3.2 Comparison of experimental and simulated deformation for synthetic biofilm
In order to validate the computational biofilm model, the experimental deformation under fluid flow was determined for synthetic biofilm and homogenized P. aeruginosa biofilm, then compared to the model (SI V3-V4). After the rheometry tests, a portion of the same synthetic biofilm was inserted into a cylindrical mount and fixed in a flow cell for the deformation test. The position of a central cross-sectional area of synthetic biofilm was monitored in real time when a constant flow was applied. The non-deformed biofilm boundary was used as the approximate model geometry (Fig. 5) (i.e., we neglected small imperfections and fissures in the real boundary data). This approximate geometry is used to simplify the mesh generation and limit the number of elements.
With the mechanical parameters from the rheometer tests, and non-deformed synthetic biofilm geometry as the input, the simulated deformation of the synthetic biofilm in the computational model was compared to the measured deformed geometry. Based on the effluent flow rate, the averaged inflow velocity was calculated and included in the computational model. The fully developed laminar flow with a Reynolds number (Re) of Re = 6 was created for the inlet boundary condition. The time-dependent simulation was performed over 20 seconds, as the experimental flow was observed for the same time duration. The synthetic biofilm boundaries from simulation and experiment were superimposed with the non-deformed one (Fig. 6). The steady-state deformation in both experiment and modeling was similar, with a relative averaged error of 12.8%.
The deformation over time was also compared (Fig. 7). Three tracking points along the synthetic biofilm boundary were selected at different depths (Fig. 7a). Specifically, three parallel lines were drawn along the sample to track the horizontal displacement. The results show that the deformations in the computational model were consistent with the experimental data, with an averaged error of 24 µm (line 1), 25 µm (line 2) and 13 µm (line 3). Besides, both the model and experiment show a gradually increased displacement over the first 4-10 seconds. Then the biofilm displacement stabilized. This was due to the small velocity near the boundary compared to the velocity required for the steady-state deformation. As expected for this flow configuration, both the model and experiments show that the displacement gradually increases from base of the specimen to its tip.
The simulated velocity profile is shown in Fig. 8a and b. From the model, the x-direction velocity near synthetic biofilm geometry was around 7×10-5 m/s, which was around one order of magnitude smaller than the averaged velocity. The fluid flow near top and bottom boundaries travels slower than the fluid in the middle. The velocity profile of the fully developed flow was parabolic with an almost-zero velocity near the biofilm boundary. Therefore, flow with a small velocity pushed the biofilm gradually and then reached an apparent steady-state deformation. This is consistent with data from Fig. 7. Comparing the deformation at different biofilm depths, we found that the top biofilm suffered a larger displacement in the horizontal direction due to its cantilever like shape (Fig. 8). The bottom biofilm had a smaller deformation since it was anchored and closer to the stagnant zone of the velocity.
Elastic and viscous components of the deviatoric stress tensor were also plotted on the synthetic biofilm domain (Fig. 8c and d, SI V5-V6). Both elastic and viscous stresses were in the same order of magnitude, which indicated that both elasticity and viscosity contributed to biofilm deformation, according to the Oldroyd-B equation. This shows that the viscous behavior of the biofilm is not negligible, even for short time periods.
Based on the results, it appears that the computational model can capture biofilm deformation with good accuracy. Rheometry tests in the previous section could provide a general idea on the averaged mechanical parameters for the biofilm. However, biofilm deformations are usually controlled by multiple factors, such as hydrodynamic conditions and biofilm morphologies. Thus, the study of biofilm mechanical parameters may not be enough. The simulation with hydrodynamics and biofilm morphology is necessary to predict biofilm behavior.