Influence of temperature and other system parameters on microbial fuel cell performance: numerical and experimental investigation

This study presents a steady state, two dimensional mathematical model of microbial fuel cells (MFCs) developed by coupling mass, charge and energy balance with the bioelectrochemical reactions. The model parameters are estimated and validated using experimental results obtained from five aircathode MFCs operated at different temperatures. Model analysis correctly predicts the nonlinear performance trend of MFCs with temperatures ranging between 20 C 40 C. The two dimensional distribution allows the computation of local current density and reaction rates in the biofilm, helping to correctly capture the interdependence of system variables and predict the drop in power density at higher temperatures. Model applicability for parametric analysis and process optimization is further highlighted by studying the effect of electrode spacing and ionic strength on MFC performance. ∗Corresponding author Email address: s.gadkari@surrey.ac.uk (Siddharth Gadkari)


Introduction
A microbial fuel cell (MFC) uses the growth and metabolic activities of microorganisms (such as exoelectrogenic bacteria) to directly convert the chemical energy in organic wastes to electricity [1]. Air-cathode MFCs in particular have been extensively researched for efficient power generation, as they help avert the need to aerate the water for the oxygen reduction reaction (ORR) at the cathode [2][3][4]. The bioelectrochemical system designed to make the energy transfer possible in an MFC involves a complex interplay between standard electrochemical kinetics and transport phenomena (fluid flow, mass & energy transfer) with biologically catalysed redox reactions [5,6]. As one would assume, the involvement of microorganisms adds to the complexity and also significantly increases the number of variables that affect the performance of these systems. In order to design efficient MFCs for electricity production and reduction of the effluent chemical oxygen demand in wastewater, the effect of the different parameters on the MFC performance must be better understood [5,[7][8][9].
One important parameter for MFCs is the operating temperature. It has been shown that temperature has a strong influence on many variables such as the conductivity of substrate solution (or wastewater), diffusion coefficient, charge transfer rates, activation energy, biochemical processes of the microbial communities, etc., the combined effect of which can significantly alter the MFC power output [6,10]. And while there have been some studies to understand the effect of temperature, there is no consensus [4,[11][12][13][14][15][16][17][18].
Liu et al. [4] used an air-cathode MFC with acetate as the substrate and observed a 9% decrease in maximum power density when the MFC operating temperature was reduced from 32 o C to 20 o C. This decrease was mainly attributed to the corresponding reduction in cathode potential. Moon et al. [11] investigated the effect of temperature on the performance of a "Sensortype" two chamber MFC fed with artificial wastewater (AW) and observed a rather nonlinear trend. The power output of MFC showed a slight increase as temperature was raised from 24 o C to 35 o C, but showed a decrease at higher temperatures, 38 o C and 41 o C. This nonlinear behaviour was associated with the changes in ohmic overvoltage [11]. Feng et al. [12] used full-strength beer brewery wastewater in an air-cathode MFC and observed a 17% decrease in power output when temperature was decreased from 30 o C to 20 o C. Their analysis showed that the primary reasons for the decrease was mainly the reduced performance of the cathodic reaction and not so much the biological effects at the (bio)anode [12].
Patil et al. [13] showed that the performance of the biofilms at any specific operation temperature is a strong function of the original incubation temperature during initial biofilm growth.They also showed that irrespective of the incubation temperature, bioelectrocatalytic steady state current densities decrease for operating temperatures above 40 o C, except for biofilms incubated at 35 o C, which show growth in performance with temperatures as high as 45 o C.
Min et al. [14] used a two-chamber MFC with domestic wastewater mixed with acetate as the substrate and observed ∼ 34% decrease in maximum power density as the operating temperature was reduced from 32 o C to 20 o C. This is starkly different from the 9% decrease observed by Liu et al. [4] in the same temperature range, and can be mainly ascribed to the different Given the complex interaction of temperature with other variables of the system, it is important to accurately quantify these variations and study local changes in the biofilm and the reaction chamber at different temperatures, something which is difficult with experiments but can be performed in a directed way using mathematical models [19][20][21][22][23]. One of the very few numerical studies where the effect of temperature on MFC was studied is the one by Oliveira et al. [24]. They coupled the heat, charge and mass balances with the bioelectrochemical reactions in the MFC to develop a onedimensional steady state mathematical model. This computational study predicted a simple linear increase in power density as temperature was increased from 20 o C to 30 o C and then 40 o C [24]. However the results were not corroborated with any experimental data and are not in accordance with the results observed by Moon et al. [11] and Li et al. [17] at temperatures above 37 o C.
In this work, we have developed a 2D mathematical model to better quantify the process-parameter relationships and obtain a deeper insight on the effect of temperature on MFC performance. The model predictions are validated using experimental results based on a single chamber MFC with air-cathode. Effect of electrode spacing and ionic strength is also studied to highlight the broader applicability of the mathematical model. Its mean pore size is 28.9 µm and porosity is 78 ± 5%. SS electrodes were first sonicated in acetone and ethanol for 15 minutes, thoroughly rinsed with distilled water and dried prior utilization. FO-SS electrodes were prepared as described in a previous study [25]. Briefly, oxidation of SS was conducted using the blue flame of a Bunsen burner fed with natural gas. Each side of the electrode was oxidized for about 30 seconds before being rinsed and dried.

Electrodes preparation
Carbon paper with gas diffusion layer (GDL) was purchased from Quintech (H2315 I2 C6, Göppingen, Germany) and further coated with 0.5 mg cm −2 Pt/C to be used as GDE.

MFC reactors and operation
Four identical single-chamber membraneless air-cathode MFCs were con- It was assumed that mature bioanodes were developed after 3 stable consecutive cycles were obtained. Polarisation tests were always carried out at

Numerical methods and calculations
The air-cathode membraneless MFC is modeled using a steady state two dimensional model, coupling bioelectrochemical kinetics with mass, charge and heat transfer. Schematic of the modeling domain is presented in figure   1. The biofilm is assumed to be present on either side of the anode and is modeled here as a porous conductive matrix [27][28][29]. The anolyte can per-meate the porous matrix where the bacteria oxidize the substrate to release electrons and hydrogen ions.
The mathematical model is based on the following assumptions: Biofilm is made up of a solid porous conductive matrix, with a fixed conductivity, σ bio . pH is strictly controlled.
Substrate is assumed to be ideally mixed in the anolyte and substrate gradient only exists in the biofilm.
A concentration boundary layer exists between the biofilm matrix and the anolyte, and exhibits linear concentration profiles.
Microbial population in the biofilm of the anode is uniformly distributed.
Equilibrium has been reached between microbial growth, decay and washout, maintaining a steady-state biofilm of fixed thickness.
Acetate and CO 2 remain in the anode chamber and do not diffuse to the cathode assembly. Similarly air does not diffuse in the anodic chamber.
Acetate is the only electron donor substrate in the anolyte.
The analysis assumes the following oxidation and reduction reactions at anode and cathode respectively:

Ohm's law and charge transfer kinetics
As described above, the biofilm is assumed to be a porous matrix capable of conducting electrons generated through substrate oxidation to the anode.
A porous electrode is typically characterized by distinct electrode and electrolyte phases. In the biofilm matrix, the biomass components (made up of bacteria, the extracellular polymeric substances (EPS) and nanowires) are the solid conducting phase. The liquid anolyte (substrate solution) enters the porous biofilm matrix where the substrate is oxidized by the bacteria.
The biofilm matrix works as a porous electrode and can be characterized by two separate current balances, one for the solid phase and one for the liquid electrolyte phase [30].
The transfer of electrons in the solid phase and the transfer of ions (protons in this case) in the electrolyte phase, both are governed by Ohm's Law.
where, I is the current density, σ is conductivity, ϕ is potential and i is the current source term.
The specific current generation due to electrons and ions in case of porous electrode is expressed as follows: where, the subscripts s and l refer to the electrode phase and electrolyte phase respectively. The effective values of conductivity (σ eff ) for the two phases are calculated based on Bruggeman model: where, s and l represent the volume fraction of the electrode and electrolyte phase respectively.
Current density in the porous biofilm matrix is a function of substrate concentration, biomass concentration and overpotential (which can be derived from Butler-Volmer equation). Assuming substrate consumption by bacteria is governed by Monod kinetics, the charge transfer kinetics at anode can be described as in Eq. 9 [30,31].
where, C s is concentration of the substrate, K sa is half max-rate substrate concentration, C x is the anodophilic bacteria concentration, α a is anodic transfer coefficient, F is Faraday's constant, η is overpotential, R is ideal gas constant, T is temperature, i 0,a is the forward rate constant of anode reaction at standard conditions.
The air-cathode used in the microbial fuel cell is a gas diffusion electrode (GDE), a special type of porous electrode which in addition to the catalyst/electrode layer also contains a gas pore phase (gas diffusion layer, GDL) that is inert to charge transfer. Air (mixture of oxygen, nitrogen and water vapor) diffuses through the GDL to the catalyst/electrode layer where oxygen is reduced to produce H 2 O.
The current density at the cathode can be described using concentration dependent Butler-Volmer equation, as in Eq. 10.
where, i 0,c is the cathode reference exchange current density, C O 2 is the con- The overpotential (η) is a function of electrode potential, electrolyte potential and the equilibrium potential of the charge transfer reaction at the particular electrode (E eq ) and is described as in Eq. 11.

Mass transport of substrate in the biofilm
Substrate is assumed to be completely mixed in the anolyte solution.
Gradient of substrate in the biofilm is expressed as is Eq. 12.
where, D eff,a is the effective diffusion coefficient, a a is active specific surface area of anode, n(= 8) is the number of electrons involved in acetate (substrate) oxidation.
As substrate cannot penetrate the solid anode, no-flux boundary condition (Eq. 13) is applied at the interface of the biofilm with the anode.
Flux continuity condition (Eq. 14) is applied at the interface of the outer surfaces of the biofilm with the anolyte, assuming a concentration boundary layer of thickness 'L' at the interface.
where, C s,bulk is the concentration and D a is the diffusion coefficient of the substrate in the bulk anolyte.

Mass transport at air-cathode
Mass transfer of air (consisting of oxygen, nitrogen and water) through the GDE (cathode) is expressed using the mixture-averaged diffusion model (Eq. 15): here, where, the subscript i refers to the different chemical species (O 2 , N 2 and H 2 O), ω refers to mass fraction, ρ denotes the mixture density, p,c porosity of the GDE, D m i refers to mixture-averaged diffusion coefficient, D i,k refers to multicomponent Maxwell-Stefan diffusivities, D e ik refers to effective multicomponent Maxwell-Stefan diffusivities, x k refers to mole fraction of species k, M is the mean molar mass, τ F is the fluid tortuosity factor (= −1/3 p,c , based on Millington and Quirk model [32]).
Reaction rates of the different species (R i ) are only applied in the catalyst/electrode layer.
where a c is the active specific surface area of cathode.
Air is assumed to be constantly present at the open boundary where the diffusion layer of the cathode assembly is exposed.
It is assumed that air does not pass into the anodic chamber, thus a no flux condition (Eq. 24) is applied at all boundaries expect the open boundary exposed to air.

Heat transport
Heat is generated in the microbial fuel cell due to the irreversible activation losses and the voltage losses during charge transport in the electrolyte and the solid conducting materials.
The steady state governing equation for heat transport in the MFC for the 2D model, is given as in Eq. 25: where, d z is the thickness of the MFC in the z-direction (the component perpendicular to the 2D domain), k is the thermal conductivity and Q h is the heat source.
In the porous electrodes, an effective conductivity, k eff , is calculated based on solid (k s ) and electrolyte (k l ) conductivities as follows: The total heat source (Q h ) is a combination of Joule heating due to charge transport (Q j,h ) and the heat generated due to the electrochemical reactions (Q r ), and are defined as in Eqs. 27-29: where the subscript r refers to either, a, for anode or, c, for cathode.  Parameter estimation: PDE solver, COMSOL, capable of handling coupled physics [33] was used for solving the numerical model. Best-fit regression analysis based on Nelder-mead simplex optimization method was used to determine the model parameters [19]. The objective function was defined as the difference between theoretical and measured power density values as a function of current density.   Some studies in the past have investigated the influence of temperature on MFC performance [4,[11][12][13][14][15][16][17]. For example, Liu et al. [4], Feng et al. [12] and Min et al. [14], all observed a linear increase in power output as the     does not lead to any significant heat generation, which is expected considering the small current densities in MFC systems.

Effect of other system parameters on MFC performance
Along with temperature, several other design and operational parameters affect the MFC performance including the ionic strength, electrode spacing, type of bacterial culture in anode biofilm, substrate composition and its concentration, etc [6]. Thus a direct correlation between power density and temperature cannot be obtained unless all other parameters have been accounted.
This necessitates the use of numerical modeling for effective optimization of MFC systems.
While the current steady state model, which couples energy balance with other physics is used for understanding the effect of temperature, it is also suitable for studying the influence of other systems parameters. The scope and applicability of the model is established by studying the change in power density as a function of ionic strength of the substrate solution and interelectrode distance. The effect of these two parameters on the MFC perfor-mance is quite well-understood and the trends predicted from the model are compared with those described in literature.  Conductivity of the solution is typically increased by adding NaCl or high concentration of buffer solution [4,12]. However very high salinity has also been reported to have a negative influence on the bacterial performance [35,37] and thus system sensitivity (specific to the type of microbial communities in the biofilm) should be carefully considered before adding any components to improve the ionic strength of the solution for improved performance.

Ionic strength
3.2.2. Inter-electrode distance or electrode spacing Figure 9 shows the effect of inter-electrode distance (IED) between anode and cathode (also referred to as electrode spacing) on the MFC performance.
IED was varied from 1 cm to 4 cm and as it can be seen from figure 9A, maximum power density increases as the distance between the two electrodes is decreased. The trend observed here is in accordance with previous experimental and numerical studies [4,6,38,39] and is typically ascribed to the decrease in internal resistance as IED is decreased.
The effect of electrode spacing is also a strong function of the ionic strength of the solution. It was observed that when using electrolytes with higher conductivities (≥ 0.01 S m −1 ), decreasing the electrode spacing does not result in any significant gain in power output, but it does when the electrolyte conductivity is small (≤ 0.001 S m −1 ). For the result shown in figure   9A, the electrolyte conductivity was 0.01 S m −1 and we observed ∼ 9% increase in power output on reduction of electrode spacing from 4cm to 1cm.
However when an electrolyte with weak ionic strength (σ l = 1e −4 S m −1 ) is used, reducing the electrode spacing leads to ∼ 130% increase in maximum power density. It can also be seen from figure 9B that the average reaction rate is highest for d=1cm and decreases linearly with increase in IED. The lower internal resistance at d=1cm enables a higher electrode potential which thereby helps in improving the reaction rate of substrate oxidation in the biofilm. It should however be noted that very close positioning of the electrodes has been found to result in decreased performance due to oxygen contamination of the anode biofilm [40], and thus IED can only be decreased to a certain optimum distance before the trend is reversed.

Conclusion
The proposed steady state model successfully captures the effect of temperature on the MFC performance as observed from the experimental study.
The 2D analysis allows us to visually represent and understand the changes in ionic and electronic current densities, and the local reaction rates in the two electrodes. This is one of the first attempts to numerically explain the non-linear performance trend with respect to temperature.
It is also shown that most of the parameters are inter-linked and it is imperative to account for these dependencies to obtain a realistic description of the MFC performance. The model proposed in this work is generic and can be applied to different MFC configurations. While the governing equations represented here for a steady state analysis, which allows for fast convergence and quick optimization, they can be easily modified to study the dynamic performance by including time dependence. It is also shown that the scope of the model is not limited to thermal analysis but can also be used for parametric studies and optimization of other system parameters.
This applicability is highlighted by studying the effect of electrode spacing and ionic strength on the system performance, the results of which are in agreement with trends reported in literature.