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# Journal Club Theme of October 2014: Microbial fuel cells - When mechanics meets bioelectrochemistry

**Introduction. **Inspired by Zhigang's blog on on lithium batteries [link], the aim of this Journal Club is to provide a forum for discussing:

- the role of applied mechanics in bioelectrochemical systems such as microbial fuel cells, and
- the potential of computational mechanics during upscaling of those systems.

In microbial fuel cells (MFCs) dissolved organic matter is oxidized at the bioanode, and an oxidant such as O2 is reduced at the cathode [1]. Flow separation is typically achieved by a proton exchange membrane that is able to permeate cations to maintain a neutral charge in the anolyte and catholyte during operation. The transfer of energy is achieved when microbial colonization forms an electrochemically active biofilm (EAB) on the fuel cell anode, causing electron transfer. A breakthrough in MFC technology was achieved when it was discovered that microorganisms in the biofilm were able to transfer electrons outside their cell towards the anode without additional chemical mediators. By harnessing the metabolism of exoelectrogens, MFCs convert chemical energy into electrical energy [2] in a self-sustaining process driven by self-replication in the biodegradable organic matter contained in wastewater. However, MFC performance is limited by low efficiency of energy recovery due to voltage and current losses. Applied and computational mechanics can play a fundamental role in achieving the needed performance improvements for the development of sustainable large-scale microbial biotechnologies. Possible contributions are:

- developing an improved understanding of the extracellular electron transfer mechanism
- creating sophisticated constitutive models of EABs that include growth, erosion, and detachment scenarios
- designing non-standard bioelectrode topologies suitable for large-scale realizations of such microbial devices

A robust computational model would account for all of these aspects and the coupling between them. Suggestions, feedback and critique on the role of computational and applied mechanics in this research are greatly appreciated.

**Physical models for extracellular electron transfer. **Exoelectrogens growing on bioanodes remove electrons from soluble electron donors, such as dissolved organic matter, and transfer those electrons to the surface of the bioanode. If the cathode potential is greater than the potential at the bioanode, the electrons flow through an external circuit to the cathode. Two main mechanisms are proposed for extracellular electron transfer. The first mechanism is 'indirect', and involves electron shuttling via mediator compounds that transfer electrons from microorganisms to the electrode through redox cycling. The second mechanism is 'direct', and relies on direct contact between microorganisms and the electrode, which is achieved through the electric conductivity of the EPS matrix or the electric conductivity of bacteria pili called 'nanowires' [3]. Numerical models of both types of electron transfer have been developed [4-6]. The former process depends highly on the diffusion coefficient of the biofilm matrix as part of the mass transport equation while the latter depends highly on the conductivity coefficient. In addition to their role in the extracellular electron transfer, microbial nanowires act as structural components of biofilms. Depending on the microorganisms, biofilm state, and enviornmental conditions, the preference for electron transfer via mediator compounds or via conductive material varies.

*What can our mechanics community contribute to better understand these mechanisms?* *What is the best way to model these mechanisms in the first place, and how can computational models be used to determine which mechanism is most likely to be occuring given an experimental data set?* Density functional theory based electronic structure calculations [7-12] (see also previous excellent Journal Clubs by Vikram [link] and Suku [link]) or coarse-grained molecular and stochastic dynamics simulations have been developed for various applications in mechanics. Contributions are welcome to discuss their applicability to improve our understanding of the physical mechanisms and the reaction kinetics taking place at the interface between the anode and the EAB [13].

**Constitutive modeling of electrochemically active biofilms. **Multiple physical considerations are important when developing coupled mathematical models and computational frameworks of EABs in operating MFCs. In [14], scalar transport equations are solved with an advection-diffusion equation in the liquid surrounding the biofilm and a diffusion-reaction equation within the biofilm itself. Under the electric field present in MFCs due to the potential difference between the electrodes, electromigration will also become a driving force for species transport. These transport equations influence the extracellular electron transfer and the biofilm growth. A highly insightful discussion about the mechanics of growth is given in a previous Journal Club by Ellen [link]. Modeling of biofilm growth by the well-established continuum-based growth models for soft-matter materials [15] seems appropriate. However, most biofilm growth models either neglect the influence of solvent flow due to swelling, or only account for this influence by assuming a highly simplified constant swelling ratio.

The biofilm itself can be understood as a microbial population in a matrix of extracellular polymeric substances (EPS) adhering to surfaces and interfaces. The EPS network consists of worm-like polysaccharide chains cross-linked by arbitrarily located junctions of different qualities. A network model currently being used for biofilms is the eight-chain model [16], originally developed for rubber elasticity, but features of more recent network models [17-19] could be employed in future research. Other approaches [20,21] view the biofilm as a biological gel composed of EPS and water. Such a gel absorbs or expels solvent in response to changing external conditions and swells or contracts accordingly due to the thermodynamic compatibility between polymer and solvent molecules. Excellent contributions from mechanicians on gels, discussed in previous blogs of Jerry [link], Wei [link], and Zhigang [link1,link2], are applicable here. Creep tests for biofilms show that they are viscoelastic in nature [22]. Transient network models [23-27], originally developed for rubber viscoelasticity, could be adapted to account for this effect.

Detachment scenarios of biofilms, caused by abrasion, erosion and sloughing, play a key role in biofilm systems, and greatly affect the performance of MFCs. The two physical mechanisms leading to detachment are an increase of external shear forces and a decrease of internal strength. These factors have been studied broadly, including the role of nutrient starvation [28], the effect of hydrodynamic conditions [29], and the influence of the biofilm structure [30,31]. Different mathematical models have been proposed to capture these effects [32-34]. In addition to modeling surface erosion, experimental results suggest that biomass loss is predominantly due to the detachment of large biofilm particles. *Can techniques using sharp [35-41] and diffusive discontinuities [42-44], developed by computational mechanicians, be adapted for the modeling of fracturing EABs?*

**Computational design and upscaling of non-standard bioelectrode topologies.** Essential for the upscaling of MFC systems is the development of optimized bioanode topologies with regard to electron transfer and biofilm attachment. Currently, processes must be scaled up from laboratory reactors at 10-6-10-3 m by orders of magnitude to industrial applications of 1-103 m [45]. Computation can play a dominant role in achieving those goals. Open macroscale porous anode materials, such as carbon cloth, carbon nanotube/graphene-coated sponge, and graphite brush, all of which enlarge the anolyte-biofilm-anode interface, have been recently developed by experimentalists [46-50]. Graphite electrodes consisting of graphite rods, plates or disks are often used due to their low cost, high stability, high conductivity, and high biocompatibility. *Can robust computational design frameworks be developed to propose optimized non-standard bioelectrode topologies in bioelectrochemical systems?*

Modeling bioelectrochemical systems remains a challenging tasks with the computational tools we have available today. Through effort from our mechanics community, we can resolve the open physical challenges and contribute to the development of a sustainable energy production through upscaled bioelectrochemical systems.

**References:**[1] B. E. Logan, Microbial fuel cells, Wiley, 2008.

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[19] A. Raina, C. Linder, A homogenization approach for nonwoven materials based on fiber undulations and reorientation, J. Mech. Phys. Solids 65 (2014) 12–34.

[20] N. G. Cogan, J. P. Keener, The role of the biofilm matrix in structural development, Mathematical Medicine and Biology 21 (2004) 147–166.

[21] T. Zhang, N. Cogan, Q. Wang, Phase field models for biofilms. II. 2-D numerical simulations of biofilm-flow interaction, Commun. Comput. Phys 4 (1) (2008) 72–101.

[22] B. Towler, R. Cory, A. Cunningham, P. Stoodley, Viscoelastic properties of a mixed culture biofilm from rheometer creep analysis, Biofouling 19 (5) (2003) 279–285.

[23] M. Green, A. Tobolsky, A new approach to the theory of relaxing polymeric media., J. Chem. Phys. 14 (1946) 80–92.

[24] J. Lubliner, A model of rubber viscoelasticity, Mech. Res. Commun. 12 (1985) 93–99.

[25] S. Govindjee, S. Reese, A presentation and comparison of two large deformation viscoelasticity models, J. Eng. Mater. Technol. 119 (1997) 251–255.

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[28] S. M. Hunt, E. M. Werner, B. Huang, A. Hamilton, P. S. Stewart, M. A. Hamilton, Hypothesis for the Role of Nutrient Starvation in Biofilm Detachment Hypothesis for the Role of Nutrient Starvation in Biofilm Detachment, Appl. Environ. Microb. 70 (12) (2004) 7418–7425.

[29] C. Picioreanu, M. C. Van Loosdrecht, J. J. Heijnen, Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study., Biotechnol. Bio- eng. 69 (5) (2000) 504–15.

[30] M. Böl, R. B. Möhle, M. Haesner, T. R. Neu, H. Horn, R. Krull, 3D finite element model of biofilm detachment using real biofilm structures from CLSM data, Biotechnol. Bioeng. 103 (2009) 177–186.

[31] N. Derlon, C. Coufort-Saudejaud, I. Queinnec, E. Paul, Growth limiting conditions and denitrification govern extent and frequency of volume detachment of biofilms, Chemical Engineering 218 (2013) 368–375.

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[33] B. M. Peyton, W. G. Characklis, A statistical analysis of the effect of substrate utilization and shear stress on the kinetics of biofilm detachment, Biotechnol. Bioeng. 41 (1993) 728–735.

[34] J. D. B. Xavier, C. Picioreanu, M. C. M. van Loosdrecht, A general description of detachment for multidimensional modelling of biofilms, Biotechnol. Bioeng. 91 (6) (2005) 651–69.

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[44] M. Borden, C. Verhoosel, M. Scott, T. Hughes, C. Landis, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Eng. 217-220 (2012) 77–95.

[45] R. A. Rozendal, H. V. Hamelers, K. Rabaey, J. Keller, C. J. Buisman, Towards practical implementation of bioelectrochemical wastewater treatment, Trends in Biotechnology 26 (8) (2008) 450–459.

[46] S. Cheng, H. Liu, B. E. Logan, Increased power generation in a continuous flow MFC with advective flow through the porous anode and reduced electrode spacing, Environ. Sci. Technol. 40 (2006) 2426–2432.

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## Comments

## The Exciting World of Energy Research !

Dear Prof. Linder,

Thank you for the interesting post.

iMechanicians may find my recent papers related to energy interesting :

** Enhanced Lithiation in Defective Graphene

** Atomistic Mechanism of Phase Boundary Evolution during Initial Lithiation of Crysalline Silicon

** Defect-induced plating of lithium metal within porous graphene networks

** Defective graphene as promising anode material for Na- and Ca-ion battery

Thank you very much.

Regards,

Dibakar

## Literature on Biofilm Modeling

Hello Christian,

Thank you for the excellent discussion emphasizing the role of computational mechanics in realizing a scalable microbial fuel cell (MFC). With the recent advances made in computational mechanics, especially, on the numerical modeling of evolving interfaces [1-3] and Eulerian solid formulations [4,5], it is now possible to revisit the detachment scenarios that greatly affect the performance of the MFC. Further, quorum sensing in biofilms can be incorporated, which is an important mechanism that affects the growth of biofilm colonies and is greatly influenced by the hydrodynamic environment [6-8]. Coming to the MFC, preliminary modeling has shown that competitive growth among bacterial species, anode geometry and the diffusion of soluble products, all affect the MFC’s performance. With all these recent developments, I believe it is now time to address the question of “how do the rate-limiting factors impact the current generated by the microbial fuel cell?” and “what is the theoretical maximum current output from an MFC for a given biomass input?” Below are some journal articles (from the Northwestern Univ. folks).

Numerical modeling of biofilm growth1. R. Duddu, D. L. Chopp and B. Moran, A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment. Biotechnology and Bioengineering, 103(1): 92-104,

2009, doi: 10.1002/bit.222332. R. Duddu, S. Bordas, D. L. Chopp and B. Moran. A combined extended finite element and level set method for biofilm growth. International Journal for Numerical Methods in Engineering, 74(5): 848-870,

2008, doi: 10.1002/nme.22003. B. G. Smith, B. L. Vaughan, and D. L. Chopp. The extended finite element method for boundary layer problems in biofilm growth, CAMCoS, 2(1): 35-56,

2007.Eulerian formulations for growth and deformation of hyperelastic solids4. R. Duddu, L. L. Lavier, T. J. R. Hughes and V. M. Calo, A finite strain Eulerian formulation for compressible and nearly incompressible hyper-elasticity using high-order B-spline finite elements. International Journal for Numerical Methods in Engineering, 89(6):762-785,

2012, doi: 10.1002/nme.32625. L. Foucard, A. Aryal, R. Duddu, F. Vernerey, A coupled Eulerian-Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries. Computer Methods in Applied Mechanics and Engineering, in Press,

2014, doi: 10.1016/j.cma.2014.09.016Quorum sensing in biofilms6. B. L. Vaughan, B. G. Smith, D.L. Chopp. The Influence of Fluid Flow on Modeling Quorum Sensing in Bacterial Biofilms, Bull. Math. Biology, 72(5): 1143-1165,

20107. M. J. Kirisits, J. Margolis, B. L. Purevdorj-Gage, B. Vaughan, D. L. Chopp, P. Stoodley, and M. R. Parsek. The influence of the hydrodynamic environment on quorum sensing in Pseudomonas aeruginosa biofilms, J. Bacteriology, 189(22): 8357-8360,

2007.8. J. D. Shrout, D. L. Chopp, C. L. Just, M. Hentzer, M. Givskov, and M. R. Parsek. The impact of quorum sensing and swarming motility on Pseudomonas aeruginosa biofilm formation is nutritionally conditional. Molecular Microbiology, 62(5): 1264-1277,

2006.Microbial fuel cell modeling9. B. V. Merkey and D. L. Chopp. The Performance of a Microbial Fuel Cell Depends Strongly on Anode Geometry: A Multidimensional Modeling Study, Bull. Math. Biology, 74: 834-857,

201210. B. Merkey, B. E. Rittmann, and D.L. Chopp. Modeling How Soluble Microbial Products (SMP) Support Heterotrophs in Autotroph-Based Biofilms, J. Theoretical Biology, 259: 670-683,

2009## Re: Literature on Biofilm Modeling

Dear Ravindra,

thank you for adressing the need to consider rate-limiting factors and theoretical maximum current output in MFCs. As indicated by the breadth of the papers you included, MFCs are intriguing because there are many possible and potentially highly coupled rate limiting factors. Computational modeling offers a route by which MFC behavior and coupling can be studied.

Regards,

Christian

## multiple time scales

Dear Christian, thanks for initiating this interesting discussion. Dear Ravindra, thanks for adding the above papers.

There are different times scales in the problem of MFC, for example growth, swelling, viscosity of biofilms, extracellular electron transfer and mass transport. How large are they? I have seen that growth is 5 orders of magnitude slower than water transportation in the biofilms. I wonder whether people consider the couple between biofilm growth and the charging process, and how they deal with the kinetics with different time scales.

## Dear Lihua,

Dear Lihua,

Thank you for pointing this out. In electrochemically active biofilms, charge transfer and growth are coupled via the bacteria metabolism. In conduction based extracellular electron transfer, the time scale can be compared to the conductivity coefficient of the biofilm ([1] reports this coefficient at 5 mS cm-1). In diffusion based transfer, the time scale can be compared to the diffusion coefficient of the biofilm ([2] reports the variations in this coefficient depending on biofilm age and condition). Though small amounts of growth may be occurring on the time scale of charge transfer (less than 1 second), measurable growth can be considered to occur over the time scale of hours or days [3]. MFC models must approach large variations in time scales to provide meaningful solutions at realistic computational cost. In [4], the problem is broken into two spatial domains that are solved with two different time steps in order to span the micro- and macro-scale. In [3], the solution algorithm utilizes the fact that the relatively slow growth of the biofilm allows the diffusion, mass transport and conduction equations to be solved as a series of steady state equations. Overall, choosing an approach to address this issue is a crucial component of MFC modeling. Further discussion of alternative approaches to this problem would be an interesting contribution to this journal club.

[1] NS Malvankar et al., Tunable metallic-like conductivity in microbial nanowire networks, Nature Nanotechnology 6 (2011) 573-579.

[2] RS Renslow et al., Diffusion in biofilms respiring on electrodes, Energy & Environmental Science 6 (2013) 595-607.

[3] AK Marcus et al., Conduction-based modeling of the biofilm anode of a microbial fuel cell, Biotechnology and Bioengineering 98 (2007) 1171-1182.

[4] C Picioreanu et al., Model based evaluation of the effect of pH and electroce geometry on microbial fuel cell performance, Bioelectrochemistry 78 (2010) 8-24.

## When mechanics meets undesired-biofilms

Thank you for posting this excellent entry.

Although the biofilms can benefit human beings in microbial fuel cells, they can also cause a number of problems in other situations. For example, biofilms and other foulings attached on the surfaces of maritime machines (e.g., ships, submarine vessels) significantly drag the vessel velocity and thus increase the fuel requirement; biofilms can clog the permeable membrane in water desalination process; biofilms can induce severe contamination in food industries and biomedical devices; biofilms on transplanted organs also can induce chronic infections. Designing environmentally friendly and biocompatible surfaces that can effectively manage biofilms and other biofoulings is an extremely challenging task. State-of-the-art approaches involve either self-polishing surfaces with controlled release of biocides, surface chemistries, or structured coatings. These approaches are generally limited to level of fouling release or may have ecological side effects.

Question: when mechanics meets undesired-biofilms, how mechanics palys a significant role in biofilm management?

Recent years, we have been working on designing active anti-biofouling coatings by harnessing the dynamic surface deformation of soft materials in response to external stimuli. We consider the biofilm as a continuum viscoelastic film bonded on the elastomer substrate. Once the substrate undergoes sufficiently large deformation, the biofilms are spontaneously detached from the substrate. Here are our two attempts:

1. How to use active surface deformation to detach marine biofilms.

Phanindhar Shivapooja#, Qiming Wang#, Beatriz Orihuela, Daniel Rittschof, Gabriel P. López, Xuanhe Zhao, Bioinspired Surfaces with Dynamic Topography for Active Control of Biofouling, Advanced Materials, 25, 1430 (2013) (#: Equal contribution)

2. How to design a urinary catheter to release biomedical biofilms on-demand.

Vrad Levering#, Qiming Wang#, Phanindhar Shivapooja, Xuanhe Zhao, Gabriel P. López, Soft Robotic Concepts in Catheter Design: an On-demand Fouling-release Urinary Catheter, Advanced Healthcare Materials, DOI:10.1002/adhm.201400035 (2014) (#: Equal contribution)

## Re: When mechanics meets undesired biofilms

Thank you Qiming for raising this important discussion. Biofilm managment via mechanical mechanisms, such as the biofilm detachment due to large surface deformation discussed in the posted papers, is a highly related area of research. Perhaps in the future a more robust computational model for the biofilm and the biofilm/substrate interface would be useful to design surfaces which eradicate biofilms. -Christian

## Re: When mechanics meets undesired-biofilms

Qiming,

One question I have on your post is to do with the continuum viscoelastic model description for the biofilm. Even if we consider a simple Maxwell type model then one needs to know the elastic modulus and viscosity coefficient. Can you please elaborate on how one can estimate such mechanical properties of the biofilm using experimental techniques and any references on this.

Also, other questions I have are: how does the spatial variation of these mechanical properties relate to the heterogeneity of the biofilm and what is the cohesive stress at the biofilm-substrate interface?

Thanks

Ravindra

## Reply to Ravindra

Dear Ravindra,

Thank you for your interest in my post.

(1) To test the viscoelastic properties of biofilms, people use sweeping test, creep test, flow test and indentation test. Besides Maxwell model, Kelvin model and Zener model may also be used. For more details, I would suggest the following two papers:

Shaw, T., et al. "Commonality of elastic relaxation times in biofilms." Physical review letters 93.9 (2004): 098102.

Böl, Markus, et al. "Recent advances in mechanical characterization of biofilm and their significance for material modeling." Critical reviews in biotechnology 33.2 (2013): 145-171.

In our paper (Advanced Healthcare Materials, DOI:10.1002/adhm.201400035 (2014)), we used frequency sweep test to characterize the viscoelastic property of biofilm. You may refer to the method part for more details.

(2) The local mechanical properties of the biofilms can be significantly affected by local compositions, nutrient supports, and others. I do not have concrete answers for you, but I can give you two examples:

-Crystalined particles in the biofilm can significantly enhance the elastic modulus of the biofilm. See Advanced Healthcare Materials, DOI:10.1002/adhm.201400035 (2014).

-Nutrient and water support can interact with the biofilm to form complex structures, see PNAS 110.3 (2013): 848-852.

(3) We may define the cohesive stress on the biofilm-substrate interface as the normal stress or shear stress that is required to debond the biofilm from the substrate. I can imagine measuring this cohesive stress will be extremely challenging.

Instead, we just consider adhesion energy density on the biofilm-substrate interface, defined as the work per area required to remove the bioﬁlms from the surface. We have not published the data of measured biofilm-substrate adhesion yet, they will come out soon.

Hope my answers have addressed your concerns.

With regards,

Qiming

## Mechanical characterization of biofilms

Thanks Qiming for the literature on the measurement of biofilm mechanical properties. I am assuming all of the tests you mentioned "sweeping test, creep test, flow test, and indentation test" would be qualify as non-destructive testing; I will have to read through the literature to confirm that. Ideally, it would be great if we could perform a test while the biofilm is growing without affecting it in anyway. - Ravindra