Flow hydrodynamics and nutrient availability

There is an inherent link between flow hydrodynamics and nutrient availability on biofilm development, owing to their influence on mass transfer and diffusion rates. The mass transfer and diffusion rates of a system are predominantly governed by the level of turbulence in the flow, which is usually estimated by the dimensionless parameter, Reynolds number, Re. The Re represents the balance between the magnitude of inertial and viscous forces:

𝑅𝑒_𝑥 =𝜌𝑈̅𝑥

𝜇 Equation 2.1

where x is a characteristic length scale (i.e. pipe diameter, D), 𝑈̅ is the average freestream velocity, ρ is the Density of fluid and μ is the dynamic viscosity of the fluid.

Using D as the characteristic length scale flows within pipes generally conforms to the following patterns; for ReD ≤ 2000, laminar flow exits; for 2000 < ReD < 4000, the flow is transitional; for ReD > 4000, the flow is turbulent. Since high Re values are associated with high velocity flows, it follows that viscous effects are less important in establishing the flow condition in the turbulent flow regime. Conversely low Re values indicate that viscous effects significantly influence the flow condition under relatively low velocites. The flow within most DWDSs and DNs is typically turbulent in nature. However, laminar flow conditions can be observed in areas of low water consumption (i.e. rural areas) and/or towards the end of long branches and the network periphery, where flow can be very low or periodically stagnant.

Conceptually, the boundary layer of turbulent flows can be divided into two regions, namely the inner and outer regions, as shown in Figure 2.2. The inner region of the boundary layer generally consists of two layers namely; (i) the viscous or laminar sublayer and (ii) the logarithmic sublayer (Schlichting 1979). The viscous sublayer is closest to the pipe wall and its thickness δ’ is given by;

𝛿′ =5𝑣

𝑢^∗ Equation 2.2

where ν is the kinematic viscosity of the fluid and u* is the shear velocity.

The shear velocity is given by;

𝑢^∗= √𝜏_𝑤

𝜌 Equation 2.3

where τw is wall shear stress.

Hence, the value of δ’ is a function of the type of fluid and the flow condition. For example, an increase in flow rate, Q leads to an increase in u* and a decrease in δ’ for the same fluid, i.e. it causes a reduction of the boundary layer thickness. Beyond the logarithmic layer lies the outer flow region, where the mean flow velocity is that of the free stream. As illustrated in Figure 2.3, there are three types of boundary layers, namely hydraulically smooth (Figure 2.3a), transitional (Figure 2.3b) and hydraulically rough (Figure 2.3c and Figure 2.3d). The classification depends upon the thickness of the absolute surface roughness height (k) relative to δ’. A boundary layer is classed as hydraulically smooth for k < δ’ and it is classed as hydraulically rough for k > δ’. For k  δ’, the boundary layer is classified as transitional.

Furthermore, in terms of the ks,Nikuradse (1933) found that for a surface consisting of closely packed, nearly mono-disperse sandgrain roughness (i.e. ks) the flow was smooth for ks+

(=ksν/u*) ≤ 5, transitionally rough for 5 < ks+

< 70, and fully rough for ks+ ≥ 70. The average sandgrain height was used to represent ks (Nikuradse 1933). For each of these classifications, the influence of the surface roughness on biofilm development is inherently different, with the greatest impact occurring under hydraulically rough conditions and the least impact under hydraulically smooth conditions.

Previous studies have shown that the boundary layer structure is altered by the presence of a biofilm (Schultz 2000; Andrewartha and Sargison 2011). Andrewartha and Sargison (Andrewartha and Sargison 2011) found that biofilms altered both the turbulent structure and thickness of the boundary layer. The altered boundary layer then impacts upon further biofilm development, thereby establishing a dynamic two-way (symbiotic) feedback relationship.

This process has a subsequent effect on flow resistance and Q. Such changes in the operating conditions affect δ’ further, as well as its relationship to k, and so on until a point of equilibrium can be reached. This complex matrix of interacting causes and effects is illustrated in Figure 2.4. If these conditional changes are significant, then they can be considered as influential upon the resulting biofilm development as flow hydrodynamics.

The degree of influence that flow hydrodynamics can have upon biofilm development is highly dependent on the system’s flow classification (Lewandowski and Stoodley 1995;

Stoodley et al. 1998a).

Figure 2.3Boundary layer classifications, including; a) hydraulically smooth, b) transitionally rough, and c)-d) hydraulically rough, for a smooth and rough surface (Barton 2006).

Figure 2.4Schematic representation of the dynamic feedback relationship that exists between the boundary layer hydrodynamics, biofilm development, operational and environmental conditions.

Flow Direction

Inner Region

Logarithmic Layer

a) Hydraulically Smooth b) Transitionally Rough

c) Hydraulically Rough (Rough Surface)

Outer Turbulent Region

δ'

δ' d) Hydraulically Rough (Smooth Surface) y

δ' δ'

y

y y

y x

Viscous Sublayer

Hydrodynamic and environmental conditions

Biofilm Development

Boundary Layer Structure

alters the…

alters the…

alters the…

Surface’s Frictional Resistance

Pressure Drop

Equivalent Roughness Scale

alters the…

In laminar flow conditions there is a relatively thick boundary layer. The ample boundary layer and the low near wall shear forces are in theory conducive to successful biofilm development (Stoodley et al. 1998a). However, such a large boundary layer combined with the inherent lack of mixing within laminar conditions is non-conducive to successful mass transfer, as it is likely to retard the influx and diffusion of microorganisms, dissolved oxygen and nutrients to the surface, thus potentially impairing overall biofilm growth rate. On the other hand, within DWDSs which utilise disinfectants, the retarded diffusion rates are likely to reduce the disinfectant’s effectiveness, which is of benefit to the biofilm. However, in reality and in most cases this is not likely to be a factor, as laminar conditions are most prevalent within DWDSs at the network periphery, where disinfectant levels are typically at their lowest.

Low flow velocities in laminar conditions promote planktonic growth, through an increase in HRT, which would subsequently increase the likelihood growth on the surface (Eisnor and Gagnon 2003). Ultimately, laminar conditions provide numerous benefits for successful and significant biofilm growth, although, its overall growth rate would be impaired by the low diffusion rates. Consequently, the resultant biofilm coverage under laminar conditions is generally irregular and isolated across the surface (De Beer et al. 1994; Lewandowski and Stoodley 1995; Stoodley et al. 1998a).

The overall effect of a biofilm on frictional resistance under laminar conditions has been found to follow the traditional smooth pipe friction law relationship (Lambert et al. 2008).

Whereby, the overall pressure drop is primarily influenced by skin friction and hence by the total surface area of the biofilm as opposed to the shape or structure of the fouled surface (Stoodley et al. 1998b).

In fully turbulent flow conditions, the laminar sublayer is reduced significantly in thickness.

In such situations, the frictional resistance of the biofouled surface is known to increase dramatically with Re (Lambert et al. 2008, Perkins et al. 2013; 2014). The overall pressure drop in turbulent conditions is influenced to a greater extent by surface roughness, which produces form drag when sufficiently great (i.e. from transitional to fully rough). Therefore, the structure, shape and nature of a fouled surface have an influence the overall pressure drop in turbulent flow conditions (Stoodley et al. 1998b). In turn, these characteristics are significantly affected by the turbulence. The considerably reduced laminar sublayer and increased turbulent mixing in the near proximity of the wall (induced by the presence of the roughness element within the logarithmic region) greatly increases the influx and diffusion of microorganisms, dissolved oxygen and nutrients to the surface. The resultant biofilm

coverage is likely to be more dense and compact than in laminar conditions (Dumbleton 1995;

Percival et al. 1999). The additional turbulence will also result in more efficient waste removal. The favourable mass transfer and diffusion rates will likely increase the degree of fouling, and the inherent link between turbulent flow and surface roughness will significantly accentuate its overall impact. For instance, Percival et al. (1999) found more rapid and extensive biofilm growth at relatively high Re (including ReD = 1.90x10⁴ and 3.50x10⁴), which was followed by a statistically steady-state. However, the inherently high shear forces associated with high Re will also reduce the likelihood of the material adhering to the surface.

For instance, Stoodley et al. (1998a) found that although, a biofilm grown under high turbulent conditions reached a statistically steady state earlier than a biofilm grown under low flow conditions its growth rate was higher under the low flow conditions. The increased accumulation rate at low flow conditions was a result of the lower detachment rate relative to the growth rate, as defined by the following mass balance relationship: accumulation rate = attachment rate + growth rate – detachment rate (Bryer and Characklis 1981). This would also explain why Lambert et al. (2008) observed a significant decrease in the biofilm thickness as a result of the increased turbulence in the vicinity of a pipe bend. Flow shear is therefore, a key controlling factor on biofilm development within pipelines, and its resultant equivalent roughness scale.

The favourable mass transfer and diffusion rates associated with turbulent flow conditions will also amplify the overall impact of nutrient loading, providing the overall shear force remains below the critical levels for biofilm detachment (which is typically equal to the conditioning shear). For example, Melo and Bott (1997) reported a 400% increase in biofilm thickness when nutrient levels increased from 4.0 to 10.0 mg/l, within a system in which the average streamwise velocity remained constant at 1.20 m/s. Similarly, for Pseudomonas aeruginosa it has been documented that high nutrient concentrations foster its formation as a biofilm within DWDSs (Peyton 1996). Lambert et al. (2008; 2009) found that an increase in nutrient loading significantly increased biofilm development both in terms of its physical thickness and equivalent roughness scale. Conversely, irrespective of the favourable mass transfer conditions, if the nutrient loading is reduced or is originally relatively low, the opposite is likely to occur, and the overall growth and development will tend to be more restricted and sparse, i.e. similar to that in laminar conditions (Melo and Bott 1997; Stoodley et al. 1998a; Volk and LeChevallier 1999; Gjaltema et al. 2004). For instance, Volk and LeChevallier (1999) found that overall density of a biofilm decreased with decreasing nutrient loading. Naturally, the starvation of a biofilm will lead a reduction in growth and ultimately, biofilm detachment (Hunt et al. 2004).

The typically dense and compact coverage inherent within turbulent conditions (with sufficient nutrient loading) may lead to “skimming flow”, i.e. the relocation of the velocity profile to the top of the roughness element – which is, in this case, the top of the biofilm layer (Stoodley et al. 1998b). Skimming flow has been documented to cause significantly higher flow resistance, and can be triggered by as little as an 8.3% surface coverage (Nowell and Church 1979). Other factors contributing to form drag, namely the biofilm’s shape and thickness, are likely to have a greater impact upon the overall pressure drop under turbulent flow conditions after the onset of skimming flow (Stoodley et al. 1998b).

Another important hydrodynamic aspect is that of the formation of elongated cell clusters in the downstream direction (known as streamers) which have been documented to occur under high flow conditions (Lewandowski and Stoodley 1995; Stoodley et al. 1998a; 1998b;

Percival et al. 1999). However, such filamentous biofilms can also develop irrespective of the hydrodynamic conditions, provided that certain bacteria species, such as Hyphomicrobium sp., Spharotilus sp. and Beggiatoa sp. are present. The resulting cell formation will further aid cell adhesion by providing a greater attachment and shelter area, in addition to providing the embedded microorganisms with a greater access to essential nutrients and dissolved oxygen within the flow (Percival et al. 1999). Consequently, systems and areas of high turbulence (i.e. contractions, expansions and bends) are likely to foster substantial and dynamic biofilm growth, but the maximum biofilm thickness is limited by the inherently high shear conditions. Therefore, unlike within laminar conditions, current design practices and theories cannot accurately evaluate the resultant growths’ frictional behaviour. This, coupled with the complex growth patterns inherent within turbulent conditions makes the task of accurately designing an efficient pipeline challenging, if not impossible.