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Abstract

Evidently, paper-based microfluidic devices, including fuel cells, have been proven to power low-power integrated miniaturized devices. However, the harvested energy depends on various design parameters, positioning and other ancillary factors. Herein, design of experiment is used to make a boisterous study of the data used in paper-based microfluidic fuel cell and to make various optimizations and studies of the raw data used in the microbial fuel cell paper. The paper-based microfluidic fuel cell was analysed for two different positioning, horizontal and vertical, and the maximum power outputs were noted. A statistical technique based on full factorial design was used to study the performance of paper-based microfluidic fuel cell. In the microbial fuel cell, a rigorous study was conducted pertaining to the electrode separation, channel variation and absorbent pad stability. In both these cases, the analysis of mean, analysis of variance, signal-to-noise ratio and desirability study were performed. For the paper-based microfluidic fuel cell, the best desirability values for the horizontal and vertical arrangements were measured to be 0.8842 and 0.92768, respectively. For the microbial fuel cell, in the case of 2 mm electrode separation, the present analysis of variance model came out to be significant. Inclusively, this work provides a pathway to realize optimum paper-based microfluidic fuel cell, and such study can be extrapolated to develop other microfluidic devices.

Keywords

Design of experiment paper-based microfluidic fuel cell microbial fuel cell analysis of mean analysis of variance optimizations desirability studies

Introduction

In this contemporary world, the amount of research data is increasing considerably and an accurate method is needed to make it useful. This work delves upon developing a dependable and dynamic floor to work upon all kinds of data, find the respective factors that vary and analyse and optimize those very factors. To do so, design of experiment (DOE)¹ has been used to evaluate the factors controlling the value of a parameter or group of parameters by planning, conducting, analysing and interpreting controlled tests.² DOE is a powerful data collection and analysis tool that can be used in a variety of experimental situations and optimization.^3,4 Analysis of variance (ANOVA) has numerous applications that help us practically. This methodology is also used in fuel cells. Fuel cells work like batteries, but they do not run down or need recharging. They produce electricity and heat as long as fuel is supplied. A fuel cell consists of two electrodes – a negative electrode (anode) and a positive electrode (cathode)–sandwiched around an electrolyte. Fuel cells are also classified by the type of electrolyte they use and by the difference in start-up time ranging from 1 s for proton-exchange membrane fuel cells (PEMFCs) to 10 min for solid oxide fuel cells (SOFCs).^5,6 A SOFC is an electrochemical conversion device that produces electricity directly from oxidizing a fuel.⁷ It has been used to show the application in resting-state fMRI data obtained from the Human Connectome project. In it various factors like amount of sleep were recorded and worked upon. The analysis of means (ANOM) is a graphical statistical technique used for comparing group of treatment means to see if any one of them differs significantly from the overall mean. It is a procedure used in quality assurance for comparing several treatment means against an overall mean.

In this context, the experimental work related to development of paper-based microfluidic fuel cell (PMMFC) has several parameters which need to be cohesively optimized.⁸ To fully understand PMMFC, it is essential that we consider all of the effects, such as significance of cell configurations, electrode, fuel concentration, thickness, etc., very carefully.⁹ Herein, an exacting study on PMMFC work has been made whereby it was concluded to consider three defining parameters, first one being the device orientations – horizontal and vertical.¹⁰ Furthermore, combinations of four different grades of pencils, HB, 2B, 6B and 2H were used to prepare the electrodes on paper using 40, 60 and 80 pencil strokes. Thus, by the proper selection of these factors, the maximum cell energy output can be obtained. A lot of research attempts were made on the same to show its deep-rooted fabrication simplicity, low-cost and self-breathing, amongst many others.¹¹

The same notion of DOE is applied to the MFC.¹² The raw data of MFC was used to extensively analyse various factors in all possible ways.¹³ In it the electrode separation was varied for three possible scenarios that are the 1 mm, 2 mm and 3 mm electrode separation.¹⁴ Furthermore, the studies on channel variations were conducted, in which the data was manipulated for different grades of Whatman cellulose paper namely grade 1, 6, 41, 43, and 3.¹⁵ The studies on absorbent pad stability were also made in which the voltage was varied along with time and it was done for different grades as well.

In this work, rigorous analysis of different parameters governing the performance of the PMMFC and MFC has been carried out.¹⁶ A specialized DOE approach was applied which empowers us to employ an organized methodology for framing parametric values for experimental studies.¹⁷ It also offers us a path to analyse multiple parameters concurrently. For PMMFC, a full factorial design method is followed, wherein the three parameters are: grade of pencil, number of strokes and fuel concentration with open circuit voltage (OCV), current density (CD) and power density (PD) act as an indicator of performance or process response.¹⁸ On the other hand, a microbial fuel cell (MFC) is a type of bio electrochemical fuel cell system that generates electric current by diverting electrons produced from the microbial oxidation of reduced compounds. These electrochemical cells are constructed using either a bio anode or a bio cathode. Whereas in the case of MFC, the study was conducted by varying the electrode separation, channel variation and absorbent pad stability for different Whatman cellulose gradients.¹⁹ The cell voltage and the CD were considered as the factors and the PD as the output response. In both of these cases, PMMFC and MFC, the mutual interactions of the various parameters were analysed through the ANOM approach, while ANOVA was carried out to establish statistically significant parameters.^20,21 Based on the ANOVA, a response equation was generated in terms of the coded values. Furthermore, to identify the robust combinations of parameters, signal-to-noise ratio (SNR) was also studied. Finally, a desirability factor-based optimization study is conducted.²² The DOE provides us with detailed and precise conclusions, however besides DOE some other design methods are also being used in the current mainstream. The method of artificial intelligence, which refers to the simulation of human intelligence in machines that are programmed to think like humans and mimic their actions, is also being used besides DOE.²³ Machine learning is also being used for the same. It is a type of artificial intelligence that allows software applications to become more accurate at predicting outcomes without being explicitly programmed to do so. Machine learning algorithms use historical data as input to predict new output values.²⁴

Therefore, analysing and optimizing all of this data are humanly very tedious and are prone to errors. Hence, the use of higher statistics and software related to such data has been utilized in this work, the data has been analysed and optimized, and interesting conclusions have been drawn.²⁵

Experiment

Actual designs for the physical experiment

For PMMFC, a full factorial method was used with three parameters, which were leveraged for the entire analysis.²⁶ ST 1 summarizes various design parameters that are grade of pencil, number of strokes and fuel concentration. For MFC, the electrode separations were analysed for three cases – 1 mm, 2 mm and 3 mm separations.^27,28 The actual designs pertaining to the three cases are shown in ST 2, ST 3 and ST 4, respectively. For channel variation, the raw data was varied for different grades of Whatman cellulose paper. The actual design for the grade 6 and grade 43 is shown in ST 5 and ST 6, respectively. For the absorbent pad stability, different grades of Whatman filter papers were varied. The actual designs for the grade 3, 6, 41 and 113 are shown in ST 7, ST 8, ST 9 and ST 10, respectively.

Selection of the factors to be investigated

An integral part of the DOE study is to come to a reasonable decision on the factors to investigate. For the PMMFC, three factors, namely the grade of pencil, number of strokes and the fuel concentration, were studied.²⁹

The simulations for MFC were carried out for different electrode separations for 1 mm, 2 mm and 3 mm, whereby two factors, cell voltage and CD, and were considered. The raw data for channel variation was varied for grades 1, 3, 6, 41 and 43 of Whatman cellulose paper. The factors, cell voltage and CD, were considered for the simulation for channel variation and absorbent pad for grades 3, 6, 41 and 113.³⁰ Finally, the studies were made for the stability of absorbent pad in which time was taken as the single factor and was varied for different grades (3, 6, 41 and 113).

Statistical analysis using DOE

One of the primary focus of the present work is the analysis of different parameters governing the performance of PMMFCs and the MFCs. DOE offers a methodical approach to frame parameter values for an experimental study and provides a mean to conduct the analysis of multiparameters simultaneously.^1,31

Further, to analyse PMMFC, full factorial design method is followed. In PMMFC, the OCV, CD and PD are taken up as the process responses. Based on this, various combination sets are formed as shown in ST 11. For the same, many parametric permutations and combinations were attempted, which are shown in ST 12.

Selection of models for the MFC

For the electrode separation of 1 mm, the linear or the 2FI model can be used. For the 2 mm and 3 mm, the linear and 2FI models were used, respectively. Similarly, the models used for other simulations are shown in various tables. The models that have significant ANOVA are shown in Table 1.

Table 1.

Method of selection and corresponding model used (Model selections for different simulations).

Method of selection	Model used
Separation of electrodes: 2 mm	Linear
Channel variations for different Whatman grades: grade 6 and grade 43	Linear
Absorbent pad for different Whatman grades: grade 3 and grade 6	Linear
Stability variation of absorbent pad for grade 3	Quartic
Stability variation of absorbent pad for grade 6	Cubic
Stability variation of absorbent pad for grade 41	Quartic
Stability variation of absorbent pad for grade 113	Quadratic or fifth

Analysis, result and discussion

ANOVA

ANOVA is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. ANOVA was performed to observe statistically significant parameters.³² The ANOVA tables of the PMMFC and MFC variations are shown in Tables 2 to 4. In the case of PMMFC, the ANOVA tables of OCV mean, CD mean and PD mean were significant.

Table 2.

OCV mean.

Source	Sum of squares	df	Mean square	F value	p value
Model	0.2135	13	0.0164	3.17	.0235	Significant
A – graphite pencil stroke	0.0174	1	0.0174	3.36	.0898
B – number of strokes	0.0557	2	0.0278	5.37	.0200
C – fuel concentration	0.0208	2	0.0104	2.01	.1738
AB	0.0014	2	0.0007	0.1360	.8740
AC	0.0091	2	0.0045	0.8752	.4400
BC	0.1090	4	0.0273	5.26	.0096
Residual	0.0674	13	0.0052
Cor total	0.2809	26

Table 3.

CD mean.

Source	Sum of squares	df	Mean square	F value	p-value
Model	2.546E + 05	5	50,923.56	2.94	.0363	Significant
A – graphite pencil stroke	36,850.70	1	36,850.70	2.13	.1593
B – permutation and combination	1.011E + 05	2	50,537.41	2.92	.0761
C – fuel concentration	1.167E + 05	2	58,346.14	3.37	.0537
Residual	3.635E + 05	21	17,307.61
Cor total	6.181E + 05	26

Table 4.

PD mean.

Source	Sum of squares	df	Mean square	F value	p value
Model	3482.78	13	267.91	2.61	0.0477	Significant
A – graphite pencil stroke	191.49	1	191.49	1.87	0.1950
B – permutation and combination	730.49	2	365.24	3.56	0.0585
C – fuel concentration	687.84	2	343.92	3.35	0.0670
AB	416.38	2	208.19	2.03	0.1710
AC	385.35	2	192.67	1.88	0.1921
BC	1071.23	4	267.81	2.61	0.0844
Residual	1333.62	13	102.59
Cor total	4816.40	26

In MFC, a significant ANOVA was achieved for the following simulations – 2 mm electrode separation (ST 14) and grade 43 (ST 15) for the channel variation. For the absorbent pad, grade 3 (ST 16) and grade 6 (ST 17) gave significant ANOVA and for stability in absorbent pad with time as a factor gave significant ANOVA for grades 3, 6, 41 and 113 shown in ST 18 and ST 19.

Diagnostics

For all of the given data, robust analysis was conducted and diagnostics was run through. Many different graphs and figures were plotted to analyse the data in all sorts of possible ways, and the data showing abnormalities was either discarded or updated to match up the experiment and the research going on. For PMMFC, all of the diagnostic figures of OCV Mean were within the extreme limits showing the accuracy of the chosen data (Figure 1). The important and relevant figures and graphs related to it are shown in Supplementary Figures 1 to 13.

Figure 1.

(a) Normal plot of residuals for open circuit voltage (OCV) mean; (b) residuals versus graphite pencil stroke for OCV mean; (c) box cox plot for OCV mean; (d) leverage versus run for OCV mean.

For MFC, on performing the diagnostics of 2 mm electrode separation, the normal plot of residuals was obtained and the residuals vs predicted was also within the limits. For the channel variation, grades 1 and 43 showed acceptable diagnostics whereas grade 6 had only the residuals versus predicted graph within limits. The stability variation of the absorbent pad of the MFC showed consistency in its diagnostics. The grades 3, 6 and 41 were well within the limit.

Membrane less microfluidic paper fuel cell design and fabrication

Corel Draw X7 software was to create Y-shape microchannel for membrane less microfluidic paper fuel cell (MMPFC). Based on the design, a porous cellulose paper was cut into the desired shape using CO₂ Laser Engraver. The detailed MMPFC design is shown in Supplementary Figure 14. The single laser cutting operation was performed for cellulose filter without tearing off with optimized cutting parameters. The detailed MMPFC fabrication and assembly procedure is presented in Supplementary Figure 15. The whole cutting process was carried out at 3 Watt power and 10 mm/sec speed in laser engraver with a single pass. Here, different MMPFC Y-shape microchannel, with two inlets and one outlet, were prepared with different Whatman cellulose paper grades such as grades 1, 3, 6, 41 and 43. The two inlets of the microchannel carried fuel and electrolyte under capillary action to allow continued power harvesting by graphite electrodes.

Final equations in terms of coded and actual factors

The equation in terms of coded factors can be used to make predictions about the response for given levels of each factor. By default, the high levels of the factors are coded as +1 and the low levels are coded as −1. The coded equation is useful for identifying the relative impact of the factors by comparing the factor coefficients.

However, the equation in terms of actual factors can be used to make predictions about the response for given levels of each factor. The response equations for the PMMFC are given in the Tables 5 to 9.

Table 5.

PMMFC response equations in terms of coded factors.

OCV	0.2352 + 0.0311A–0.0541B[1]–0.0030B[2]–0.0185C[1]–0.0207C[2] + 0.0006AB[1] + 0.0106AB[2] + 0.0006AC[1] + 0.0272AC[2] + 0.0607B[1]C[1] + 0.0296B[2]C[1]–0.0837B[1]C[2]–0.0348*B[2]C[2]
CD	108.08481481481–45.246666666667A–55.168148148148B[1]–30.144814814815B[2]–91.925925925926C[1] + 33.916296296296*C[2]
PD	8.1240740740741–3.2616666666667A–4.7007407407407B[1]–2.5496296296296B[2]–7.002962962963C[1] + 4.6981481481482C[2] + 2.0066666666667AB[1] + 4.625AB[2] + 3.89AC[1]–6.5016666666667AC[2] + 5.522962962963B[1]C[1] + 2.3251851851852B[2]C[1]–7.7414814814815B[1]C[2]–4.5125925925926*B[2]C[2]
A: graphite pencil stroke; B: permutation and combinations; C: fuel concentration.

The MFC response equations for different simulations are shown in the Tables 6 to 8.

Table 6.

MFC response equations for different electrode separations in terms of coded factors.

1 mm separation	276.3298125 + 276.3298125A + 274.9764375B + 274.9764375*A
2 mm separation	−9.5093864269884 + 1576.0999698416A + 1585.1450996769B
3 mm separation	48.267505 + 48.267505A + 48.267505B + 48.267505*AB
A: cell voltage; B: current density.

Table 7.

MFC response equations for different grades of channel variations in terms of coded factors.

Grade 1	37.635707881522 + 1044.8977837194A + 1076.8525257455B
Grade 3	107.06 + 107.06A + 107.06B + 107.06*AB
Grade 6	−9.5093864269884 + 1576.0999698416A + 1585.1450996769B
Grade 41	48.267505 + 48.267505A + 48.267505B + 48.267505*AB
Grade 43	8.8378863232862 + 204.21533736236A + 198.28849820002B
A: cell voltage; B: current density.

Table 8.

MFC response equations for different grades of absorbent pads in terms of coded factors.

Grade 3	0.30736267409249 + 315.72924443801A + 314.1745494218B
Grade 6	−8.9780974723708 + 1835.7920445683A + 1838.0108923477B
Grade 41	−0.059701306512331 + 43.259994704676A + 43.468011738645B
Grade 113	39.16432 + 39.16432A + 39.16432B + 39.16432*AB
A: cell voltage; B: current density.

Table 9.

MFC response equations for different grades of stability variation of the absorbent pad in terms of coded factors.

Grade 3	0.28970187261674–0.0015063099984698A + 0.19679366632363A²–0.19748896458826A³–0.29327411806912A⁴
Grade 6	0.48897279658699 + 0.075963789398256A–0.21302707181226A²–0.33419264701649*A³
Grade 41	0.19790752809508–0.032215922424208A + 0.13358411181629A²–0.13130266953337A³–0.16799679825766A⁴
Grade 113	0.46883754962197–0.043878040712094A-0.17650493119333A²–0.52347663713014A³–0.028075711433606A⁴ + 0.31227690164202*A⁵
A: cell voltage; B: current density.

Optimizations and desirability

To investigate the optimal values of the parameters and to maximize the responses, an optimization study was performed based on the desirability factor. In statistical analysis, the concept of desirability plays an important role where the response functions are more than one. In such a situation, the direction towards the maxima of individual responses may be different, thereby achieving the simultaneous maximization of all responses is critical. Hence, the factor ‘desirability’ consolidates the maxima or minima requirements of multiple responses. The individual desirability of each factor is defined between zero and one. The overall desirability (S) is mathematically a geometric mean of individual desirability values (si), for ‘n’ number of responses, as presented in the following equation:

S = (s_{1} \times s_{2} \dots \times s_{n})^{\frac{1}{n}} = {(\prod_{i = 1}^{n} s_{i})}^{\frac{1}{n}} .

(1)An optimization scheme starts iterative search to locate the maxima of ‘S’ by optimizing the individual desirability. In the case of PMMFC, all the three responses were graded equally with the same weightage function for maximization. As a result of optimization, the overall desirability value for the PMMFC came out to be 0.576 as shown in Figure 2.

Figure 2.

Desirability value for paper-based microfluidic fuel cell (PMMFC).

For the MFC, our main objective was to maximize the PD and obtain the desirability for the same. To do so, the cell voltage was set to be minimized in the given range, and the desirability for maximum PD was obtained. The desirability ramps are shown below for the MFC and its different variations. The results have been tabulated in ST 13.

For the stability variation of absorbent pad, the data can similarly be manipulated. The voltage can be maximized or minimized for a specific target of time or for any other range, which will depend upon the situation and conditions.

Conclusions

This work manifests that DOE is a multipurpose approach that can be applied in an array of circumstances where a methodical examination of factor effects and especially their interaction effects are vital to shed light on complex aspects of a decision problem.

Herein, a simple PMMFC and MFC have been proposed, which have been reviewed in great depth and detail.

For the given set of data, the horizontal PMMFC has been demonstrated a maximum PD and CD of 69.53 µW/cm² and 753.39 µA/cm², which is in very close agreements to the actual maximum PD.

For details, with analysis of the parameters affecting the performances of the PMMFC and MFC, DOE-based performance analysis was carried out to understand the relative influence of the parameters to eventually achieve the robust design.

The interactions of the parameters were found to be the most leveraging part of these experiments. For the electrode separation, the 2-mm separation gave a significant ANOVA, and its desirability is also very high at 0.972, hence making it the best choice for electrode separation. For the channel variation, the maximum desirability was 0.972, which was for grade 6, making it a good choice amongst all the other grades in channel variation. The maximum desirability for absorbent pad was 0.975 for grade 6.

For the research and analysis of DOE, there can also be some other influencing factors apart from design like pressure and temperature, which can also become a part of our further study and research. The current experiments were done under controlled circumstances and ambient temperature. The other influencing factors can become a good topic of research in the future.³³

In conclusion, with DOE enabled to analyse the effects of several factors and their interactions, the rigorous statistical study helped us to develop robust design and optimized parameters for many realistic applications.

Supplemental Material

sj-docx-1-pie-10.1177_09544089221142427 - Supplemental material for Statistical analysis and optimization of fuel cells using the design of experiment

Supplemental material, sj-docx-1-pie-10.1177_09544089221142427 for Statistical analysis and optimization of fuel cells using the design of experiment by Sarthak Dwivedi, Lanka Tata Rao, Shashwat Goel, Satish Kumar Dubey, Arshad Javed and Sanket Goel in Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iDs

Arshad Javed

Sanket Goel

Supplemental material

Supplemental material for this article is available online.

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