One of the most crucial aspects relating to EFC development concerns design engineering. Since the first enzymatic fuel cell prototype, researchers have spent many efforts in optimizing cell design, with the purpose of reducing the distance between anode and cathode to increase power output. Main objective of this work is to present a comprehensive review on flow-based EFCs, which result to be promising applications for powering biosensors and wearable devices.
4.1. Microfluidic Configurations
Microfluidic enzymatic biofuel cells (MEFCs) are currently arousing great interest in the scientific world thanks to the continuous operating mode and the possibility to be integrated in various low-powered miniaturized bio-devices [
40]. Examples of application areas are in vivo operation to power sensing or micro-recording systems (as, for example, self-powered glucose biosensor), supercapacitors for energy conversion and storage or power generation in remote areas through wireless networks. The advantages obtained at the micro-scale with miniaturized EFCs include higher mass transfer and reaction rates, higher surface to volume ratio (SVR), lower reagent volume and power consumption, automated fluid delivery, faster response times and reduced operational costs.
Microfluidic technology uses fluids working in co-laminar regime: the Reynolds number (Re) related to fluid flow, which equates the inertial force to the viscous force, is typically lower than 2000. By establishing a co-laminar flow, the streaming interface between the fluids inhibits anolyte and catholyte mixing, allowing the development of membraneless configuration (M-MEFCs). In enzymatic fuel cell technology, there is a great incentive to eliminate the separator membrane, which induces high internal resistance, makes the cell bulky and costly and causes often the reduction of cell lifetime. Moreover, membrane can be toxic towards redox enzymes. Although the presence of a membrane separator can be generally avoided due to the specificity of redox enzymes, possible crossover reactions may induce enzyme inhibition by generation of reactive oxygen species, thus reducing the power output. On the other hand, the presence of a physical barrier impermeable to gases is strictly required in the particular case of H2/O2 EFCs, in order to avoid the risk of explosion.
In a microfluidic fuel cell system, the processed fluid volumes are very small, usually in the range from femtoliters (10
−15 L) to microliters (10
−6 L). The fluids are guided in micro-channels (diameter 1–1000 μm), where parameters, as capillary forces, surface and interfacial tensions, play important roles. Specifically, the viscous forces dominate the inertial forces: the fuel and oxidant flows can be conducted as parallel streams, establishing a virtual interface that physically separates the fluids, enabling at the same time the ionic exchange along the micro-channel. Fluids mix, due to diffusion phenomenon, is limited to a narrow interfacial zone, whose thickness can be controlled by the microchannel dimensions and flow rates [
5].
The distance between the two electrodes can be reduced to overcome problems related to the low diffusion of protons; moreover, different electrolytes can be used on the anode and cathode sides, optimizing pH value for each enzyme.
The specificity of enzyme catalysis allows the combination of fuel and oxidant streams in a single manifold [
5], with multiple benefits in terms of fuel cell design and operation. Firstly, the use of a proton exchange membrane can be avoided, thus eliminating the water management issues associated with PEM (Proton Exchange Membrane) fuel cell technologies. Furthermore, requirements related to sealing, manifolding and fluid delivery are significantly reduced [
10]. The optimization of electrical parameters leads also to the decrease of internal ohmic losses. The reaction kinetics for both anode and cathode can be improved by adjusting the fuel and oxidant streams composition, in order to obtain optimal enzymatic activity and great stability [
41].
An important feature of this technology is the reduced costs, also related to the absence of membranes, thus making enzymatic fuel cells competitive for small-scale power supplies with other conventional systems. On the other hand, biological enzymes are abundant, since naturally derived from organisms or produced using low-cost fermentation techniques. Other advantages are the possibility of operation at room temperature and the realization of compact units produced by well-established and often inexpensive microfabrication techniques [
41].
Microfluidic EFCs are compatible with simple microfabrication methods, such as soft lithography, prototyping xurography and paper-based technology. The fabrication process mainly employed to realize single microchannel is the soft lithography, while multi-level and 3D microfluidic systems can be based on the stacking of different technologies [
41]. Microfluidic prototypes manufactured with soft lithography technique are usually made in poly-dimethylsiloxane (PDMS), an inert elastomeric liquid organic polymer easy to handle and cost-effective, characterized also by important features for potential implantable devices, as biocompatibility, flexibility and transparency. Other polymers sealed to solid substrate, as glass or silicon, can be also used. Soft lithography procedure allows the design of microfluidic enzymatic cells with different geometries: T-shaped, Y-shaped or I-shaped. For what concerns soft-lithography, a sustained power production from continuous flow-through EFC up to one month without the use of external redox mediators has been demonstrated in [
42].
Xurography technique allows the fast realization of very thin microstructures (down to 20 μm) using various flexible polymer films. In paper-based devices, fluids flow via capillary action through a passive liquid transport without the need of an external pressure source. A fully wetted flow regime is established whose flow rate depends only on the paper type. Porous filter papers are used as matrix, frequently by attaching an absorbent pad at one end of a paper strip in order to realize a self-pumping. These microfluidic systems are biocompatible, disposable and cost-effective. They also present good compatibility with many chemicals and can be combined with other low-cost materials, such as plastics, to offer additional mechanical support.
4.1.1. 3D-Printing MEFCs
3D-printing technology has been recently applied to MEFC systems. This fabrication method is particularly suited for the realization of micro-channels for miniaturized devices and allows also the production of many types of composite materials. It also offers many advantages, since is simple, cost-effective and time-efficient, eliminating the requirement of post-processing activities [
43]. In [
42], the authors demonstrate a sustained power production from continuous flow-through enzymatic biofuel cells for periods of up to one month without the use of external redox mediators. Two different designs carried out by means of 3D printing were compared for use in blood vessels (
Figure 4). Indeed, the continuous flow through operation leads to the benefit by having higher concentrations of glucose and oxygen by means of uninterrupted supply of blood. The electrodes were made by highly porous gold (hPG) because of their remarkable properties, such as high conductivity, non-toxicity, large surface area, three-dimensional open porosity and biocompatibility.
In the first design, the anode and the cathode are fit in two parallel channels separated by a PDMS wall (
Figure 4A). The second design is characterized by a single channel containing the two electrodes, which are positioned so that the electrolyte would flow over the cathode and the anode sequentially (
Figure 4B). Nevertheless, these designs show, with reference to the polarization curves in
Figure 5, an OCV 90 mV lower, due to the back diffusion of H
2O
2 to the cathode that causes an electrochemical short-circuit at the Laccase electrode. Both configurations were tested by continuously feeding with an aerated PBS (phosphate buffered saline) solution containing 27 mM glucose, at a rate of 0.35 mL/min and under the constant temperature of 37 °C.
Moreover, configuration A was assessed as more stable during the time, exhibiting continuously an enzymatic activity for a period up to 1 month, as evident in
Figure 5 in terms of registered power output.
The power output of miniaturized MEFCs can be improved through cell stacking. In [
44] a micro-EFC stack composed of 3D printing four cells is realized with an air-breathing cathode design: the channels, made of silicone elastomer film, are contained between two plates made of poly-methyl methacrylate (PMMA), with two separated inlets for the anolyte and the catholyte (
Figure 6). The same electrolytes and fuel are reused for all the cells, obtaining a cascade-style microfluidic device: the resulting decrease in glucose concentration doesn’t affect system performance, since a very low amount of fuel is used in each enzymatic cell, limiting, at the same time, the cross-over phenomenon. The cells in the stack are connected employing different configurations, as series, parallel or combined series/parallel, as indicated in
Figure 6.
The maximum open circuit potential (OCP) (1.27 V) was achieved in series configuration, while the highest current density (2007 µA cm−2) and power density (579 µW cm−2) are obtained in the case of parallel connection. As interesting output of this research activity, the parallel-series (P-S) connection is characterized by a voltage close to the serial configuration (1.23 V). Generally, the OCP values obtained were lower than the expected ones according to Kirchhoff’s law, due to the different performance and the high total resistance of each individual cell and the presence of shunt currents between cells. Potential applications of the system are devices that demand low currents and a voltage above 1.2 V, as an alternative to the use of boosters or current transformers.
4.1.2. Soft Lithography MEFCs
Another design based on laminar flow is illustrated in [
45]. The authors developed a device fabricated using a two-part PDMS elastomer and a standard soft lithography method (
Figure 7). This cell consists of a Y-shaped microfluidic channel in which fuel and oxidant streams flow laminarly in parallel at gold electrode surfaces. At the anode, the glucose is oxidized by the enzyme GOx whereas at the cathode, the oxygen is reduced by the enzyme Laccase, in the presence of 2,2-azinobis (3-ethylbenzothiazoline-6-sulfonate) (ABTS) redox mediators. In this work, a sensitivity analysis was carried out concerning the evaluation of the optimal flow rate in order to enhance the current density of the cell by limiting the mass transport effect, while accepting a convective mixing in a narrow depletion boundary layer. Specifically, the OCV of 0.55 V and a current density up to 0.69 mA cm
−2 were registered. The maximum power density (obtained with a flow rate of 1000 µL/min) delivered by the assembled biofuel cell reached 110 µW cm
−2 at 0.3 V with 10 mM glucose at 23 °C.
4.1.3. Xurography MEFCs
Xurography technique, frequently used for MEFCs manufacturing, is based on the use of a cutter plotter applied on thin and flexible, adhesive or double adhesive, polymer films. The width and length of the microfluidic channel is defined by the patterning process, whereas the height of the channel is related to the thickness of the film. Therefore, this fabrication process is easier and significantly less expensive than conventional photolithography-based methods, avoiding clean room facilities, costly photomask and photoresists [
41]. The related microfluidic EFC devices are compact micropower sources, able to deliver power output in a minimum volume, thus favoring the scale-up of the manufacturing process. Moreover, xurography method is very fast, allowing the production of microfluidic chips in a few minutes. The first developed membraneless glucose/O
2 microfluidic biofuel cell with laminated materials based on adhesive polymer led to the realization of a device constituted by a single Y-shaped microchannel with immobilized enzymes on pyrolyzed photoresist film electrodes.
By using the xurography methodology, it is also possible to realize 2D and multi-level microfluidic enzymatic cells, constituted by arrays of microchannels both in series or parallel configurations [
41]. The fabrication process of the microfluidic device implicates the stacking of double-sided adhesive tape layers alternated to transparent sheets and equipped with appropriate holes to connect the microchannels for substrate feeding. The multi-level microfluidic enzymatic cell is developed in order to increase the power delivered by a single device in a minimum volume, operating with glucose and oxygen solutions (
Figure 8). Two electrode configurations are used, with the electrodes connected in series, to maximize the voltage (
Figure 8a) and in parallel, to increase the electrical current (
Figure 8b). Two layers of double-face adhesive film are successively deposited, one to form the microchannels in contact with the electrodes and the other to obtain the correct distribution of fluids, which flow both vertically and laterally without mixing (
Figure 8c). The two double-face adhesive films are then sealed by means of two semi-rigid transparent films, obtaining the final structure of the enzymatic device shown in
Figure 8d.
The experimental results show that the system is 183% more efficient, in terms of maximum delivered power, than the 2D device based on a single microchannel with the same chemical energy and the same number of inlet and outlet holes. The interest on this multi-layer system relies on the maximization of power output in a minimum volume, which is an important challenge for microfluidic biofuel cells operation. The choice between the two configurations depends on the target application and the input resistance of the system supplied by the EFC.
4.1.4. Paper-Based MEFCs
A different approach towards the development of a cost-effective enzymatic glucose/O
2 microfluidic fuel cell is the realization of a paper-based system, in which the fluid transport is based on capillary action [
40]. An advantage of paper-based matrixes as substrates for microfluidic fuel cells is their intrinsic capability of establishing laminar flow, so that fuel and oxidant streams can flow in parallel without mixing. The capillary flow of reactants allows the movement of liquids without outer pressure sources, thus avoiding the power requirements of external equipment. An important property of the papers selected as substrate for the systems is a high wicking rate, normally obtained by attaching an absorbent pad at one end of a paper strip: the liquid moves through the strip and fills it, reaching the wicking pad and establishing a fully wetted flow regime. In paper-based fuel cells, the increase of cathode dimension with respect to the anode, to compensate the lower activity of oxygen reduction enzymes and the low solubility of oxygen in liquid media, is not feasible, since the planarity of the electrolyte moving in a thin layer of paper imposes a reduced distance between the electrodes, in order to minimize the resistance of the electrolyte [
46].
Regarding system design, in [
40] the enzymatic cell is supported on a glass slide: the electrodes of the microfluidic cell are made of carbon paper (active area 0.10 cm
2), and their outer parts are connected using a conducting copper foil (
Figure 9). Two possible configurations, Y-shaped and I-shaped, can be implemented. The most common paper-based system typology is the Y-shaped cell, constituted by two separated inlets for the reactants, resulting in two parallel flows. In order to achieve simplicity in use, in the I-shaped configuration both fuel and electrolytes are added together in the inlet stream, combining in a single flow anolyte and the catholyte components. Therefore, the fuel cell has to work with a single electrolyte using a specific pH value (sodium phosphate buffer solution at pH 5.5), which represents a compromise between anolyte (pH 4.5) and catholyte (pH 7.4) requirements. Glucose oxidase from Aspergillus niger and Laccase from Trametes Versicolor are selected as anodic and cathodic enzymes respectively.
The experimental results evidence, for the I-shaped cell, a maximum open circuit voltage of 0.55 V and maximum current and power density of about 225 µA cm
−2 and 24 µW cm
−2, respectively (
Figure 10). Even if system performance decreases compared to the Y-shaped configuration, the single-stream microfluidic cell can be easily implemented in a real application. These paper-based fuel cells can become an alternative for supplying energy to power microelectronics with low power consumption demand, for example small single use point-of-care devices.
Another interesting system design is reported in [
46]. The device consists of a thin paper strip acting as flow channel and a circular paper piece, constituting the absorbent pad, placed at one end of the paper strip (
Figure 11). Glass fiber characterized by uncompact filaments is used as channel material, thus realizing a capillary flow with very low fluidic resistance. The absorbent pad is made of cellulose: a constant capillary pressure is established, thus obtaining a homogenous fluid front. The flow channel and the absorbent papers are assembled on a transparent poly methyl methacrylate (PMMA) holder, used for fluid storage. In this microfluidic system, operating in physiological conditions (5 mM of glucose and pH 7.4), the liquid moves by capillarity through the first paper strip, in contact with the electrodes, and then reaches the absorbent pad. When the wet volume of paper increases, the fluid front moves from the reservoir; at the same time, the increase of viscous forces decelerates the movement of the fluid. On the other hand, the circular geometry of the absorbent pad enhances the total fluid front surface area as it is pulled into the absorbent material, thus improving the capillary driving force. These two opposing forces allow the realization of a quasi-steady flow rate inside the system. Different flow rates have been obtained by modifying the paper materials that constitute the adsorbent pad of the device. The experimental results demonstrate that an increase in the amount of power and current extracted in a paper-based fuel cell can be attained establishing a quasi-steady capillary flow. Moreover, it has been proved that the convective mass transport induced by the capillary flow improves the overall fuel cell performance.
4.1.5. Microfluidic Fuel Cell Modeling
Mathematical models are often used to understand, predict and optimize the performance of enzymatic electrodes and complete biofuel cells as a function of main experimental parameters, such as the amount of substrates, the loading of biocatalysts, the diffusivity of the different species, the effectiveness of the used strategy for enzyme immobilization and the influence of mediator species or possible inhibitors [
37]. The aim is the enhancement of microfluidic enzymatic fuel cell structure, in order to provide guidelines for the realization of novel architectures in the design and fabrication techniques and to reduce the time involved in prototyping, building and characterizing the actual devices [
6].
Numerical CFD models of microfluidic enzymatic fuel cells are present in literature, including Navier–Stokes equations for conservation of mass and momentum, the equation for mass conservation of solute species and the equation for the current. The first computational study related to the MEFC technology investigated the complex mechanism involving species transfer, heterogeneous chemical reactions and enzyme kinetics based on microchannel geometry [
5]. The authors tested different enzyme patterning strategies, involving both spatially distributed or mixed enzymes on the electrode surface, with the purpose to optimize overall current density and fuel utilization. According to the model, a decrease of flow rates leads to fuel utilization improvement, while higher enzyme turnover numbers are responsible for the enhancement of system performance. Enzymatic fuel cell activity was shown to be limited by the reaction rates associated with enzyme kinetics, rather than by diffusion phenomena. Consequently, system optimization can be achieved implementing mixed enzyme patterning tailored with respect to individual turnover rates, enabling high current densities combined with nearly complete fuel utilization.
Regarding oxygen reduction reaction in MEFCs, an interesting simulation study, realized by solving the governing 3-D conservation equations related to flow and species transport, reveals that oxygen availability limits the performance of the cathode [
47]. Specifically, an exponential decay in oxygen availability is observed along the length of the microchannels, consistently with experimental observations. The increase of electrolyte flow rates leads to the reduction of the diffusion boundary-layer thickness. Consequently, a decrease of oxygen mass transfer resistance is attained, thus improving mass transport phenomena at cathodic side. However, disparity between anolyte and catholyte flow rates can induce wastage of dissolved oxygen.
Modeling can also be helpful to clarify the complex effects regarding electrochemical aspects and mass transfer in MEFC components. The first developed CFD based model for microfluidic fuel cells considered a T-shaped microchannel using tapered electrodes and proposing methods to improve fuel utilization. Theoretical models for the electrochemical kinetics have also been proposed, considering Y-shaped or F-shaped microchannels. In [
48], the work focuses on the development and validation of a complete computational model applied to a microfluidic fuel cell with flow-through porous electrodes. The model takes into account the main phenomena present in a microfluidic fuel cell, including fluid flow in microchannels and porous media, electrochemical kinetics and mass transport, investigating both individual half-cells (anode and cathode) and the entire fuel cell.
4.2. Non-Microfluidic Configurations
A particular membraneless fully enzymatic cell integrating a flow-through anode and an air-breathing cathode (
Figure 12) was described in [
49]. Fuel was pumped within the cell through a peristaltic pump at a flow rate of 3 mL/min. Specifically, two anodic NAD+-dependent dehydrogenase enzymes (MDH-malate dehydrogenase and ADH-alcohol dehydrogenase) were compared in continuous flow-through operation with the same cathodic enzyme (Laccase).
For ADH-Laccase EFC, the biofuel cell sustained an OCV of 0.618 V, slightly higher than that of the MDH-laccase biofuel cell (0.584 V). The maximum power density was determined to be about 26 µW cm−2 at 0.372 V, which is almost three times higher than that obtained for the MDH-laccase biofuel cell (9 µW cm−2). Furthermore, MDH-Laccase demonstrated some limitations in the anode performance that were reflected in a lower limiting current (~65 µA) with respect to the ADH-Laccase (~160 µA). The higher performance of the ADH-Laccase is attributed to higher enzymatic activity of ADH.
A particular glucose/O
2 biofuel cell system was also realized using a concentric configuration [
21], constituted by two tubular electrodes with the cathode inserted in the anode (
Figure 13). The electrolyte (10 mM of glucose in a Nitrogen saturated PBS solution, pH 7.4) is contained in the annular area between the electrodes and glucose oxidation is performed in the inner surface of the anode by glucose oxidase (GOD). At the same time, an O
2 saturated solution continuously circulates through the internal cavity of the biocathode, where oxygen is reduced by BOD. The peculiar design allows anode and cathode chambers separation: the dissolved oxygen flows without a direct contact with the electrolyte, thus avoiding the undesired hydrogen peroxide formation due to secondary reactions at the anode side. The electron transfer was assisted by anodic and cathodic mediators (8-hydroxyquinoline-5-sulfonic acid hydrate, HQS and 2,2-azinobis-3-ethylbenzothiazoline-6-sulfonate, ABTS2-diammonium salt respectively) co-immobilized with the corresponding enzymes on carbon-based electrodes by means of polypyrrole films obtained by electropolymerization.
The optimized biofuel cell (bioanode modified by a 2 µm thick polypyrrole film followed by glutaraldehyde treatment to favor enzyme cross-linking and biochatode modified by a 1.4 polypyrrole film without enzyme cross-linking) was operated at OCV 0.44 V, obtaining a maximum power density of 42 µW cm
−2 at 0.30 V. The experimental results obtained for the optimized biofuel cell are indicated in
Figure 14.
The overall performance of enzymatic biofuel cells is the consequence of the interaction between several physical and bio-electrochemical phenomena, as species transport, enzymatic reactions and heterogeneous electron transfer processes between the electrode and the enzyme or a mediator, in the cases of DET and MET, respectively. Modeling and simulation of these processes allows understanding and optimizing the performance of enzymatic electrodes and consequently of the entire fuel cell. Specifically, the focus involves the mathematical resolution of the corresponding non-linear reaction–diffusion problems [
38,
50], including reaction and transport kinetics, statistical analysis and metabolic control analysis. Theoretical, numerical and experimental methods for estimating the biofuel cell performance was discussed by various authors. In [
51], the authors modelled the effects of convective flux and temperature on the performance of an enzymatic glucose fuel cell based on flow design. The cell employs a cation exchange membrane and glucose oxidase enzyme at the anode. The model schematizes the cell as a plug flow reactor, assuming total lateral mixing for glucose and hydrogen ion transfer through the cell. The glucose fuel cell domain is consequently reduced to one dimension and is divided into five sections: the anode diffusion layer (ADL), the enzyme layer (EL), the anion exchange membrane, the cathode catalyst layer (CCL) and the cathode diffusion layer (CDL) (
Figure 15). The model assumes that the membrane is only permeable to hydrogen ions and not to glucose; moreover, glucose reacts exclusively in the enzyme layer at fuel cell anodic side in presence of GOx enzyme, and the transport of glucose is only due to diffusion and convection.
Figure 16a shows the variation of glucose concentration with time across the half-cell composed by anode diffusion layer, enzyme layer and membrane, as a function of inlet glucose concentration and inlet flow rate. At the first time step, a rapid drop in glucose concentration profile across the ADL occurs, due to limitations to diffusion phenomenon. Then, the concentration profile across the ADL increases with time and becomes stable.
Figure 16b shows the variation of glucose concentration across the ADL, the EL and the membrane as a function of inlet glucose flow rate, revealing a drop in glucose concentration in the enzyme layer, due to the reaction with glucose oxidase enzymes. At the increase of flow rate, the diminution in glucose concentration in EL is less marked, depending on the reduced contact time between the enzyme and the substrate. On the contrary, across the ADL, no drop is observed in the concentration of glucose species, since the high flow rates determine a well-established convective flux that overcomes the diffusive one.
Figure 16c illustrates the variation of glucose concentration across the ADL, the EL and the membrane as a function of temperature. The concentration of glucose remains almost constant in ADL, depending on the high value of the diffusion coefficient established in the range of the investigated temperatures. Differently, the glucose concentration drops across the EL at operating temperature increase: Increasing system temperature, the reaction rate in the enzymatic cell is strongly enhanced and, consequently, higher consumption rate of glucose molecules is observed.
The variation of hydrogen ions across the enzymatic cell (anode diffusion layer, enzyme layer, membrane, cathode catalyst layer and cathode diffusion layer) can be seen in
Figure 17, assuming a complete consumption of hydrogen ions at the cathodic side (CCL and CDL). In
Figure 17a, the concentration of hydrogen ions increases in the enzyme layer, since they are generated by the glucose oxidation reaction. Then, hydrogen ions concentration sharply decreases in the cathode catalyst layer, due to H- consumption for the cathodic reduction reaction. The occurrence of hydrogen ions in the anode diffusion layer evidences also a backward diffusive flux, caused by the presence of a potential across the cell. The peak concentration of hydrogen ions is observed roughly near the enzyme layer at steady state, since migration and cathode kinetics become dominant factors, reducing the effect of diffusion phenomena and generation of hydrogen ions in the enzyme layer [
52].
Figure 17b shows the variation of hydrogen ions across the enzymatic cell as a function of temperature: Higher operating temperature results in higher concentration of hydrogen ions in the enzyme layer, depending on the enhanced diffusive flux and reaction rate, as in the case of glucose concentration variation along the cell. Hydrogen ions concentration is also improved at the increasing of enzyme layer thickness, because, in this case, more sites for oxidation are available, resulting in higher H- generation.
Near the cathode region, the concentration of hydrogen ions is higher initially, mainly due to slower migration rate. When the system approaches steady state, migration and cathode kinetics become dominant factors, reducing the effect of diffusion and generation of hydrogen ions in the enzyme layer. Due to the interplay of these competing phenomena, the peak concentration of hydrogen ions is observed roughly near the enzyme layer at steady state.
Another interesting approach for modeling enzymatic fuel cells was presented in [
53]. In a theoretical study, the authors investigated possible kinetic limitations in an osmium-mediated glucose oxidase/laccase enzymatic biofuel cell by means of metabolic control analysis (MCA) methodology. Oxygen concentration in the cathodic solution represents a crucial parameter for enzymatic fuel cell operation, since oxygen is required at the cathode, but it participates in a non-productive reaction at the anode. The total mediator and oxygen concentrations have opposing effects on the distribution of control between the two electrodes. Increasing the total mediator concentration shifts the control to favor the GOx anode under most operating conditions, so that fuel cell performance appears to be dominated by the anode. On the contrary, the increase of oxygen concentration shifts the control to favor laccase at the cathode. Between these two limiting cases, a distribution of control between the two enzymes can be observed. Therefore, selecting specific conditions, the enzymatic biofuel electrodes can operate under a balanced control distribution over the current production, thus improving fuel cell stability.
A mathematical modeling based on Homotopy perturbation method is reported in [
50] for an enzymatic glucose membraneless fuel cell with direct electron transfer. The solution of the time independent non-linear reaction-diffusion differential equations describing glucose concentration and hydrogen ions concentration, both inside and outside the enzyme layer, led to the estimation of fuel cell kinetic parameters and their effect on power density. Moreover, these analytical solutions are compared with zero order ones.