A two-phase flow model of biofilm detachment Ashkan Safari, Alojz Ivankovic, Aleksandar Karac, Maik Walter, Eoin Casey School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Ireland [email protected]

Introduction Biofilms are formed when bacterial cells attach to the surface of submerged solid objects and accumulate to form a multilayered cellular structure. The following steps are typically involved in biofilm development processes: 1) Initial adhesion of planktonic cells to the surface, 2) Accumulation to form multilayered cell clusters surrounded by an extra-cellular polymeric substance (EPS), 3) Biofilm maturation with the development of a characteristic morphology and, 4) Detachment which is a term used to describe the release of individual cell and/or cell clusters from a biofilm. Detachment of biofilm which disseminates to other parts in the body may cause infections [1]. Failure of biofilm may occur in the form of detachment of whole cell clusters (adhesive failure) or breaking of a streamer tail (cohesive failure) [2]. The main aim of this work is to develop a numerical model to predict the detachment of biofilm in a fluid flow system. In a flowing system, interaction between the bulk fluid and the attached biofilm depends on both hydrodynamics and the mechanical properties of the biofilm. The fundamental simplification made in this investigation concerns the material properties of the biofilm. It is well accepted that biofilm exhibits viscoelastic properties under fluid induced stresses [3 and 4]; however in this study we model the biofilm as a Newtonian incompressible viscous fluid whose viscosity is much larger than that of the external bulk fluid. Similar assumption was used in previous studies [5].

Numerical and Experimental procedures In this numerical study, motion of biofilm and the bulk fluid is governed by Navier Stokes equations. The two phases are separated by an interface defined by using volume fraction of fluids. The two-phase algorithm is developed in OpenFoam package based on the volume of fluids (VOF) method using a transport equation to determine the relative volume fraction of two fluids, or phase fraction (γ) for each computational cell [6]. Fraction can have a value between 0 and 1. The interface is never sharply defined in VOF method and it smeared in a volume around the region where a sharp interface should exist. Governing equations and discretisation procedure is described in [6 and 7]. The rectangular channel flow cell used in this simulation is representative of that employed in the experimental part of this work. The flow cell is made of glass with a rectangular cross section of 3 mm x 3 mm and length of 100 mm. In

the numerical simulation, the flow channel is approximated by a 2D rectangular solution domain with height of 3 mm and length of 20 mm. A square shape block of biofilm (1 mm x 1 mm) was placed at the centre of channel bottom (Figure 1).

Biofilm block at the centre of channel

Figure 1. Two-dimension geometry used in the simulations Initial simulations were run at flow velocities in the range of 0.0001-0.1 m/s applied at the inlet of the flow cell (X=0) under laminar flow conditions. Higher flow velocities up to 1 m/s were also applied in order to investigate turbulent conditions. At the inlet boundary, uniform velocity distribution is specified together with zero pressure gradient boundary condition. At outflow boundary (X=0.02 m), fixed pressure boundary condition is applied where pressure on the boundary is fixed to atmospheric value and a zero gradient condition is applied to the velocities. At wall, zero slip condition was applied for the velocity which means that the fluid at the wall takes the velocity of the wall. The values indicator function (gamma) and the pressure, are unknown at a wall. In the case of the indicator function, it is sufficient to apply a zero gradient boundary condition. A wall adhesion phenomenon is implemented at wall to describe the wetting behaviour based on static contact angle [7]. Materials properties of each Newtonian fluid (water & biofilm) used in the simulations are listed in Table 1. Property 3

Water density kg/m

2

Value

Source

1000

-

Water kinematic viscosity m /s

0.000001

-

Biofilm density kg/m3

1010

Assumed

Biofilm kinematic viscosity m2/s

10

Assumed

Biofilm surface energy N/m-1

0.065

Calculated

Table 1. Parameters used in the simulations

At the substrate boundary (Y=0), work of adhesion model is used to describe wetting behaviour of biofilm on the substrate surface. In a solid-liquid-vapour system, adhesion energy at the surface (Wsl) can be expressed by Young- Dupre’s equation [9]:

Wsl = γ lv (1 + cosθ )

(1)

Where γlv is liquid-vapour interfacial free energy and θ is equilibrium contact angle in the system. Equation 1 can be applied to a substrate-biofilm-bulk fluid system in this study.

Figure 2a shows distribution in axial flow velocity along the flow cell length at 2.5 mm distance from the bottom at time instants of 5, 10 and 20 Sec for initial inlet flow velocity of 0.01 m/s. Figure 2(b-d) shows gamma distribution corresponding to these three time steps. As can be seen in Figure 2a flow velocity (also fluid shear stress) reached the maximum value over the biofilm block followed by a sharp decrease to initial value when it passed the biofilm. There is insufficient stress applied on biofilm within 20 Sec to considerably change the biofilm structure and cause detachment (see Figures-2(b-d)). Flow velocity distribution

cos θ = −1 + 2(γ sv γ lv ) 2 .γ lv−1 + 2(γ sv γ lv ) 2 .γ lv−1 d

d

1

p

p

1

Axial flow velocity (m/s)

Contact angle of biofilm on glass substrate and biofilm surface energy were measured using the DATAPHYSICS OCA 20 Contact Angle System. Biofilm surface energy was measured using three different liquids: Water, Diiodomethane (CH2I2) and Ethyleneglycol (Ethane-1, 2-diol). The Surface Energy was calculated according to the model of Owens,Wendt, Rabel and Kaelble (OWRK) [10]. In that method, surface tension γsv of the solid surface and its dispersive and polar components as unknown parameters can be determined by using different liquids with known contact angles, and applying Equation 2:

0.05

Time=5s Time=10s Time=20s

0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0

0.005

0.01

0.015

0.02

Distance along flow cell length (m)

(a)

(2)

Where γsv and γlv are solid-vapour and liquid-vapour free energies respectively and θ is equilibrium contact angle (superscript d and p denote dispersive and polar components respectively).

(b)

Results and Discussion The mean value of biofilm contact angle on glass substrate at equilibrium state was found to be approximately 72o and the mean value of the biofilm surface energy based on the OWRK model was 65±3.14 mNm−1. Values of disperse and polar components of surface energies are presented in Table 2. Sample Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample7 Sample8 Sample9 Sample10 Sample11

Surface Energy in mNm−1 disperse part polar part total value 19.4 43.82 62.86 18.01 49.36 67.37 23.07 44.57 67.64 23.72 35.64 59.36 22.84 41.96 64.8 23.04 44.06 67.1 22.30 40.01 62.31 16.31 52.80 69.10 15.49 51.26 66.75 21.02 45.85 66.67 20.21 40.83 61.04

Table 2. Dispersive and polar component values for biofilm surface energy

(c)

(d) Figure 2. (a) Velocity distribution for initial flow velocity of 0.01 m/s along the cell length at the distance of 2.5 mm from the bottom for different time steps. Gamma distribution at (b) 5 Sec, (c) 10 Sec and (d) 20 Sec. In a similar manner, Figure 3(a-d) presents results for initial inlet flow velocity of 0.5 m/s for turbulent flow conditions. As can be seen in Figure 3a, the flow velocity downstream of the biofilm is greater than the inlet velocity and increases with time. In this case biofilm detaches from the surface after 5 Sec and it is ‘washed’ away by applied bulk fluid stresses after 20 Sec.

Flow velocity distribution

Axial flow velocity (m/s)

2

Time=5s Time=10s Time=20s

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.005

0.01

0.015

0.02

Distance along flow cell lenght (m)

(a)

The main observation is that the detachment process is promoted by higher initial flow velocities (above 0.1 m/s). Results suggest that biofilm detachment occurred due to increasing stresses applied by the flowing fluid to the biofilm, similar to the previous finding [3]. Results obtained using a viscoelastic biofilm model which exhibits both solid and fluid behavior showed that higher flow velocities were required for detachment to occur compared to the present results [1]. It should be noted that in that study detachment of biofilm was investigated by increasing flow velocity applied on biofilm which were grown in laminar and turbulent flow conditions. In the present study, a growth of biofilm was not accounted for.

Conclusions

(b)

This work demonstrates that a two-phase fluid model may be useful to describe detachment of the biofilm from the substrate and a breakdown of biofilm itself. The work of adhesion model at substrate boundary seems to be a sound description of adhesive failure of biofilm. It may be also concluded that biofilm detachment is greatly influenced by hydrodynamic conditions. Work is in progress on developing a viscoelastic model for biofilm response to fluid flow, which will consider both flow and deformation behaviour of biofilm.

(c)

Acknowledgements Financial support for this work is provided by Science Foundation Ireland.

(d) Figure 3. (a) Velocity distribution for initial inlet flow velocity of 0.5 m/s at inlet along the cell length at the distance of 2.5 mm from the bottom for different time steps. Gamma distribution at (b) 5 Sec, (c) 10 Sec and (d) 20 Sec For the laminar range, it was found that biofilm tends to detach from the surface after 360 Sec at flow velocity of 0.1 m/s (see Figure 4) whereas at lower flow velocities (i.e 0.001 &0.01 m/s) biofilm structure did not change significantly nor detached at a larger time of 3600 Sec after which the simulations were stopped.

Figure 4. Gamma distribution at the simulation time of 360Sec for initial inlet flow velocity of 0.1 m/s

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