Failure through expanding voids in bacterial streamers

We investigate the failure of thick bacterial floc-mediated streamers in a microfluidic device with micro-pillars. We found that streamers could fail due to the growth of voids in the biomass that originate near the pillar walls. The quantification of void growth was made possible by the use of 200 nm fluorescent polystyrene beads. The beads get trapped in the extra-cellular matrix of the streamer biomass and act as tracers. Void growth time-scales could be characterized into short-time scales and long time-scales and the crack/void propagation showed several instances of fracture-arrest ultimately leading to a catastrophic failure of the entire streamer structure. This mode of fracture stands in strong contrast to necking-type instability observed before in streamers.


Introduction
Bacterial streamers are filamentous biofilm-like structures that are usually known to form under sustained hydrodynamic flows 1 . Like biofilms, streamers consist of bacterial cells embedded in a matrix of self-secreted extracellular polymeric substances (EPS) and are excellent examples of soft materials of biological origin. Due to their morphology, streamers can colonize closed channels significantly faster than surface-hugging biofilms; recently streamers forming in very low Reynolds number conditions ( ≲ 1) have been implicated for their role in rapid fouling of biomedical devices [2][3][4] , filtration units 5,6 and even colonization of porous media 1, 7,8 . In many of these applications, a better understanding of deformation, fracture and failure of streamers is crucial 5 . Valiei et al. 8 had reported failure and disintegration of streamers in microfluidic device, but this phenomenon was not discussed in detail. Das and Kumar 9 had investigated instabilities and break-up of streamers when they were idealized as highly viscous liquid jets. In a later work, Biswas et al. 5 utilized a microfluidic device with micro-pillars to investigate far-from-wall failures of streamers. They focused exclusively on 'thin' streamers, i.e. streamers whose aspect ratio , i.e. ratio of longitudinal to transverse characteristic length, is typically >10, and found that these streamers could fail through a necking like failure mode in steady flow typical of ductile materials under creep. They also found a power law relationship between the critical strain (strain at instability) and fluid velocity scale, which yielded valuable insights into material behavior.
Recently, Hassanpourfard et al. 10 showed that failure of streamers is not limited to the earlier stages but can also be found in the final clogged state of the device where localized failures lead to intricate water-channels coursing through the clogged biomass. Despite these studies, it is almost certain that more failure modes exist. This is because streamers like other biofilms represent a composite and extremely heterogeneous, active soft material. However, reporting and quantification of these phenomena is sparse.
One of the most fundamental challenges stems from the visualization issues since the EPS matrix embedding the microbe is very difficult to image due to its transparent nature. Furthermore, the nature of this type of set up results in several overlapping sources of nonlinearity in addition to failure and instability. These include creep behavior of the polymeric EPS, fluid-structure interaction, moving interfaces and life processes, all of which cannot be independently controlled easily. In addition, time scale of streamer formation can vary considerably 3,7,8,11 and very long-time scales can let significant changes in the background conditions affecting these nonlinear behaviors.
In this communication we report an entirely new type of streamer failure mechanism not observed before. This type of failure originates near the micropillar wall, rather than further downstream as previously noted, and yet distinct from shear failure at the micro pillar wall typically seen at higher flow rates 5 . We use floc-mediated 5, 7, 10 rather than biofilm mediated 3,8 streamer formation, where either of these refer to the mode of inception of the streamers 1 . Floc mediation allows for rapid streamer formation which helps us isolate mechanical factors and reduce streamer formation time thus reducing biophysical complications such as cell division 7 . A microfluidic device was specially fabricated so as to allow streamers to freely form from micro pillars into the downstream flow without any more attaching surfaces on the free side. Our imaging clearly showed that the inception of failure occurs with a pronounced void almost with the geometry of a small coin shaped crack near the point of attachment and only after the streamer structure was already well formed (i.e. when streamer length is several times the pillar characteristic length). Once this 'crack' was observed, it was found to rapidly extend resembling crack propagation quickly rupturing the streamer. We found this behavior repeatedly, always originating near the pillars and only for some but not all streamers. This failure mode did not occur anywhere farther down the streamer length. The flow rate was kept constant for individual experiments. To the best of our knowledge, this is first report on this type of failure mode in streamers formed in micro fluidic environments.

Microfluidic chip fabrication
A PDMS (Polydimethylsiloxane) microfluidic device was made by using traditional photolithography technique for this study. A 4´´ silicon wafer was utilized to make the master mold of the microfluidic device. The microfluidic device design consists of a straight channel with a singlet inlet and outlet (Fig. 1a). The length of the channel, L, was 11.5 mm and its width, W, was 0.436 mm. In the central section of the channel, 14 micro-pillars were arranged in a staggered pattern. Using photolithography process as detailed by Hasanpourdfard et al. 12 PDMS microchannels were prepared from a silicon master. The PDMS micro-pillars had a diameter, d, of 50 µm, height, h, of 50 µm and the pore-gap, p, was 10 µm (Fig. 1b). The dimensions w 1 and w 2 demarcated in Fig. 1b were 60 µm and 104 µm respectively. Glass cover-slips (thickness 0.13 to 0.17mm) (Fisher Scientific, ON, Canada) and PDMS were bonded by using oxygen plasma and the devise was then annealed at 70℃ for 10 minutes to seal perfectly.

Bacteria culture preparation
We used Pseudomonas fluorescens CHA0 (wild type) 13 bacteria strain for this study. This gramnegative aerobic bacteria is found naturally in water and soil, and plays a vital role in plant health 14

Microscopy
The bacterial solution was injected to the microfluidic chip by using a syringe pump (Harvard Apparatus, ON, Canada). The microfluidic chip was placed under an inverted fluorescence microscopy system (Nikon Eclipse Ti) to observe the streamer behavior during the experiment.
Confocal images were captured using an inverted spinning-disk confocal microscope (Olympus IX83). For epi-fluorescence imaging GFP Long-pass green filter cube (Nikon and Olympus) and Texas red filter cube (Nikon and Olympus) were used. Streamer breaking events were recorded at a rate of 10 frames per second. Image processing was performed by using NIS-Element AR software interface (Nikon). The software is capable of fitting ellipses to images.

Results
When the P. fluorescens bacteria solution was injected through the microfluidic channel, streamers form downstream of the micro-pillars with a characteristic streamer formation time scale, ,-./ .
For a floc laden bacteria solution, as in this experiment, ,-./~( 10 23 − 10 4 ). Streamer formation in these cases occurs because the flocs adhere to the micro-pillar walls and are rapidly sheared into the form of streamers by traction forces generated by the flow (Fig. 1c). This mode of streamer formation has been investigated and characterized previously 5,7 . Figure  propagation dynamics is depicted in Fig 3a. The LTF events occurred such that the set of fracture events occurred slower and for these events ,.IJKL.M~1 0 E (Fig. 3b). Fracture time-scales that lie in-between these two extremes were also observed, and similar crack-propagation behavior was observed (data not shown). In addition to crack extension with time, we also plot crack propagation velocity normalized with background flow with time and crack length for both LTF and STF events. This is depicted in Fig. 4.

Discussions:
This work highlights a hitherto unreported route of streamer disintegration -one starting right at the base of streamer near the pillar. It is interesting to note that the background fluid flow in the current problem would lead to a traction field in the crack propagation direction, which is not a very favorable crack opening force field. Therefore, by itself it is not the immediate cause of the We describe these zones below.
The first zone is the initial crack propagation zone which marks the beginning of the instability and lengthening of the initial flaw. However, as soon as the instability begins likely due to accumulation of damage due to creep at the fracture tip, there is a decrease in crack propagation velocity with time leading to a plateau zone. Note that this plateau is more pronounced for the LTF than the STF. After some time, the plateau zone gives way to a final monotonic increase in crack length for both types of fractures leading to the final disintegration of the streamer. These plots clearly show that as the crack length increases, there is an initial resistance to the crack propagation. This behavior is also seen in many materials which is often a clear indication of nonlinear behavior at the crack tip [15][16][17] . This figure also shows that within these broad three-zone behaviors there are further intricacies such as multiple micro regions of crack growth resistance in the plateau zone. However, in all cases, these resistance mechanisms finally fail to stop the crack which then transitions into the final runaway instability zone from which there is no recovery. The streamers ultimately disintegrate.
The broad reason for initial resistance to crack growth likely shares its physical origin to polymeric composite materials which results in overall similar behavior between LTF and STF behavior [18][19][20] . However, lack of clear trends in STF may indicate that these streamers may have much higher heterogeneity in their structure leading to more flaws which precipitate the fracture early in their life. This would also explain why the initial crack propagation velocity is much higher for STF, Fig. 3a,b which can be attributed to much weaker interfaces and flaws.
We refrain from developing a complete multi physics model for this system in this communication since its validation would require more precise measurements of flow, material and diffusive parameters.

Conclusions:
In this communication, we discovered a yet unreported failure mode of streamer disintegration which originated near the micro-pillar walls and is yet distinct from simple shear failure or tearing.
This failure was observed to co-exist with other previously reported failure modes in streamers.
This further supports the notion that this mode of failure is completely independent from previously reported data. We quantify the void/crack extension behavior using PS micro beads as tracers to aid microscopy and conclude that the crack is through the thickness of the streamer and