.
1. Introduction
The Zn-MnO2 primary alkaline battery has been widely used in portable low-power electronics, such as toys,
radios, and flashlights. It has dominated the market for single-use batteries, and its global market is expected
to grow by USD 494 million from 2020 to 2024 (Business Wire, 2020). Unfortunately, 90% of used primary
alkaline batteries end up in landfills due to their disposable nature (Edison et al., 2019). This has prompted
research on the recovery of valuable metals from spent primary alkaline batteries (Rarotra et al., 2020) and the
redesign of Zn-MnO2 into a rechargeable chemistry for grid-scale storage (Seo et al., 2018).
An alternative paradigm for increasing the utility of a primary alkaline battery is to maximize its energy density,
which can be achieved by optimizing the allocation of materials in the battery. This type of research has been
successfully performed for other battery chemistries via multiphysics modeling, which simulates a battery based
on fundamental laws in physics and chemistry. The model can then be optimized according to an objective
function, such as energy density. Hosseinzadeh et al. (2017) determined the thicknesses and porosities of
electrodes in a lithium-ion battery to maximize its energy and power density.
Moreover, multiphysics models can determine the distribution of quantities such as the concentration,
temperature, potential, material usage, and porosity in a battery. This lends insights on how the battery design
can be improved. For instance, Samba et al. (2014) used the electrode usage and temperature profiles in a Li-
ion battery to ascertain the best orientation and width of the current collector tabs in a lithium-ion battery.
Alagheband et al. (2017) designed current collector grids for lead-acid batteries to improve the uniformity of the
electrode potential and reaction current density.
Multiphysics models have been developed for primary alkaline batteries. Notable contributions include the work
of Sunu and Bennion (1980), in which the transport of zinc ions in zinc anodes were described, and the study
of Podlaha and Cheh (1994), wherein a multiphysics model of the Zn-MnO2 primary alkaline battery was
301
presented. There has also been interest from the industry to design batteries via multiphysics modeling, with
Chadderdon and Wendling (2019) from Energizer Holdings Inc. presenting their primary alkaline battery model
to the 2019 COMSOL Conference. Despite the numerous efforts on modeling primary alkaline batteries,
however, their optimization has yet to be performed.
In this work, the energy density of an AA primary alkaline battery was maximized via multiphysics modeling. A
multiphysics model of the battery was formulated in COMSOL Multiphysics® and validated with experimental
data. The operating mechanism (i.e., reactions and ion transport) of the battery over time was inferred by
analyzing the porosity and concentration profiles. Afterwards, batteries with varying anode and cathode
thicknesses were simulated, and the corresponding energy densities were calculated. The porosity profiles in
these alternative scenarios were also compared with those in the base scenario to reveal any changes in the
operating mechanisms. This study demonstrates the use of multiphysics modeling for maximizing the
performance of a primary alkaline battery, since design optimization was not performed in previous studies.
2. Methodology
This section first presents the experimental discharge curves. This is followed discussion on the multiphysics
model and the optimization of the primary alkaline battery.
2.1 Experimental data
The voltage vs. discharge curves considered in this work are those of an Energizer AA primary alkaline battery
as reported in its datasheet (Energizer, 2018). The 250 mA discharge curve was selected due to the moderate
discharge current.
2.2 System description
A schematic diagram of the primary alkaline battery is illustrated in Figure 1. At its core is a brass anodic current
collector, which draws electrons from the zinc anode during discharge. The zinc anode reacts with OH- from the
KOH electrolyte and oxidizes into Zn(OH)42- as shown in Eq(1). The Zn(OH)42- ion may precipitate into ZnO if
the OH- concentration is insufficient as given by Eq(2). At the cathode, MnO2 reacts with water and reduces into
MnOOH while generating OH- as described by Eq(3). Electrons for the cathodic half-reaction are supplied by a
steel current collector. The separator is made from polyvinyl alcohol (PVA).
Zn(s) + 4OH―(aq)→Zn(OH)2―4 (aq) + 2e
― (1)
Zn(OH)2―4 (aq)⇌ZnO(s) + H2O(l) + 2OH
―(aq) (2)
MnO2(s) + H2O(l) + e―→MnOOH(s) + OH―(aq) (3)
Figure 1: Schematic diagram of a primary alkaline battery.
2.3 Multiphysics model
The multiphysics model of the primary alkaline battery is illustrated in Figure 2. It consists of a 1D axisymmetric
model, which describes the mass and charge transport across the battery. This is coupled with particle-scale
models for each electrode. The anode has no specific geometry, but the particle-scale model tracks the volume
fractions of zinc and ZnO. The cathode is described using a core-shell model with MnO2 as the core and MnOOH
as the shell. The volume fraction of ZnO precipitate is also recorded by the cathode particle-scale model.
The mass and charge transport in the ternary system of K+, Zn(OH)42-, and OH- is modeled by Newman’s
concentrated solution theory, which considers the interaction between ions unlike the Nernst-Planck equation
(Newman and Thomas-Alyea, 2004). The mathematical formulation the mass and charge transport equations
302
differ for the anode, cathode, and separator, and are detailed by Podlaha and Cheh (1994). The anodic reaction
obeys Butler-Volmer kinetics as discussed in the work of Mao and White (1992), while the cathodic reaction
kinetics follows the core-shell model described by Podlaha and Cheh, (1994). Precipitation of ZnO occurs when
the Zn(OH)42- concentration exceeds its equilibrium with OH-. The formation of ZnO reduces the area available
for the anodic and cathodic electrochemical reactions and increases the mass transfer coefficient for ZnO
deposition on the electrodes (Podlaha and Cheh, 1994). The model also considers the changing porosities of
both electrodes due to the dissolution of zinc, precipitation of ZnO, and conversion of MnO2 to MnOOH.
Figure 2: The battery is treated as a 1D axisymmetric system (a). The zinc anode is not modeled as any specific
particle geometry, while the MnO2 cathode is described via a core-shell model MnOOH (b).
2.4 Input model parameters
The input parameters to the multiphysics model are presented in Table 1. The reference current density and
diffusion coefficient at the cathode were adjusted to fit experimental data, since the values of these parameters
for Energizer’s primary alkaline batteries are unknown. Moreover, there is notable uncertainty in these
parameters. The reference current density varies with the surface characteristics of the electrode. Meanwhile,
the diffusion coefficient in MnO2 cathodes has a wide range of values in reported literature (Podlaha and Cheh,
1994) and depends on the pore structure of the cathode particle (Farrell and Please, 2005).
Table 1: Input parameters to the multiphysics model.
Parameter Anode Separator Cathode
Thickness [cm] 0.361 [a] 0.025 [a] 0.230 [a]
Diffusivity in the solid phase [cm2 s-1] N/A N/A 8.00×10-11 [†]
Diffusivity of K2Zn(OH)4 [cm2 s-1] 6.00×10-6 [b] 6.00×10-6 [b] 6.00×10-6 [b]
Diffusivity of KOH [cm2 s-1] 2.19×10-5 [b] 2.19×10-5 [b] 2.19×10-5 [b]
Transport number of K2Zn(OH)4 0.04 [c] 0.04 [c] 0.04 [c]
Transport number of KOH 0.74 [c] 0.74 [c] 0.74 [c]
Electrical conductivity of the solid phase [S cm-1] 1.83×105 (Zn) [c]
0.01 (ZnO) [c]
0.00 (PVA)
0.01 (ZnO) [c]
19.8 (MnX) [c]
0.01 (ZnO) [c]
Electrical conductivity of the liquid phase [S cm-1] Correlation in [c] Correlation in [c] Correlation in [c]
Reference current density [A cm-2] 0.03 [b] N/A 1.00×10-5 [†]
Mass transfer coefficient of ZnO [cm s-1] 0.005 [c] 0.005 [c] 0.005 [c]
Mass transfer coefficient of K2Zn(OH)4 [cm s-1] 0.001 [c] 0.001 [c] 0.001 [c]
Initial concentration of Zn(OH)42- [mol cm-3] 5.34×10-4 [c] 5.34×10-4 [c] 5.34×10-4 [c]
Initial concentration of OH- [mol cm-3] 0.007 [c] 0.007 [c] 0.007 [c]
Initial volume fraction of the solid phase 0.26 (Zn) [c]
0.00 (ZnO)
0.20 (PVA) [c]
0.00 (ZnO)
0.76 (MnX) [c]
0.00 (ZnO)
Initial volume fraction of the liquid phase 0.74 [c] 0.80 [c] 0.24 [c]
Initial volumetric surface area [cm-1] 50 [c] 10 [*] 760 [a]
Equilibrium potential [V] 0 N/A Correlation in [c]
Equilibrium constant for ZnO dissolution Correlation in [c] Correlation in [c] Correlation in [c]
[*] Assumed [†] Fitted to experiment [a] (Chadderdon and Wendling, 2019) [b] (Mao and White, 1992)
[c] (Podlaha and Cheh, 1994)
2.5 Case studies
In the base scenario, the primary alkaline battery was simulated under a 250 mA constant discharge current.
The calculated voltage vs. time curve was compared with experimental data to validate the model. In addition,
the porosity and concentration profiles in the battery were generated to analyze changes in the battery during
discharge. The optimization was performed by simulating the battery under a 250 mA discharge current and
0.8 V cutoff voltage with anode thicknesses from 1 cm to 5 cm. For each anode thickness, the energy capacity
was calculated using Eq(4). The anode thickness that results in a battery with the highest energy content was
303
selected as the optimum. The separator thickness was held constant, while the cathode thicknesses were
adjusted so that the total thickness of the battery remains the same as in the base scenario. The porosity and
concentration profiles of these batteries were also investigated to determine if the battery’s operating
mechanism changes with the electrode thicknesses.
𝐸 =
𝑡dc
0
𝐼𝑉(𝑡) 𝑑𝑡 (4)
3. Results and discussion
3.1 Experimental validation
A comparison between the simulated and experimental voltage vs. time data is presented in Figure 3. The
discharge curve generated by the model follows the same trend as the experimental data, but the model
overpredicts the voltage. Zhang and Cheh (2004) attribute this to the discrepancy between the theoretical (i.e.,
Nernstian) and actual electric potential of the MnO2 cathode during discharge. Experiments by Kozawa and
Powers (1966) suggest that the deviation is caused by the formation of Mn2O3 instead of MnOOH towards the
end of discharge. The energy density according to experimental and simulated data are 2.86 Wh and 3.00 Wh,
respectively, which corresponds to a 4.93% error in energy density prediction.
Figure 3: Comparison between experimental and simulated voltage vs. time data.
3.2 Base scenario
The porosity and concentration profiles over time are shown in Figure 4. The porosity profiles show how the
solid phase compositions change over time. The ZnO precipitate has a larger molar volume than zinc, so a
porosity decrease in the anode and separator indicates a buildup of ZnO. Similarly, MnOOH has a higher molar
volume than MnO2, so a lower porosity implies a higher conversion or utilization of the cathode. ZnO deposition
at the cathode is negligible since the high concentration of OH- dissolves ZnO back into Zn(OH)42-. The zinc
anode dissolves into Zn(OH)42- near the anode-separator interface, which in turn precipitates into ZnO
throughout the anode and separator. Consequently, the Zn(OH)42- concentration profile is maximum at the
anode-separator interface, and diminishes towards the left of the anode-separator interface and in the separator.
The OH- concentration rises in the cathode since it is produced by the cathodic reaction, while it decreases in
the anode since it is consumed by the anodic reaction. In the anode, the OH- concentration is highest near the
separator since OH- is produced by the precipitation of Zn(OH)42-. It is worth noting that the porosity and
concentration profiles generated in this work are identical to those obtained by Podlaha and Cheh (1994).
Figure 4: Evolution of the porosity (a), Zn(OH)42- concentration (b), and OH- concentration (c) profiles in the
primary alkaline battery over time.
304
3.3 Optimization scenarios
The energy capacities and discharge curves of primary alkaline batteries with various electrode thicknesses are
presented in Figure 5. An anode thickness of 2 cm results in the highest energy density. The 1 cm anode
thickness is suboptimal due to discharge suddenly stopping after less than 10 hours of operation. On the other
hand, anode thicknesses of 3 cm and greater result in shorter discharge durations because the lower cathode
content results in MnO2 being converted to MnOOH at a faster rate.
Figure 5: Comparison of the energy capacity (a) and voltage vs. time curves (b) when the anode thicknesses
are varied from 1 cm to 5 cm.
The abrupt end of discharge in the battery with a 1 cm anode is explained by the porosity profile shown in Figure
6. The ZnO precipitate builds up at the separator, which stops the ionic current and ends the discharge. The
separator is plugged only under the 1 cm anode scenario since the small anode content and large cathode
content results in a larger Zn(OH)42- concentration increase and a smaller OH- concentration decrease per
coulomb of discharge. The low OH- concentration cannot stabilize the Zn(OH)42-, so more precipitation occurs.
This would also explain why the minimum porosity increases with the anode thickness.
The porosity profile of the battery with a 2 cm anode thickness shows that the anode dissolves not only at the
anode-separator interface, but at the current collector-anode interface as well. This is supported by the uptick
of Zn(OH)42- and drop-off of OH- concentrations near the current collector-anode. The additional anode
dissolution occurs due the smaller amount of zinc relative to the MnO2 content. Unfortunately, this increases the
likelihood of the zinc anode detaching from the current collector, which would render the anode unusable since
current cannot flow towards it. The battery would also cease operating if the anode were to be detached.
An anode thickness of 3 cm would therefore be the best compromise between performance and mechanical
stability. Based on the porosity profiles, the zinc anode is consumed near the separator and dissolution near the
current collector does not occur. Increasing the anode thickness further diminishes the energy content of the
battery since the MnO2 cathode is exhausted faster as suggested by the porosity profiles.
Figure 6: Comparison of the porosity (a), Zn(OH)42-concentration (b), and OH- concentration (c) profiles at the
end of discharge when the anode thicknesses are varied from 1 cm to 5 cm.
4. Conclusions
In this work, the energy capacity of an AA primary alkaline battery was maximized via multiphysics modeling.
The multiphysics model of the battery was formulated in COMSOL Mutliphysics®, and this was validated with
experimental data published by Energizer Holdings Inc. The reactions and ion transport in the battery were
determined by analyzing the porosity and concentration profiles. The optimization was then performed by
simulating batteries with various electrode thicknesses while taking note of their energy capacity. The porosity
profiles were also observed to reveal any changes in the reaction and ion transport mechanisms.
305
The multiphysics model was able to replicate the general trend of the experimentally measured voltage vs. time
data, although the model tends to overpredict the voltage. The porosity and concentration profiles show that the
zinc anode is consumed near the anode-separator interface, while ZnO deposits in the anode and the separator.
The optimization study reveals that a 2 cm anode maximizes the energy capacity of the primary alkaline battery,
however this also results in the dissolution of the zinc anode at the current collector-anode interface. This would
compromise the mechanical stability of the anode, hence a 3 cm anode thickness is recommended, despite its
lower energy capacity.
Nomenclature
𝐸 – energy capacity, Ah
𝐼 – current, A
𝑡 – time, h
𝑡dc – discharge time, h
𝑉 – voltage, V
Acknowledgments
The authors would like to acknowledge the Department of Science and Technology (DOST) through the Niche
Centers in the Regions for R&D (NICER) Program and The Commission on Higher Education – Philippine
California Advanced Research Institutes (CHED-PCARI) through the CIPHER Project (IIID 2018-008).
References
Alagheband A., Azimi M., Hashemi H., Kalani M., Nakhaie D., 2017, Optimization of grid configuration by
investigating its effect on positive plate of lead-acid batteries via numerical modeling, Journal of Energy
Storage, 12, 202–214.
Business Wire, 2020, Alkaline battery report – World market to hrow by USD 493.35 million by 2024, Business
Wire accessed 13.03.2022.
Chadderdon X.H., Wendling M.T., 2019, Mathematical modeling of primary Zn/MnO2 alkaline batteries,
COMSOL accessed 13.03.2022.
Edison T.N.J.I., Atchudan R., Karthik N., Xiong D., Lee Y.R., 2019, Direct electro-synthesis of MnO2
nanoparticles over nickel foam from spent alkaline battery cathode and its supercapacitor performance,
Journal of the Taiwan Institute of Chemical Engineers, 97, 414–423.
Energizer, 2018, Product datasheet Energizer E91, Enegizer
accessed 13.03.2022
Farrell T.W., Please C.P., 2005, Primary alkaline battery cathodes, Journal of The Electrochemical Society, 152,
A1930.
Hosseinzadeh E., Marco J., Jennings P., 2017, Electrochemical-thermal modelling and optimisation of lithium-
ion battery design parameters using analysis of variance, Energies, 10. 1278.
Kozawa A., Powers R., 1966, The manganese dioxide electrode in alkaline electrolyte: The electron-proton
mechanism for the discharge process from MnO2 to MnO1.5, Journal of The Electrochemical Society, 113,
870–878.
Mao Z., White R.E., 1992, Mathematical modeling of a primary zinc/air battery, Journal of The Electrochemical
Society, 139, 1105–1113.
Newman J., Thomas-Alyea, K.E., 2004, Electrochemical Systems, John Wiley & Sons, New Jersey, USA.
Podlaha E.J., Cheh H.Y., 1994, Modeling of cylindrical alkaline cells: VII. A wound cell model, Journal of The
Electrochemical Society, 141, 1751–1758.
Rarotra S., Sahu S., Kumar P., Kim K.H., Tsang Y.F., Kumar V., Kumar P., Srinivasan M., Veksha A., Lisak G.,
2020, Progress and challenges on battery waste management: A critical review, Chemistry Select, 5, 6182–
6193.
Samba A., Omar N., Gualous H., Capron O., Van Den Bossche P., Van Mierlo J., 2014, Impact of tab location
on large format lithium-ion pouch cell based on fully coupled tree-dimensional electrochemical-thermal
modeling, Electrochimica Acta, 147, 319–329.
Seo J.K., Shin J., Chung H., Meng P.Y., Wang X., Meng Y. S., 2018, Intercalation and conversion reactions of
nanosized β-MnO2 cathode in the secondary Zn/MnO2 alkaline battery, Journal of Physical Chemistry C,
122, 11177–11185.
Sunu W.G., Bennion, D.N., 1980, Transient and failure analyses of the porous zinc electrode: II. Experimental,
Journal of The Electrochemical Society, 127, 2017–2025.
306