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.