In proofofprinciple experiments, we used the system to investigate the initial phases of E. coli biofilm formation on opaque stainless steel foils, with periodic 5 μm surface features fabricated using direct laser interference patterning [52], which may affect biofilm formation. In addition, we calculated the oxygen concentration in the flow chamber, taking into account bacterial growth. To the best of our knowledge, no oxygen profile in a flow chamber of the type presented here has been previously presented. Some models of oxygen distribution in a flow device with an oxygen diffusible PDMS layer have been published [55, 56], but they are not relevant to a microfluidic system such as ours. Simulated and empirically determined oxygen consumption rates by films of mammalian cells have also been published [35], but again the system used was not comparable to the one described here.
3.1 Hydrodynamics characterization
To establish optimal experimental conditions, we first characterized the hydrodynamics within the flow chamber, because for a uniform flow profile the flow must be incompressible, steady, and laminar [57]. We estimated the flow velocity within the chip using the continuity equation presented by Costerton et al. [58], simplified by assuming that the medium had a constant density approximating that of water at 30°C (ρ = 995.7 kg/m^{3}). Therefore, the continuity equation can be expressed as:
 (1)
where is the change in biomass over time t, S is the surface area, V is the timedependent liquid volume in terms of S, u is the velocity vector in terms of S, and n is the outward normal vector in terms of S.
The following assumptions were made. First, the system is in a steady state and there is a constant liquid density. This leads to the following simplification [Eq. (2)].
 (2)
Second, flow velocity perpendicular to the channel surfaces is zero, and the surface areas of the volumes the flow pass through are designated A1 for the tube and A2 for the chamber channel. Accordingly, Eq. (3) is obtained:
 (3)
Transposing Eq. (3), the following term is obtained:
 (4)
The incoming flow u is calculated from the volumetric flow rate q and the flow crosssection of the tubing (A), with Eq. (5).
 (5)
With a volumetric flow rate q of 1.23 × 10^{−8} m^{3}/s and the tube's inner diameter of 1 mm, the average flow velocity in the flow chamber is 2.05 × 10^{−3} m/s for a fluidic chip with no subdivision into separate channels (10 mm × 0.6 mm), and 2.74 × 10^{−3} m/s for a fluidic chip with subdivision into three channels with the same crosssection (i.e. three times 2.5 mm × 0.6 mm).
The Reynold's number (), often used to describe flow characteristics, can be calculated using Eq. (6), with the hydraulic diameter of the flow crosssection .
 (6)
The estimated Re values were 2.90 (without subdivision) and 3.31 (with subdivision), assuming that the density (ρ) and viscosity (η) parameters of the medium were equal to those of water at 30°C (995.7 kg/m^{3} and 7.977·10^{−4} kg/ms, respectively). This describes a laminar flow, since the transition from laminar to turbulent flow in pipes occurs at Re > 2300 [31].
In addition, we constructed a laminar model using Comsol Multiphysics 3.2 software, which we applied to calculate the flow and associated Reynolds numbers within the flow chamber (Fig. 3). For this simulation, we used an incoming flow u of 1.57 × 10^{−2} m/s, in order to compare the results of the calculations and simulations.
As can be seen in Fig. 3, under the chosen conditions there is no turbulence, the flow velocity inside the channels is regular and laminar (shown in blue and green). The maximal Reynolds number is 30, well within the laminar flow regime. Nevertheless, the microscopic analysis focused on the second half of the channel to minimize any disturbance of the growth that might have been caused by turbulence and irregularities. A simulation of the hydrodynamics in the chip with no subdivision yielded identical results for the flow regime (data not shown).
3.2 Characterization of oxygen consumption
To estimate oxygen consumption rates within the flow chamber during the microbial growth period, changes over time in the oxygen concentration were simulated as a function of the maximal oxygen uptake rate and initial biomass (1 h after inoculation) and time, assuming that the specific growth rate at a given time was exponentially related to the maximal growth rate (μ_{max}).
If in Eq. (10) becomes negative, the system becomes increasingly anaerobic, starting from the outlet, and moving toward the inlet.
Assuming that a single E. coli cell has a volume of 1 μm^{3} and dry weight of ca. 3 × 10^{−13} g [61], the biomass volumes obtained from COMSTAT 2 can be converted into biomass values with Eq. (12). The assumptions applied for this are that the bacteria grow evenly over the whole channel surface area, that their size is constant, and that the medium has a saturated oxygen concentration ( = 7.55 mg/L at 30°C):
 (12)
where 1.25 × 10^{8} μm^{2} is the surface area of the flow channel.
Equation (13) describes the exponential growth of the bacteria. Thus, their maximal growth rate μ_{max} can be calculated, when the measured biomass (μm^{3}/μm^{2}) after 17 h incubation is transformed into biomass (g), using Eq. (12).
 (13)
Mean measured and calculated biomass values are shown in Table 1, based (inter alia) on simulated oxygen consumption rates, obtained after transforming the Comstat biomass values (in μm^{3}/μm^{2}) into biomass values in grams.
Table 1. Mean measured biomass (X_{Comstat}) and calculated biomass (m_{x}) values, assuming that a single cell of Escherichia coli has a volume of 1 μm^{3} and dry weight of ca. 3 × 10^{−13} g [61]), after 1 h and at the end of the experiments (17 h) with estimated μ_{max} [Eq. (13)]  μ_{max} (h^{−1})  X_{Comstat, 1h} (μm^{2}/μm^{3})  (g)  X_{Comstat, 17h} (μm^{2}/μm^{3})  (g) 


Unpatterned spring band steel  0.30  0.00072  2.7 × 10^{−8}  0.0865  3.24 × 10^{−6} 
DLIPstructured steel (lines perpendicular to the flow direction)  0.28  0.00104  3.9 × 10^{−8}  0.0993  3.73 × 10^{−6} 
DLIPstructured steel (lines in the flow direction)  0.15  0.0059  2.21 × 10^{−7}  0.0652  2.44 × 10^{−6} 
Clearly, if the initial biomass is high (Fig. 5A), oxygen depletion occurs within the experimental time of 17 h, with μ > 0.2 h^{−1}. However, with lower initial biomass (Fig. 5B), oxygen depletion occurs with μ > 0.3 h^{−1}. This confirms our calculated data in Table 1.
3.3 Experimental results
The aim of the initial proofofprinciple experiments presented here was to assess the utility of our flow cell for studying the initial phase of biofilm formation on microstructured surfaces in order to characterize their antiadhesive properties. To ensure that the biofilm patches originated solely from the inoculum, and not from bacteria that had left the grown biofilm and formed new colonies, a short cultivation time of 17 h was chosen.
Figure 6 shows 3D images taken from an unstructured surface (A) and a surface structured in the flow direction (B). At the end of the experiments, patches of biomass could be clearly distinguished from their surroundings, but they were also clearly unevenly distributed. The 15 randomly taken microscopic images cover only about 1/64 of the entire channel surface. Furthermore, the calculated oxygen consumption rates (see above) clearly indicate that there were probably regions in the flow cell, at least at the outlet end, where bacteria could not grow under aerobic conditions throughout the experiments. This may explain the large deviations of biomass we found on both microstructured and unstructured reference surfaces (Fig. 7).
Nevertheless, our observations are in accordance with the literature [62, 63]. Attachment point theory holds that it is difficult for a cell slightly larger than the microtexture wavelength of a surface to attach because there are only two theoretical attachment points. In the experiments reported here, linelike arrays with 5.0 μm pitch were directly patterned onto the steel surface, which are unlikely to have strong antiadhesive properties.