Biofilm development and the dynamics of preferential flow paths in porous media

Simona Botteroa, Tomas Storcka, Timo J. Heimovaarab, Mark C.M. van Loosdrechta, Michael V. Enzienc andCristian Picioreanua*aFaculty of Applied Sciences, Department of Biotechnology, Delft University of Technology, Delft, The Netherlands; bFaculty of CivilEngineering and Geosciences, Department of Geoscience and Engineering, Delft University of Technology, Delft, The Netherlands;cDOW Microbial Control, The Dow Chemical Company, Buffalo Grove, IL, USA

(Received 16 May 2013; final version received 17 July 2013)

A two-dimensional pore-scale numerical model was developed to evaluate the dynamics of preferential flow paths inporous media caused by bioclogging. The liquid flow and solute transport through the pore network were coupled with abiofilm model including biomass attachment, growth, decay, lysis, and detachment. Blocking of all but one flow pathwas obtained under constant liquid inlet flow rate and biomass detachment caused by shear forces only. The stable flowpath formed when biofilm detachment balances growth, even with biomass weakened by decay. However, shear forcescombined with biomass lysis upon starvation could produce an intermittently shifting location of flow channels.Dynamic flow pathways may also occur when combined liquid shear and pressure forces act on the biofilm. In spite ofrepeated clogging and unclogging of interconnected pore spaces, the average permeability reached a quasi-constantvalue. Oscillations in the medium permeability were more pronounced for weaker biofilms.

Keywords: biofilm; porous media; clogging; channeling; numerical model; decay

Introduction

Biofilms are complex structures consisting of microorgan-isms held together by extracellular polymeric substances(EPS). Biofilm morphology varies widely depending ona balance between biomass formation and biomassdetachment rates (van Loosdrecht et al. 1995). Biomassformation is the result of several processes, mostimportantly the microbial growth and the EPS excretion.Microbial cells grow using nutrients, mostly solublechemical compounds (substrates), transported bydiffusion and convection, whose availability therefore canalso be influenced by the liquid flow. On the other hand,biomass detachment means removal of biofilm pieces(either single cells or larger clusters), which can becarried away by the flow.

Microorganisms can develop biofilms in many naturaland engineered porous media systems. Numerous studiesshowed that the establishment of organized biofilmcommunities can be of advantage for some engineeringapplications such as biofilm barriers to control and reme-diate groundwater pollution (Waybrant et al. 1998; Kaoet al. 2001; Cunningham et al. 2003; Komlos et al. 2004;Kim et al. 2006). Biofilm barriers are structures made bystimulating the activity of microorganisms in soils.Formation of thick biofilms may cause pore clogging,thus providing a substantial decrease in permeability anda reduction in groundwater flow, therefore isolating thepollutant into specific subsurface zones. Other authors

have suggested the application of biofilm barriers toenhance storage of supercritical carbon dioxide in thesubsurface (Mitchell et al. 2009). Another application ofbiofilm formation is the biologically enhanced oil recov-ery technique (Lappin-Scott et al. 1988; MacLeod et al.1988; Cusack et al. 1992). Through this technique, bio-films are used to selectively plug areas of high permeabil-ity, thus diverting the fluid flow towards low permeabilityregions. Oil trapped in low permeability zones can bethen recovered by injection of a fluid such as water orsupercritical carbon dioxide. In other engineering applica-tions such as in water desalination systems, wheremembranes are used to purify saline and brackish water,biofouling and induced mineralization are undesiredprocesses that may lead to membrane clogging with aconsequent decrease in the system performance (Baker &Dudley 1998; Vrouwenvelder et al. 2009; Radu et al.2010).

Thus, understanding biofilm development and itsinteraction with fluid flow in porous media becomesimportant for the successful development and applicationof many engineering techniques. Quasi two-dimensionalexperimental micro-models have been developed toinvestigate and directly visualize biofilm growth and itseffect on fluid dynamics (Paulsen et al. 1997; Sharpet al. 1999, 2005; Stewart & Fogler 2001, 2002). Insome experiments (Stewart & Fogler 2002), one of theinteresting findings was the dynamics of preferential

*Corresponding author. Email: C.Picioreanu@tudelft.nl

Biofouling, 2013Vol. 29, No. 9, 1069–1086, http://dx.doi.org/10.1080/08927014.2013.828284

� 2013 Taylor & Francis

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

fluid flow pathways induced by bacterial growth. It wasnoticed that the location of the main flow channel wouldcontinuously shift, with repeated events of clogging andre-opening of pore space to fluid flow. Stewart andFogler (2002) carried out a series of experiments in amicro-model setup composed of a triangular networkwith pore bodies and pore throats etched in glass thatrepresented the porous medium. Under constant fluidflow rate, they observed a preferential flow pathdeveloped during the first stage of biofilm formation.However, later in time repeated events of channel plug-ging and re-opening lead to a shift in the location of thefluid flow pathways. Sharp et al. (2005) performed a setof experiments in a micro-model setup that consisted ofa flat plate reactor with diamond-shaped pillar elementsthat served as a porous medium. They also noticed thatunder constant inlet flow rate, channels developed andbecame more defined as the biofilm accumulationincreased. After 15 days, the flow channels weredynamic, changing in size, number, and location.

One of the critical factors, still not well understood,which controls biofilm formation and therefore thedevelopment of flow pathways in porous media, is thebiomass detachment mechanism. Physical forces can leadto erosion and sloughing, which cause the release ofmicrobial cells and their associated matrix (EPS) fromthe biofilm (Stoodley et al. 2002). An important issuewhen considering biofilm detachment caused by externalforces is quantification of the mechanical characteristicsof the biofilm. Several experiments have been carried outto characterize the mechanical properties of biofilms.Möhle et al. (2007) applied shear stress induced by fluidflow on the biofilm and a critical cohesive shear strengthranging between 6 and 8Nm�2 was found. In the samerange, critical shear strength varying between 2 and13Nm�2 was also measured by Coufort et al. (2007). Incontrast, other laboratory experiments showed a biofilmcritical tensile strength of two to three orders of magni-tude larger than the biofilm cohesive shear strength.Poppele and Hozalski (2003) found that the tensilestrength varied from 400Nm�2 to a maximum of15,000Nm�2. Ohashi et al. (1999) carried out experi-ments to evaluate the tensile strength of biofilms andobtained values varying from 500 to 1000Nm�2. Acomparison between these experiments suggests that bio-films may have a dual mechanical behavior dependingon whether normal (tensile/compressive) or tangential(shear) forces are applied. Larger forces are needed tobreak down the biofilm bulk, whereas lower forces haveto be exerted to detach cells from the biofilm surface.Thus, this dual mechanical behavior could be taken intoaccount in numerical models to better describe themechanical behavior of biofilms.

Several micro-scale (pore-scale) models for biofilmgrowth in porous structures without accounting for

biomass detachment have been proposed, first intwo-dimensional (eg Knutson et al. 2005) and laterin three-dimensional geometries (eg Graf von derSchulenburg et al. 2009; Picioreanu et al. 2009). Whenincluding biofilm mechanics and detachment, a commonassumption made in numerical models is that only shearforces due to fluid flow are acting on the biofilm surface(Picioreanu et al. 2001; Kapellos et al. 2007; Dudduet al. 2009; Pintelon et al. 2009, 2012). However, in aporous medium with complex geometry the local fluidpressure acting normal to the biofilm surface may alsoplay an important role. Local clogging due to biofilmformation may cause an increase in the fluid pressureexperienced by the biofilm surface at different locations.Picioreanu et al. (2001) and Duddu et al. (2009) modeledthe development of a biofilm on a flat surface by consid-ering shear forces responsible for biofilm detachment.Kapellos et al. (2007) and Pintelon et al. (2009) used asimilar approach to describe biomass detachment in aporous medium model with more complex geometry. Amore accurate approach was adopted by Böl et al.(2009), by using fluid–structure interaction (FSI) meth-ods to simulate biofilm detachment as a result ofmechanical processes. In their model, the load appliedon the biofilm structure accounted for both fluid pressureand viscous forces induced by the fluid flow. The modeldescribed only detachment and did not account forbiomass growth; the initial biofilm geometry for eachsimulation was based on confocal laser scanning micro-scope images. Moreover, the FSI method was used todescribe biofilm detachment from a flat surface, as muchmore computational resources would be required for asimulation at a significant scale of complex geometriessuch as porous media.

Besides the forces exerted by the fluid flow, otherfactors that have been found to be important in biofilmdetachment include matrix-degrading enzymes (Allisonet al. 1998), quorum-sensing signals (Hentzer et al. 2002),and nutrient availability. A number of researchers haveshown that the time of starvation for nutrients such asnitrogen or oxygen may be a trigger inducing biofilmdispersal (Applegate & Bryers 1991; Sawyer &Hermanowicz 2000; Hunt et al. 2004; Thormann et al.2005). Although the role of starvation in biofilm dispersalis not well understood, this was still considered in severalnumerical models (Hunt et al. 2004; Pizarro et al. 2004;Picioreanu et al. 2007). Moreover, biofilm detachmentrelated to enzymatic matrix degradation was modeled byXavier, Picioreanu, Abdul Rani, et al. (2005).

The aim of this work is to investigate theoreticallythe importance of various biofilm processes in relation tofluid flow, solute transport, and biofilms mechanics onthe development of dynamic flow pathways in porousmedia. Consequently, a two-dimensional pore-scalenumerical model is proposed, combining the fluid

1070 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

dynamics and transport of a soluble substrate with abiofilm model including cell attachment, growth, decay,lysis, and mechanical detachment.

Model description

In order to study formation of flow pathways in a porousmedium and the change of these pathways due to biofilmdevelopment, a pore-scale representation of the system ismore appropriate than a continuous approach. Thepore-scale methodology allows a direct calculation offlow and mass transport based on first principles. Themodel porous medium was represented within a rectan-gular domain, Ω, of dimensions L�H. Initially, thedomain Ω contained only a dispersed solid phase madeof grains (Ωg, unchanged in time) surrounded by a liquid(fluid) phase, the sub-domain Ωf (t). In time, a biofilmphase represented by the computational sub-domainΩb(t) developed on the grains and on the upper/lowerdomain walls. The biofilm sub-domain was bounded bya moving biofilm–fluid interface, Γbf (t). The otherboundaries, impermeable solid grain surface Γg, liquidinlet Γin, liquid outlet Γout, top wall Γtop, and bottomwall Γbot did not change in time (Figure 1). To modelthe biofilm development in the porous medium and itseffect on the flow pattern, several sub-models were

constructed for the liquid flow, solute (substrate)transport, and biofilm formation.

Liquid flow

Various physical, chemical, and biological processesleading to biofilm formation occur at different timescales (Picioreanu et al. 2000). The time scale forrelaxation of a perturbed flow is of the order of seconds,whereas a characteristic time for biofilm formation is inthe order of days or even weeks. Therefore, it is reason-able to assume stationary fluid flow at each time stepcalculating the dynamics of biofilm growth. For the slowliquid flow in porous medium channels (sub-domain Ωf),the incompressible laminar Navier–Stokes equationswere used:

qðu � rÞuþrp ¼ r � ðgruÞr � u ¼ 0

�ð1Þ

where u is the liquid velocity vector, rp is the pressuregradient, ρ is the liquid density, and η is the liquiddynamic viscosity. At the inlet boundary Γin, a laminarvelocity profile with a constant average velocity uin wasimposed. The outlet Γout was a zero pressure condition.No-slip boundaries (u = 0) were assigned at the top and

Figure 1. Schematic representation of the computational domain. Model sub-domains: Ωg solid grains, Ωf fluid (liquid) phase, andΩb biofilm phase. Model boundaries: Γbf moving biofilm-fluid interface, Γg impermeable solid grain surface, Γin liquid inlet, Γoutliquid outlet, Γtop top wall, and Γbot bottom wall. Flow is from left to right.

Biofouling 1071

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

bottom of the domain (Γtop and Γbot), as well as at thesurfaces of solid grains Γg. Because the hydraulic con-ductivity of biofilm was found to be very low, in theorder of 10�16m2 (Fowler & Robertson 1991), no flowwas assumed through the biofilm and therefore the bio-film–fluid interface, Γbf, was also assigned as a no-slipwall. If high pressure is applied in the system, as forexample in the case of reverse osmosis with biofouledmembranes (Radu et al. 2010), then the flow through apermeable biofilm would have to be considered (egPintelon et al. 2012).

Solute transport

The microbial cells in biofilms grow as a function of thelocal concentration of soluble substrates. Only onelimiting substrate having the concentration CS was con-sidered here, for simplicity. This could be, for example,dissolved oxygen for aerobic biofilms, but also organicmatter in typically oligotrophic systems like rocks andsoils. Again, the same steady state assumption has beenadopted for the substrate concentration at each biofilmdevelopment time step. This is justified by the fact thatat the modeled-scale advection and diffusion of smallsolute molecules are much faster (of the order of secondsto minutes) compared to biofilm growth (of the order ofdays to weeks) (Picioreanu et al. 2000). The stationaryconcentration of substrate CS in the fluid Ωf and in thebiofilm matrix Ωb was determined from the mass balanceequation:

DSr2CS � urCS þ rS ¼ 0 ð2Þ

including diffusion (DS is the diffusion coefficient ofsoluble substrate), convection and reaction (rS is the netsubstrate consumption rate). A constant concentration ofsubstrate CS,in was assigned at the inlet, Γin, and onlyconvective flux was active on the outlet boundary, Γout.The top, the bottom, as well as the surface of the solidgrains were considered as impermeable walls (zero-fluxcondition). A continuity condition was applied at thebiofilm–fluid internal boundary.

Biofilm formation model

To describe biofilm formation in a porous medium, themodel proposed by Picioreanu et al. (2001) was furtherextended to include, besides the biomass attachment,growth, and spreading and also biomass decay and a dif-ferent detachment mechanism more suitable for complexgeometries. In this model the biomass is represented ona grid of square elements meshing the whole computa-tional domain. Each square is occupied by biomass witha variable concentration in the sub-domain Ωb, while inthe liquid Ωf or solid grains Ωg the biomass concentra-tion is set to zero. A distinction was made between

active biomass with concentration CX and inert biomasswith concentration CXi, both having the same density. Ateach time step the biomass–liquid interface Γbf movesand its position depends on the interplay of biomassgrowth, decay, attachment, and detachment rates.

Biomass attachment

Initially, there are only fluid and grain sub-domains.Biofilm formation begins with attachment of biomass tothe grains and top/bottom walls. Throughout the numeri-cal experiment, biomass attachment is represented in themodel by converting at each time step a number ntata ofliquid-occupied square elements in contact with grainsurfaces or walls into a biomass sub-domain containing acertain concentration of active biomass CX0. The attach-ment place was chosen randomly on the grain surfacesand on the walls. Because biomass particles are trans-ported by fluid flow and no motile individual cells wereconsidered in this model, no attachment (inoculation)occurred in regions with stagnant fluid (eg pores totallyenclosed by biomass). However, further model versionsshould consider the cell attachment places directlyrelated to hydrodynamic conditions (eg local liquidvelocity or shear levels).

Biomass growth and decay

In each grid element occupied with biomass, the activebiomass concentration CX changes in time due tomicrobial growth and decay (with rates rXg and rXd,respectively) according to:

dCX

dt¼ rXg � rXd ð3Þ

while the concentration of inert material CXi changes as:

dCXi

dt¼ rXd ð4Þ

The growth rate of active biomass is governed byMonod kinetics, rXg= μmaxCXCS/(KS+CS), with amaximum specific growth rate μmax and Monod half-saturation coefficient KS. The substrate consumption rateis related to growth of active biomass through the yieldYXS so that rS=�rX/YXS. First-order biomass decay rateis considered, rXd= kdCX, with kd the biomass decaycoefficient.

Biomass spreading and lysis

When the total biomass concentration in any square gridelement exceeds a maximum value CX,max, then thatbiomass amount is divided in two equal parts. One part

1072 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

is kept in place, whereas for the second-half free spaceis searched among the neighboring grid elements. Ifmore free elements are available then the biomass isplaced in one of those elements chosen randomly withequal probability. When no free neighboring elementsare available, a randomly chosen neighbor is displaced,and the search for free space continues following cellularautomaton rules developed in Picioreanu et al. (1998).This repeated transport process eventually leads tobiomass spreading.

In addition, lysis occurs when in any biomass grid ele-ment the percentage of inert material CXi is >60% of themaximum active biomass concentration CX,max. In thiscase, a zero biomass value is assigned to that grid elementto indicate the presence of water phase. In this model, thelysed biomass is assumed to be instantly lost and not to berecycled into the pool of available substrate.

Biofilm stress and detachment

Biofilm detachment was assumed to be related to thestress developed in the biofilm volume due to forces act-ing on the biofilm surface. As a crude simplification ofbiofilm mechanics, it was assumed that biofilms behaveas elastic materials, and that small deformations will notaffect the flow pattern. Not considering the bidirectionalFSI greatly reduces the computational complexity.

Stress in the biofilm. The set of governing equationsdescribing a linear elastic biofilm material understatic conditions is based on tensor partial differentialequations for the momentum balance, without any bodyforces (Bower 2010):

r � r ¼ 0 ð5Þ

where σ is the tensor of stress in the biofilm. Hooke’slaw was used as the constitutive stress–strain relationship,r ¼ De:e, where De is the elasticity matrix depending onYoung’s modulus E and the Poisson’s ratio ν and

e ¼ ðrd þ ðrdÞT Þ=2 is the strain tensor expressed bythe strain–displacement relation (Bower 2010). In an x-yplane, the components of the stress tensor σ are reducedto the x and y components of the normal stress (σx andσy) and the shear stress (τxy). Similarly, the displacementvector d is reduced to two components (dx, dy).

The boundary conditions applied were zero-displace-ment, d= 0, at the grain-biofilm interface Γgb and loadedbiofilm–fluid interface Γbf as r � n ¼ FA � n. The loadforces per unit area FA imposed by the liquid acting on thebiofilm surface were in this model either viscous (shear)

FA;S ¼ gðruþ ðruÞTÞ ð6Þ

or total forces including both shear (tangential) andpressure (normal):

FA;T ¼ gðruþ ðruÞT Þ � p I ð7Þ

where p is the local fluid pressure, I is the identitytensor.

By solving the plane stress Equation 5 with the asso-ciated boundary conditions, a distribution of thevon Mises stress within the biofilm sub-domain isdetermined:

rmises ¼ ðr2x þ r2

y � rxry þ 3s2xyÞ1=2 ð8Þ

Biofilm detachment. In this model, the biomass detach-ment due to erosion is related to the stress in the biofilmstructure. Similar to Xavier, Picioreanu, and van Loosdr-echt (2005), the method adopts a positive detachmentspeed function, Fdet, defined as the speed of retreat ofthe biofilm/liquid interface (Γbf) due to an erosion-likedetachment process. The Eikonal equation:

�FdetjrTðxÞj ¼ 1 ð9Þ

allows for the calculation of the time T(x) at which themoving detachment front would cross a point x locatedinside the biofilm. The detachment front starts on thebiofilm–liquid interface and travels inside the biofilm.Thus, given the distribution of speed function Fdet(x)within the biofilm and the biofilm geometry, values forT(x) are determined for all points inside the biofilm bysolving Equation 9 at each time step. Further, allbiomass elements contained between the interface Γbfand the detachment front at time T(x) =Δt (thus allbiomass with calculated T smaller than the time step Δt)are removed from the computational domain. Thisdetachment stage resembles biofilm erosion. In a secondstage, biomass clusters that become disconnected fromthe biofilm (‘islands’) are also removed from the systemto mimic the so-called biofilm sloughing. It was assumedthat the detached biofilm is ‘simply’ washed out by thefluid flow and does not re-attach, which in porous mediamay not be such a good approximation.

Xavier et al. (2005) considered the detachment speedfunction Fdet dependent on the biomass density in thebiofilm and on the distance from the fluid–biomass inter-face. In this model, the speed function Fdet calculatedwithin the whole sub-domain Ωb is dependent on theratio between the calculated mechanical stress (σmises) ateach position within the biofilm and the local biofilmstrength. It was assumed that the biofilm strength isrelated to the local ratio between active biomass and inert

Biofouling 1073

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

material concentrations (CX and CXi), each characterizedby a certain yield strength (σX and σXi), so that:

Fdet ¼ kdetrmises

ðCXrX þ CXirXiÞ=ðCX þ CXiÞ ð10Þ

where kdet is a detachment speed coefficient. Equation 10therefore implies that at a certain position within the bio-film, the biomass is more prone to detachment(ie the detachment front would travel at a faster speed)when the local stress σmises is large or when there ismore inert content CXi resulted from biomass decay. Itwas assumed that the cohesive strength of inert materialis smaller than that of active biomass, σXi < σX. Furtherexperimental studies are needed to address the relation-ship between the detachment speed function and stressesin the biofilm.

Model solution

A sequential approach in model solution was used, basedon the assumption that hydrodynamics, solute masstransport, and biofilm development occur at differenttime scales (Picioreanu et al. 2000). As in previous work(see also Picioreanu et al. 2009; Radu et al. 2010), themain solution algorithm is implemented in MATLAB(MATLAB® 2007b, MathWorks, Natick, MA, www.mat-works.com) with calls to COMSOL Multiphysics (COM-SOL® 3.5a, Comsol Inc., Burlington, MA, www.comsol.com) routines for solving partial differential equationsgoverning flow field, solute transport-reaction, and stres-ses in the biofilm. A Java code was adopted to computethe biomass spreading by a cellular automaton method(Picioreanu et al. 1998). In the first section of theMATLAB script, the model input parameters, initialdomain geometry, and grains location are defined,together with biomass inoculation on several grains. In asecond section, a loop in time is performed. At each timestep, the new boundaries and sub-domains are identified,and then model equations are assigned and solved.

The following sequence of calculations was used ateach time step: (1) For the current geometry, the biofilmand the liquid sub-domains have to be identified,together with their associated boundaries. This is neededbecause the biofilm volume changes with time leading toa problem with moving boundaries. COMSOL applica-tion modes are then defined on these sub-domains andboundaries for flow Equations (1), solute convection, dif-fusion, and reaction (2) and plane stress in the biofilm(5–7). (2) A new triangular finite element mesh is cre-ated with a maximum mesh size of 10 μm. Preliminarytests revealed that this mesh size ensures an accurate andconvergent solution. (3) Hydrodynamic equations aresolved under steady state assumption to obtain u and p.Then, the 2d distribution of substrate concentration CS in

the domains is found by solving the transport-reactionequation using just the calculated velocity u. (4) Biofilmdevelopment occurs in different sub-steps: (a) biomassgrowth consists of calculating the new biomass concen-tration in each grid element according to Equations 3and 4, based on existing local substrate CS(x,y) and bio-mass CX(x,y) concentrations; (b) biomass division andspreading occurs when the biomass concentration in agrid element exceeds a maximum imposed value (CX,max)according to the cellular automaton method described inPicioreanu et al. (1998); biomass attaches randomly onthe surface of the grains, on the upper and lower wallsof the domain and on the biofilm surface; (c) biomassdetachment is performed to represent: erosion, sloughing,and removal by lysis processes.

The model allows a choice between two detachmentmechanisms due to erosion, either induced by shear orby total forces. For the detachment induced by shearforces, steps d1–d6 are executed by loading shear forcesin step d2, and assigning yield shear strengths in stepd4. For the detachment induced by total forces, routined1–d6 is executed twice. In a first pass, steps d1–d6 arecomputed loading total force at the biofilm/fluid inter-face, and assigning normal yield strengths in step d4.Then, all steps are again executed with the biomassgeometry and flow field from before the first pass, load-ing shear forces in d2 and assigning yield shear strengthsin step d4.

The steps to be executed are: (d1) First the flowpattern is recalculated for the new biomass distributionresulted after growth, spreading and attachment steps.(d2) The boundaries of the biofilm sub-domain areloaded either with shear forces or total forces. (d3) Theplane stress equations are computed, and a scalar VonMises stress is calculated in each biomass grid element.(d4) The level-set speed function Fdet (Equation 10) iscalculated assigning to the biofilm either shear yieldstrength (σs,X and σs,Xi), or normal yield strength (σn,Xand σn,Xi). (d5) The travel time of the detachment frontis calculated by the Accurate Fast Marching Method(available www.mathworks.com/matlabcentral/fileex-change/24531-accurate-fast-marching). (d6) Biomassdetachment occurs by removing all biomass elements forwhich the calculated traveling time T is smaller than thetime step Δt. Detached cells are simply turned into liquidelements and it is assumed that they instantly leave thecomputational domain. Unlike in the detachmentalgorithm presented in Picioreanu et al. (2001) and Raduet al. (2010) (where several flow/stress/removal stepswere executed until a mechanical equilibrium betweenflow and biofilm was reached), the current algorithm(based on Xavier et al. 2005) needs only one flow/stress/level-set/removal step and it is therefore much fastercomputationally.

1074 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

After eventual detachment, some biomass elementsmay have become disconnected from biofilm or grains(‘islands’) and they will be removed, a process similar tosloughing. The model has the capability of includingdetachment due to lysis processes. Lysis occurs in anybiomass grid element where the percentage of inert is>60% of the maximum active biomass concentrationbefore division. Also in this case, a zero biomass value isassigned to that grid element to indicate a water phase.

Results and discussion

To investigate biofilm formation and its effect on thedevelopment of fluid flow pathways in a porous medium,two main series of simulations were carried out in atwo-dimensional domain 4mm high and 6mm long, with

randomly distributed grains 300 μm in diameter. First,only shear (or tangential) forces induced by the fluidflow were exerted on the biofilm surface. In a secondseries of simulations, both tangential and normal forcesinferred by the fluid were applied. The model parametersare listed in Table 1 and a summary of the simulationsperformed is presented in Table 2.

Effect of shear forces, decay and biomass lysis

A common assumption made in models for biofilmmechanics and detachment is that only shear forces due tofluid flow act on the biofilm surface (Picioreanu et al.2001; Kapellos et al. 2007; Duddu et al. 2009; Pintelonet al. 2009). On the other hand, it has also been observedthat release of biofilm cells cannot be attributed only to theeffect of the physical impact of flow. For example, nutrient

Table 1. Model parameters.

Parameters Description Value Unit

Domain geometry

H Height of the computational domain 4 mmL Length of the computational domain 6 mmdx, dy Biomass grid spacing 1 μmrg Grain diameter 300 μmdg Minimum distance between two grains 30 μm/ Initial porosity 0.625 –

Hydrodynamics

ρ Liquid density 1000 kgm�3

η Liquid dynamic viscosity 0.001 Pa suin Average inlet liquid velocity 0.5 mm s�1

Substrate

CS,in Inlet substrate concentration 0.5 molm�3

DS Diffusion coefficient of substrate 1�10�9 m2 s�1

Biomass growth, attachment, and detachment

YXS Yield of biomass on substrate 0.15 Cmolmol�1

μmax Biomass maximum specific growth rate 1.95� 10�5 s�1

Ks Monod half-saturation coefficient 0.1 molm�3

kd Biomass decay coefficient 2� 10�6 s�1

n0ata Grid elements initially inoculated with biomass 35 –ntata Grid elements randomly filled with biomass during simulation (biomass ‘attachment’) 2 h�1

CX0 Initial active biomass concentration in a grid element 6000 Cmolm�3

CX,max Maximum biomass concentration before division 8000 Cmolm�3

Δt Time step 1 hkdet Detachment constant 1/3600 m s�1

Biofilm mechanics

E Young modulus 5000 Nm�2

ν Poisson ratio 0.49 –σn,X Normal yield strength of active biomass See Table 2 Nm�2

σs,X Shear yield strength of active biomass See Table 2 Nm�2

σn,Xi Normal yield strength of inert biomass See Table 2 Nm�2

σs,Xi Shear yield strength of inert biomass See Table 2 Nm�2

Biofouling 1075

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

limitation and starvation were shown to induce detachment(Hunt et al. 2004; Thormann et al. 2005). Three cases aretherefore considered to examine which factors are essentialfor the development of dynamic flow paths.

In Case A, it was assumed that biomass does notdecay, therefore all cells were kept active in time byimposing no biomass decay (kd= 0 in Equation 4). Themechanical yield strength for the active biomass whenexposed to shear forces was set to σs,X = 10Nm�2, valuein the range measured by Coufort et al. (2007) andMöhle et al. (2007).

In Case B, the active biomass decayed with the raterd (Equation 4) and accumulated as inert biomass. As aconsequence of biomass decay, the cohesive strength ofbiofilm was assumed to decrease (Ohashi & Harada1996). Because no data for the yield strength of decayedbiomass are available in the literature, σs,Xi was chosenone and two orders of magnitude smaller than the yieldstrength assigned to the active biomass (σs,Xi = 1Nm�2

in Case B1 and σs,Xi = 0.1Nm�2 in Case B2).In a third Case C, it was assumed that inert biomass is

subjected to degradation (lysis) and dispersal process asreported by microscope observations (Applegate & Bryers1991; Webb et al. 2003; Thormann et al. 2005; Davies &Marques 2009). Biomass lysis was assumed to beginwhen the local concentration of inert biomass reached60% of the maximum biomass concentration, CX,max.Above this threshold (arbitrarily chosen), all inert solidbiomass was instantly turned to liquid to mimic lysis pro-cess. Changing biofilm properties from ‘solid’ to liquid issimilar to the observations of Hunt et al. (2004), whoreported that after cell and extracellular matrix materialdegraded, motile cells in the biofilm were able to swim,indicating a substantial decrease in the biofilm viscosity.The yield strength was set to σs,X = 10Nm�2 for activebiomass and to σs,Xi = 1Nm�2 for decayed biomass.

Two-dimensional biofilm distribution, substrateconcentration, and development of the flow pathways forCase A is shown in Figure 2A, and Movie 1 from Sup-plementary Material is an animation of these results.[Supplementary material is available via a multimedialink on the online article webpage.] Initially, biomassattached on grain surfaces and on upper/lower walls,then grew to form clusters by consuming substrate. Asthe biofilm clusters merged to form larger colonies, these

plugged the pore space with consequent isolation ofsome areas from fluid flow (t = 100 h). Because aconstant flow rate was imposed at the inlet boundary, areduction of local pore space increased the local flowvelocity and hence the shear forces exerted on thebiofilm surface. Due to the increase in the local shearforces, stresses in the biofilm also increased, making itvulnerable to detachment events. Cells at the biofilmsurface subjected to higher shear stresses were firsteroded and biofilm patches detached from the grainswere eventually removed (Figure 3A and B). In theregions isolated from flow (Figure 2A), due to limitednutrient (substrate) supply the biofilm stopped growing,but there was no biofilm detachment because the shearwas absent, therefore no pore re-opening could occur.Consequently, after 200 h the fluid flow was directed in asingle channel and its location was maintained in time(t= 360 h). Along this channel, an equilibrium wasestablished between biofilm growth (volume increase)and detachment (volume decrease). Thus, after a primarychannel is formed, no re-opening of old flow pathwaysor formation of new channels is anymore possible.

Also, when the active biomass decayed into inertmaterial with lower cohesive strength (Case B1), thedeveloped biofilm led to formation of preferentialpathways and isolated pore volume from flow (100 h inFigure 2B and Movie 2 from Supplementary material).Along the flow channels, due to continuous nutrientsupply the biofilm colonies expanded. The substrate wasgradually depleted so that cells far from the open channelwould begin to decay. Therefore, a gradient of active bio-mass concentration was obtained: more active biomassclose to the liquid (dark gray in Figure 2B) and less in thedepth of the colony (light gray in Figure 2B). The modelassumes in this case that the decrease in biofilm activityalso induced the loss of cohesive strength, making inertbiomass more prone to detachment. Only along the flowchannel, however, there are shear forces on the biofilmsurface. As a consequence, the mechanical stress is largernear the surface exposed to flow and decreased deep inthe biofilm. Inert material, although having low cohesivestrength, would be detached only after the first layers ofactive biomass were removed. Although the decayed bio-film was considered more vulnerable to detachment, theabsence of shear forces did not allow biofilm removal in

Table 2. The model parameters in the different simulated cases A–I.

Biofilm yield strength [Nm�2]

Shear forces Shear and normal forces

A B1 B2 C D E F G H I

σn,X – – – – 400 1000 1�105 400 400 400σs,X 10 10 10 10 10 10 10 10 10 10σn,Xi – – – – 40 40 40 80 120 –σs,Xi – 1 0.1 1 1 1 1 2 3 –Lysis No No No Yes No No No No No No

1076 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

regions that became isolated from flow and, thus, re-open-ing of new channels. At 360 h, the flow was already con-centrated in a single channel whose location did not

change thereafter. In this unique flow channel, the bio-mass continued to grow, balanced by detachment. Similarresults were also obtained with even smaller yield strength

Figure 2. Selected images of substrate concentration, biomass, and development of flow pathways when only shear forces areexerted on the biofilm surface. The flow is from left to right. Substrate concentration changes from a maximum of 0.5molm�3 (red)to a minimum of zero (dark blue). Dark gray and light gray denote active and inert biomass, respectively. (A) Simulation in Case Awithout biomass decay; (B) simulation in Case B1 with biomass decay.

Biofouling 1077

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

of the inert biomass (Case B2). In conclusion, if the liquidflow induced only shear forces on the biofilm, the biomassweakening by decay could not lead to ‘dynamic’ or multi-ple flow channels.

When biomass decay is accompanied by lysis (CaseC), dynamic flow channeling occurs. Figure 4 showsimages of substrate concentration, formation of biomasscolonies, and development of flow pathways (see alsoMovie 3 from Supplementary material). Similar to thecase without lysis (Case B), after 200 h the flowappeared to be directed in a main flow pathway. Alongthis path, cells near the biofilm surface remained active,whereas decayed material formed in the biofilm depth. Inregions isolated from fluid flow, decay processes wouldtake place everywhere, both inside and at the surface ofa colony. After long starvation periods (200 h), the lysisprocess formed cavities within colonies. Voids in biofilmstructures were observed by Webb et al. (2003) andDavies and Marques (2009). Hunt et al. (2004) andDavies and Marques (2009) reported that hollowingoccurred in cell clusters that had reached a sufficientsize, and that voids were always centrally located in thebiofilm. Hunt et al. (2004) hypothesized that these char-acteristics were related to nutrient limitations as bacteriadeep in the biofilm would be more vulnerable to starva-tion compared to bacteria close to the liquid flow. Asdecay and lysis progress in time, more pores becomeinterconnected and a pathway previously clogged wouldeventually re-open. Along the new channels, the flow of

water provides new substrate, enhancing biofilm forma-tion and refilling of pathways. Repeated events of porerefilling and re-opening result in periodic shifts in thelocation of the flow pathways, as shown in the sequenceof images in Figure 4. Thus, the presence of shear forcesin association with biomass decay and lysis may lead tothe change of flow channels in time.

Significant biofilm growth in porous media reducesthe pore space available for flow and therefore affectsthe permeability. The permeability, k, can be calculatedfrom Darcy’s Law:

k ¼ Q

A

L

Dpg ¼ L g

Z H

0

uout dy

Z H

0

pin dy

�ð11Þ

where Q is volumetric flow rate [m3 s�1], A [m2] is theflow cross-section area, L is the length of the domain, Δpis the pressure drop [Pa], and η is the fluid dynamic vis-cosity [Pa s]. The pressure drop was computed with theaverage inlet pressure (pin) and zero-imposed pressure onthe outlet boundary. The average permeability k wasnormalized by the initial average permeability k0, andplotted against time (Figure 5a). In all simulated cases,the normalized permeability decreased rapidly from 1 to0.1 in the first 100 h and leveled out to an asymptoticvalue. Because a constant flow was imposed in the inlet,total clogging did not occur and zero-permeability couldnot be achieved. Permeability reduction is obviously

Figure 3. Stresses distribution within biofilm structures when only shear forces from fluid flow are exerted on the biofilm surface, insimulation Case A: (A) before detachment at 200 h and (B) after detachment at 205 h. Red and blue colors represent large and lowstresses, respectively. Larger stresses are observed at the surface of the biofilm in contact with the fluid flow. Arrows: fluid velocityvector.

1078 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

associated to biofilm formation as shown in Figure 5b,where the biofilm fraction (biofilm volume/total volume)

is plotted against time. In this specific case, a biofilmfraction of 20% caused >95% permeability reduction, as

Figure 4. Selected images of substrate concentration, biomass, and development of flow pathways when shear forces are exerted onthe biofilm surface and inert biomass lyses, in simulation Case C. Substrate concentration changes from a maximum of 0.5molm�3

(red) to a minimum of zero (dark blue). Dark gray and light gray indicate active and inert biomass, respectively. Active biomassunder limited nutrient supply decays to become inert, which is subsequently lysed leading to cavities in the biofilm. This combinationof fluid forces, decay, and lysis leads to dynamic flow pathways that change in size and location over time.

Biofouling 1079

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

shown in Figure 5c. A reduction in permeability up tothree orders of magnitude due to biofilm formation hasbeen reported in many experimental studies carried out inthe laboratory (Cunningham et al. 1991; Kim et al. 2006)as wells as in a field demonstration (Cunningham et al.2003) and in many other studies reviewed in Gerlach andCunningham (2010). Because the biofilm growth affectsmainly the pores open to flow, two interesting effects canbe noticed in Figure 5. First, the initial strong permeabil-ity decrease is due to simultaneous blocking of manypossible pores with biofilm. Later (after 200 h), althoughthe biofilm continues to grow almost linearly (Figure 5b)it will not change the average permeability significantlybecause the growth occurs in pores that do not affect theflow (ie the effective porosity is no longer affected by thebiomass growth). Secondly, the average permeabilitymaintains an asymptotic trend (Case C in Figure 5a),although the location of flow pathways shifts repeatedlywith time (see Figure 4). The local pore filling/openingcycles could only lead to fluctuations in the averagepermeability around the steady value.

Effect of total forces and biomass decay

Total forces are a combination of both normal (pressure)and tangential (shear) forces exerted by the fluid on thebiofilm. Performing mechanical tests on biofilms is adifficult task due to biofilm heterogeneity and the smallscale involved. How biofilm mechanics is influenced bythe growth environment is also an open question. Never-theless, a comparison of available experimental data(Ohashi et al. 1999; Poppele & Hozalski 2003; Coufortet al. 2007; Möhle et al. 2007), revealed differentmechanical behavior of biofilms depending on whetherthey are exposed to tangential or normal forces. Reportedvalues for the critical shear strength vary between 2 and12Nm�2 (Coufort et al. 2007; Möhle et al. 2007),whereas critical strengths ranging between 400 and105Nm�2 were found when normal forces were exertedon the biofilm (Ohashi et al. 1999; Poppele & Hozalski2003). This suggests that cells at the biofilm surfacecould be detached easily when exposed to shear (tangen-tial) forces. In contrast, larger normal forces are neededto break down the biofilm bulk due to the strongcohesion forces. The approach to account for this dualmechanical behavior in the current numerical model wasto assign two different biofilm yield strengths, one forshear σs,X and another one σn,X for the normal yieldstrength (σn,X >> σs,X). A set of simulations was carriedout to investigate the effect of total forces and biofilmyield strengths on the development of flow pathways.The parameters used in these simulations are listed inTable 1, and a summary of the simulations performed isreported in Table 2.

0 0.05 0.1 0.15 0.2 0.250

0.2

0.4

0.6

0.8

1

Fraction biomass [-]

k/k 0 [

-]

Case ACase B1Case B2Case C

0 100 200 300 4000

0.05

0.1

0.15

0.2

0.25

time [h]

Frac

tion

biom

ass

[-]

Case ACase B1Case B2Case C

0 100 200 300 4000

0.2

0.4

0.6

0.8

1

time [h]

Case ACase B1Case B2Case C

(a)

(b)

(c)

k/k 0 [

-]

Figure 5. Effect of decay and lysis on: (a) change ofnormalized permeability (k/k0) over time; (b) biomass fractionover time; and (c) normalized permeability function of biomassfraction. Results refer to simulation Cases A, B, and C, whereonly shear forces are exerted on the biofilm surface.

1080 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

Formation of dynamic flow paths

The first simulated case (Case D) considers a biofilmwith mechanically weak active biomass, having low nor-mal yield strength, σn,X= 400Nm�2 and a shear yield

strength of σs,X = 10Nm�2. It was also assumed that bothyield strengths of inert biomass are 10% ofthose assigned to the active biomass (σs,Xi = 1Nm�2,σn,Xi = 40Nm�2). Formation of dynamic flow paths with

Figure 6. Selected images of substrate concentration, biomass, and development of flow pathways when shear and pressure forcesare exerted on the biofilm surface, in simulation Case D. Substrate concentration changes from a maximum of 0.5molm�3 (red) to aminimum of zero (dark blue). Dark gray and light gray indicate active and inert biomass, respectively. Fluid flow pathways are inthis case dynamic, with continual pore clogging and unclogging events repeatedly changing the flow.

Biofouling 1081

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

these assumptions for biofilm strength can be seen inFigure 6 and in Movie 4 from the Supplementary mate-rial. Biomass grows and forms large clusters that wouldocclude pores forcing the flow through preferential path-ways. As the biofilm grows, the dominant flow pathwaysare gradually filled by biomass and the pore throat sizesdecrease. To maintain a constant inflow, the inlet pres-sure must increase, with a consequent increase in thelocal fluid pressure and flow velocity. This causes anincrease in the load forces applied on the biofilm surface.In regions where the fluid flow is negligible, stresses inthe biofilm are mainly due to the normal forces and notto shear forces. Different pressure loads exerted on theopposing surfaces of a biomass plug between two grainscan result in a stress gradient within the biofilm. Furtherincrease in the normal loads above some critical valuewould make the biofilm vulnerable to detachment. As aresult of sudden detachment of a biofilm plug, the fluidpressure is relieved, areas excluded to flow become againaccessible to fluid and new flow channels are formed. Inthe newly opened channels, the liquid flow will begin toremove inert biomass accumulated under stagnant condi-tions, quickly enlarging the pore size. On the other hand,the new supply of nutrients promotes biofilm re-growth,which once more decreases the effective pore space.Eventually, growth and detachment events, in which bothnormal and shear forces are involved, result in a continu-ous plugging and re-opening of flow channels (visible inFigure 6 from t = 200 to t = 450 h). To assess whetherthe shift in the location of dominant flow pathways isreproducible with different grain arrangements in thedomain, an additional set of three replicate simulationswas carried out, all using the same parameters as in CaseD. The continuous change of the flow pathways occurredsimilarly in all replicate simulations.

Experimental data on plugging of porous mediainduced by biofilms and observations of periodic shiftsof flow pathways have been reported by several authors.Stewart and Fogler (2002) carried out a series of experi-ments in a micro-model consisting of triangular pillarsetched in glass to form a network of connected porethroats and pore bodies. Images taken in time revealedthat, under constant inlet flow rate, dominant flow pathsformed initially in a network of large pore throats.However, under continuous nutrient supply, the biomasscontinued to fill the large pores and the flow was laterdiverted towards the smaller pores. As the experimentsproceeded in time the small pores were also occludedand a shift in the location of the dominant flow pathswas noticed repeatedly with time. Sharp et al. (1999,2005) also performed experiments with a constant flowrate fed into a flat-plate micro-channel obstructed by amatrix of diamond-shaped pillars. A nigrosine dye tracerwas used to identify flow paths. Their results showedthat a thin biofilm led to disperse flow in the porous

medium, whereas thick and structured biofilms inducedstrong channeling. After 14 days, the flow adopted pref-erential paths, which were later plugged and the flowwas forced to find different channels.

Effect of biomass strength

To investigate the role of biomass strength on thedevelopment of flow pathways, a set of simulations wascarried out with different biofilm yield strengths (Table 2).The normal yield strength of active biomass wasincreased to 1000Nm�2 (Case E) and 100,000Nm�2

(Case F). Further, the normal yield strength of inertbiomass was 20% (Case G) and 30% (Case H) of the ref-erence yield strength of active biomass. An additionalsimulation assumed no biomass decay (Case I).

In all the simulations performed, periodic shifts inthe location of flow channels were observed. However,the change of flow paths occurred less frequently forstronger biofilms (Case F), or without accumulation ofweak inert material (Case I). Figure 7a and c showsnormalized permeability (k/k0) vs time. A general trendcan be noticed in all simulations: a rapid decrease in per-meability in the first 100 h and an asymptotic behavior atlater times. The decrease in the first 100 h was due tobiomass growth with a consequent decrease in the effec-tive porosity. Later, pore clogging and re-opening wasresponsible for changes in the location of the preferentialflow paths, although the average permeability remainedalmost the same. For the weaker biofilm (Case D), thepermeability kept oscillating because the biomass wasmore susceptible to detachment (see the permeabilitypeak at 300 h), followed by re-growth, leading againto decreased permeability. Changes in permeabilitywere correlated with variations in the biomass fraction(Figure 7b and d), clearly associated with repeated andconsecutive events of growth and detachment.

Domain size

It is reasonable to assume that for smaller computationaldomains, the effects of random detachment and growthare more pronounced and the oscillations in permeabilityand the amount of biomass would be enhanced. Toassess the importance of the domain size on the results,simulations were carried out in a smaller computationaldomain of 1� 6mm2, maintaining parameters as in thereference Case D. The results are plotted in Figure 8aand b and compared with those obtained for the larger(4� 6mm2) domain. Indeed, both normalized permeabil-ity and the biomass fraction showed more frequentoscillations in time for the smaller domain, associatedwith sequential development of biomass plugs and chan-nel breakthroughs. In particular, permeability oscillationswere related to pressure drop fluctuations across the

1082 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

domain: a pressure maximum can be associated with thedevelopment of a plug, while minimum pressureindicates a channel opening.

Oscillations in pressure drop in porous media due tobiofilm formation were also observed in micro-modelexperiments by Stewart and Fogler (2001, 2002), and inthe experiments carried out in consolidated core samplesby Lappan and Fogler (1992, 1996). Stewart and Kim(2004) modeled the experiments, by Stewart and Fogler(2002), by a pore network numerical approach with a

regular array of nodes connected by cylindrical tubes(pore throats). Although their model results showed afirst steep decrease in permeability due to biofilmpropagation, the model could not properly describeconsecutive oscillations at later times. For example, over-estimated oscillations of the medium permeability couldbe related to the fact that the detachment mechanismaccounted only for biomass sloughing and not for grad-ual removal of biofilm layers. Their biofilm detachmentremoved the entire biofilm and reset the cylinder

Figure 7. Effect of biofilm yield strength on: (a and c) change of normalized permeability k/k0 over time; (b and d) fraction ofbiomass over the entire computational domain vs time. Simulations including both tangential and normal forces applied on thebiofilm surface were carried out with the different biofilm yield strengths from Table 2.

Biofouling 1083

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

diameter to the initial value. Moreover biomass washomogeneously distributed along the wall of a cylinder,not accounting for the biofilm morphology and its impacton the hydrodynamics. Also, not accounted for wasbiofilm growth in void junctions, which would havelimited the flow in all connected pore throats, with aconsequently larger impact on permeability decrease. Inthis respect, the model proposed in the present study,although more complex and computationally moreintensive, can represent in more detail the dynamics ofbiofilm growth and detachment.

Conclusions

A two-dimensional micro-scale numerical model forbiofilm formation was developed to study the dynamicsof preferential flow pathways in porous media. Flow andsolute transport equations were coupled with a biofilmmodel including biomass attachment, growth, decay,lysis, and detachment computed from biofilm mechanics.The results showed that under constant liquid flow ratein the inlet, shear forces alone could lead to the forma-tion of a preferential flow path that maintains the samelocation in time and a quasi-steady state permeabilitywas reached. Similar results were obtained with biomassdecay and shear forces only, suggesting that the strengthof decayed biomass does not play a role in the shift inthe location of the flow pathway.

When biomass decay and lysis processes wereconsidered in combination with shear forces, the model

could reproduce intermittent shifting in the location offlow channels as a result of repeated events of cloggingand unclogging of interconnected pore spaces. In regionsisolated from fluid flow, due to the slow nutrient transport,prolonged starvation conditions caused biomass decay andlysis. The biomass was so weakened and unclogging ofsome pores eventually led to new continuous flow paths.Repeated events of pore clogging and unclogging with aconsequent shift in the location of the flow pathways isalso observed when both shear and normal forces aretaken into account. In areas isolated from fluid flow, dif-ferential fluid pressure on the biofilm structure could trig-ger biofilm detachment and re-opening of new pathways.

AcknowledgmentsThe authors are grateful to DOW Microbial Control, BuffaloGrove, IL, USA, for the financial support. The work ofC. Picioreanu was financially supported also by the NetherlandsOrganization for Scientific Research [NWO VIDI grant 864-06-003]. Conceptual discussions with Dr Robin Gerlach fromMontana State University are kindly acknowledged.

ReferencesAllison DG, Ruiz B, Sanjose C, Jaspe A, Gilbert P. 1998.

Extracellular products as mediators of the formation anddetachment of Pseudomonas fluorescens biofilms. FEMSMicrobiol Lett. 167:179–184.

Applegate DH, Bryers JD. 1991. Effects of carbon and oxygenlimitations and calcium concentrations on biofilm removalprocesses. Biotechnol Bioeng. 37:17–25.

Figure 8. Effect of computational domain size on: (a) change of normalized permeability k/k0 over time; (b) biomass fraction vstime. Two domains sizes were considered, with a length� height of 6� 4mm and 6� 1mm. Both tangential and normal forces wereapplied on the biofilm surface.

1084 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

Baker JS, Dudley LY. 1998. Biofouling in membrane systems –a review. Desalination. 118:81–89.

Böl M, Mohle RB, Haesner M, Neu TR, Horn H, Krull R.2009. 3D finite element model of biofilm detachment usingreal biofilm structures from CLSM data. Biotechnol Bio-eng. 103:177–186.

Bower AF. 2010. Applied mechanics of solids. Boca Raton(FL): CRC Press/ Taylor & Francis Group.

Coufort C, Derlon N, Ochoa-Chaves J, Liné A, Paul E. 2007.Cohesion and detachment in biofilm systems for differentelectron acceptors and donors. Water Sci Technol. 55:421–428.

Cunningham AB, Characklis WG, Abedeen F, Crawford D.1991. Influence of biofilm accumulation on porous mediahydrodynamics. Environ Sci Technol. 25:1305–1311.

Cunningham AB, Sharp RR, Hiebert R, James G. 2003. Sub-surface biofilm barriers for the containment and remedia-tion of contaminated groundwater. Bioremed J. 7:151–164.

Cusack F, Singh S, McCarthy C, Grieco J, De Rocco M, Ngu-yen D, Lappin-Scott H, Costerton JW. 1992. Enhanced oilrecovery – three-dimensional sandpack simulation of ultra-microbacteria resuscitation in reservoir formation. J GenMicrobiol. 138:647–655.

Davies DG, Marques CNH. 2009. A fatty acid messenger isresponsible for inducing dispersion in microbial biofilms. JBacteriol. 191:1393–1403.

Duddu R, Chopp DL, Moran B. 2009. A two-dimensional con-tinuum model of biofilm growth incorporating fluid flowand shear stress based detachment. Biotechnol Bioeng.103:92–104.

Fowler JD, Robertson CR. 1991. Hydraulic permeability ofimmobilized bacterial cell aggregates. Appl Environ Micro-biol. 57:102–113.

Gerlach R, Cunningham AB. 2010. Influence of biofilms onporous media hydrodynamics. In: Vafai K, editor. Porousmedia: applications in biological systems and biotehnology.Boca Raton (FL): CRC Press/Taylor and Francis Group; p.173–230.

Graf von der Schulenburg DA, Pintelon TR, Picioreanu C, vanLoosdrecht MCM, Johns ML. 2009. Three-dimensionalsimulations of biofilm growth in porous media. AIChE J.55:494–504.

Hentzer M, Riedel K, Rasmussen TB, Heydorn A, AndersenJB, Parsek MR, Rice SA, Eberl L, Molin S, Hoiby N,et al. 2002. Inhibition of quorum sensing in Pseudomonasaeruginosa biofilm bacteria by a halogenated furanonecompound. Microbiol SGM. 148:87–102.

Henze M, Gujer W, Mino T, van Loosdrecht MCM. 2000. Acti-vated sludge models ASM1, ASM2, ASM2d and ASM3. In:Henze M, Gujer W, Mino T, van Loosdrecht MCM, editors.IWA task group on mathematical modelling for design andoperation of biological wastewater treatment. IWA scientific& technical report. London: IWA; p. 24–25.

Hunt SM, Werner EM, Huang B, Hamilton MA, Stewart PS.2004. Hypothesis for the role of nutrient starvation in bio-film detachment. Appl Environ Microbiol. 70:7418–7425.

Kao CM, Chen SC, Liu JK. 2001. Development of a biobarrierfor the remediation of PCE-contaminated aquifer. Chemo-sphere. 43:1071–1078.

Kapellos GE, Alexiou TS, Payatakes AC. 2007. Hierarchicalsimulator of biofilm growth and dynamics in granularporous materials. Adv Water Resour. 30:1648–1667.

Kim G, Lee S, Kim Y. 2006. Subsurface biobarrier formationby microorganism injection for contaminant plume control.J Biosci Bioeng. 101:142–148.

Knutson CE, Werth CJ, Valocchi AJ. 2005. Pore-scale simula-tion of biomass growth along the transverse mixing zone ofa model two-dimensional porous medium. Water ResourRes. 41:1–12.

Komlos J, Cunningham AB, Kamper AK, Sharp RR. 2004.Biofilm barriers to contain and degrade dissolved trichloro-ethylene. Environ Prog. 23:69–77.

Lappan RE, Fogler HS. 1992. Effects of bacterial polysaccha-ride production on formation damage. SPE Prod Eng.7:167–171.

Lappan RE, Fogler HS. 1996. Reduction of porous media per-meability from in situ Leuconostoc mesenteroides growthand dextran production. Biotechnol Bioeng. 50:6–15.

Lappin-Scott HM, Cusack F, Costerton JW. 1988. Nutrientresuscitation and growth of starved cells in sandstone cores:a novel approach to enhanced oil recovery. Appl EnvironMicrobiol. 54:1373–1382.

MacLeod FA, Lappin-Scott HM, Costerton JW. 1988. Pluggingof a model rock system by using starved bacteria. ApplEnviron Microbiol. 54:1365–1372.

Mitchell AC, Phillips AJ, Hiebert R, Gerlach R, Spangler LH,Cunningham AB. 2009. Biofilm enhanced geologicsequestration of supercritical CO2. Int J Greenh Gas Con.3:90–99.

Möhle RB, Langemann T, Haesner M, Augustin W, Scholl S,Neu TR, Hempel DC, Horn H. 2007. Structure and shearstrength of microbial biofilms as determined with confocallaser scanning microscopy and fluid dynamic gauging usinga novel rotating disc biofilm reactor. Biotechnol Bioeng.98:747–755.

Ohashi A, Harada H. 1996. A novel concept for evaluation ofbiofilm adhesion strength by applying tensile force andshear force. Water Sci Technol. 34:201–211.

Ohashi A, Koyama T, Syutsubo K, Harada H. 1999. A novelmethod for evaluation of biofilm tensile strength resistingerosion. Water Sci Technol. 39:261–268.

Paulsen JE, Oppen E, Bakke R. 1997. Biofilm morphology inporous media, a study with microscopic and imagetechniques. Water Sci Technol. 36:1–9.

Picioreanu C, Kreft JU, Klausen M, Haagensen JAJ,Tolker-Nielsen T, Molin S. 2007. Microbial motilityinvolvement in biofilm structure formation – a 3D model-ling study. Water Sci Technol. 55:337–343.

Picioreanu C, van Loosdrecht MCM, Heijnen JJ. 1998. A newcombined differential-discrete cellular automaton approachfor biofilm modeling: application for growth in gel beads.Biotechnol Bioeng. 57:718–731.

Picioreanu C, van Loosdrecht MCM, Heijnen JJ. 2000. Effectof diffusive and convective substrate transport on biofilmstructure formation: a two-dimensional modeling study.Biotechnol Bioeng. 69:504–515.

Picioreanu C, van Loosdrecht MCM, Heijnen JJ. 2001.Two-dimensional model of biofilm detachment caused byinternal stress from liquid flow. Biotechnol Bioeng.72:205–218.

Picioreanu C, Vrouwenvelder JS, van Loosdrecht MCM. 2009.Three-dimensional modeling of biofouling and fluiddynamics in feed spacer channels of membrane devices. JMembr Sci. 345:340–354.

Pintelon TR, Graf von der Schulenburg DA, Johns ML. 2009.Towards optimum permeability reduction in porous mediausing biofilm growth simulations. Biotechnol Bioeng.103:767–779.

Biofouling 1085

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014

Pintelon TR, Picioreanu C, van Loosdrecht MC, Johns ML.2012. The effect of biofilm permeability on bio-clogging ofporous media. Biotechnol Bioeng. 109:1031–1042.

Pizarro GE, Garcia C, Moreno R, Sepulveda ME. 2004. Two-dimensional cellular automaton model for mixed-culturebiofilm. Water Sci Technol. 49:193–198.

Poppele EH, Hozalski RM. 2003. Micro-cantilever method formeasuring the tensile strength of biofilms and microbialflocs. J Microbiol Methods. 55:607–615.

Radu AI, Vrouwenvelder JS, van Loosdrecht MCM, PicioreanuC. 2010. Modeling the effect of biofilm formation onreverse osmosis performance: flux, feed channel pressuredrop and solute passage. J Membr Sci. 365:1–15.

Sawyer LK, Hermanowicz SW. 2000. Detachment of Aeromonashydrophila and Pseudomonas aeruginosa due to variationsin nutrient supply. Water Sci Technol. 41:139–145.

Sharp RR, Cunningham AB, Komlos J, Billmayer J. 1999.Observation of thick biofilm accumulation and structure inporous media and corresponding hydrodynamic and masstransfer effects. Water Sci Technol. 39:195–201.

Sharp RR, Stoodley P, Adgie M, Gerlach R, Cunningham A.2005. Visualization and characterization of dynamic pat-terns of flow, growth and activity of Vibrio fischeri biofilmsgrowing in porous media. Water Sci Technol. 52:85–90.

Stewart TL, Fogler HS. 2001. Biomass plug developmentand propagation in porous media. Biotechnol Bioeng.72:353–363.

Stewart TL, Fogler HS. 2002. Pore-scale investigation ofbiomass plug development and propagation in porousmedia. Biotechnol Bioeng. 77:577–588.

Stewart TL, Kim DS. 2004. Modeling of biomass-plugdevelopment and propagation in porous media. BiochemEng J. 17:107–119.

Stoodley P, Cargo R, Rupp CJ, Wilson S, Klapper I. 2002.Biofilm material properties as related to shear-induceddeformation and detachment phenomena. J Ind MicrobiolBiotechnol. 29:361–367.

Thormann KM, Saville R, Shukla S, Spormann AM. 2005.Induction of rapid detachment in Shewanella oneidensisMR-1 biofilms. J Bacteriol. 187:1014–1021.

van Loosdrecht MCM, Eikelboom D, Gjaltema A, Mulder A,Tijhuis L, Heijnen JJ. 1995. Biofilm structures. Water SciTechnol. 32:35–43.

Vrouwenvelder JS, Hinrichs C, van der Meer WGJ, vanLoosdrecht MCM, Kruithof JC. 2009. Pressure dropincrease by biofilm accumulation in spiral wound RO andNF membrane systems: role of substrate concentration,flow velocity, substrate load and flow direction. Biofouling.25:543–555.

Waybrant KR, Blowes DW, Ptacek CJ. 1998. Selection ofreactive mixtures for use in permeable reactive wallsfor treatment of mine drainage. Environ Sci Technol.32:1972–1979.

Webb JS, Thompson LS, James S, Charlton T, Tolker-NielsenT, Koch B, Givskov M, Kjelleberg S. 2003. Cell death inPseudomonas aeruginosa biofilm development. J Bacteriol.185:4585–4592.

Xavier JB, Picioreanu C, Abdul Rani S, van Loosdrecht MCM,Stewart PS. 2005. Biofilm-control strategies based onenzymic disruption of the extracellular polymeric sub-stance matrix – a modelling study. Microbiol SGM. 151:3817–3832.

Xavier JB, Picioreanu C, van Loosdrecht MCM. 2005. Ageneral description of detachment for multidimensionalmodelling of biofilms. Biotechnol Bioeng. 91:651–669.

1086 S. Bottero et al.

Dow

nloa

ded

by [

Bib

lioth

eek

TU

Del

ft]

at 0

5:38

06

Janu

ary

2014