Fluid-driven interfacial instabilities and turbulence in bacterial biofilms

strong dependence of the instability formation on biofilm viscosity explaining the different surface corrugations observed. Turbulence through Kelvin– Helmholtz instabilities occurring at the interface demonstrated that the biofilm flows like a viscous liquid under high flow velocities applied within milliseconds. Biofilm fluid-like behavior may have important implications for our understanding of how fluid flow influences biofilm biology since turbulence will likely disrupt metabolite and signal gradients as well as community stratification.


Introduction
Biofilms are surface-attached microbial communities surrounded by a self-produced matrix of extracellular polymeric substances (EPS), which include polysaccharides, proteins, lipids and nucleic acids (Hanks and Ruo, 1966;Flemming and Wingender, 2010). Biofilms are ubiquitous in the natural environment and have been identified in the fossil record (Stoodley et al., 2002a). Biofilms colonize all man-made surfaces such as ship hulls, industrial pipelines and biomedical implants, as well as human tissues and oral surfaces (Costerton et al., 1999;Marsh, 2004;Schultz et al., 2011). A common feature of these surfaces is that they are in contact with fluid flow. The hydrodynamic flow is known to affect biofilm formation, behaviour, structure and propagation. Biofilms are not static but are highly dynamic with their structure shaped by growth, detachment and response to mechanical forces acting on them (Stewart, 2014). The EPS network provides the main source of biofilm versatility in response to physical forces and also endows the biofilm with non-trivial mechanical properties (Fabbri and Stoodley, 2016).
Biofilms are widely acknowledged to be viscoelastic materials (Wilking et al., 2011;Billings et al., 2015;Peterson et al., 2015;Fabbri and Stoodley, 2016). As with all viscoelastic materials, they can be dominated by an elastic response, a viscous response or a viscoelastic response depending on (1) the magnitude of the imposed load, (2) the time scale over which the load is imposed and (3) the rate at which the load is imposed. The same biofilm can behave like a fluid under certain conditions, a solid under others, and a mixture of the two under others. In addition, biofilms can change their shape through growth and detachment process to adapt their life under different fluid flows conditions (B€ ol et al., 2009;Blauert et al., 2015). Flow cell experiments have shown that biofilms can structurally reorganize in response to elevated shear to form drag reducing forms such as streamers or ripples over days (Stoodley et al., 1999c). Wave-like pattern biofilms have also been found inside endotracheal tubes (Inglis, 1993) and venous catheters (Rusconi et al., 2010). Biofilm rippling has also been related to the large pressure drops and drag associated with biofilms in systems ranging from industrial pipelines (Lappin-Scott and Costerton, 1989) to ship hulls (Schultz et al., 2011). Similar structures have been observed in the natural environment, ranging from modern biofilms grown under high-velocity flows in in vitro streamside (Stoodley et al., 1999b;Battin et al., 2003) to ancient microbially induced sedimentary structures (MISS) (Noffke et al., 2001;Porada et al., 2008). Whether the interaction between biofilms and hydrodynamic forces is an adaptation of biofilms as multicellular entities to withstand shear forces still remains a fundamental research question (Drescher et al., 2013). Recent studies have raised the hypothesis that ripple structures formed in ancient fossils may be the result of Kelvin-Helmholtz Instabilities (KHI) which occur between the microbial biofilm and the overlying fluid flow (Thomas et al., 2013). KHI manifest in two-fluid systems (such as water-air) that are stratified by density variations with a velocity differential between the fluids (Miles, 1959). Shear forces generated from the velocity difference lead to unstable vortices at the interface which grow exponentially until the distorted interface overturns into spiral forming rippled features (Funada and Joseph, 2001).
Streptococcus mutans is a gram-positive and facultative anaerobic microorganism that is considered a causative agent of human dental decay (Loesche, 1986). S. mutans biofilms have been widely used in research to investigate biofilm mechanical properties and detachment (Vinogradov et al., 2004;Cense et al., 2006). We previously performed high-speed camera (HSC) videography during the exposure of in vitro S. mutans interproximal dental biofilms to high-velocity (60 m/s) impacts from micro water jets and sprays using an interdental cleaning device [Air-Floss (AF), Philips] (Rmaile et al., 2013;2015;Fabbri et al., 2015). We demonstrated that biofilms exhibited fluid-like behaviour on the order of milliseconds in response (Fabbri et al., 2015). The videos not only recorded a quasi-instant biofilm fluidisation, but also suggested the formation of migratory ripple-like structures.
Since microsprays generated from the AF device have very complex flow hydrodynamics and proceed through a series of pulses (Rmaile et al., 2014), here, we used a well-defined and steady compressed air jet that allowed the study of the rippling phenomenon under conditions where flow rate could be controlled. We report for the first time that ripple-like structures (i.e., series of small surface waves that propagate along the interface between differing media) in Streptococcus mutans and Staphylococcus epidermidis biofilms and wrinkle-like structures (i.e., deformations caused by compression when a material is 'bunched' together) in Pseudomonas aeruginosa biofilms can form extremely rapidly. We modelled the observed ripple morphology using a multiphase model (Cogan and Keener, 2004). Theoretical treatment of the process as a Kelvin-Helmholtz instability indicated that the rippling phenomenon was primarily due to physics rather than chemistry or biology. In addition, we discovered that biofilm viscosity can dramatically influence instability formation explaining the different surface corrugations observed. Turbulence through Kelvin-Helmholtz instabilities occurring at the interface demonstrated that the biofilm flows like a viscous liquid under high flow velocities applied within milliseconds. KHI are a prelude to mixing and turbulence (Geyer et al., 2010) and direct evidence of their formation in biofilms has potentially important implications for disruption of gradients and microniches, antibiotic delivery and mechanical removal and dissemination.

Results and discussion
Ripples formation in S. mutans biofilms exposed to rapid high velocity microsprays Recently, we had developed a microfluidic flow channel system for investigating rapid high velocity water and air microspray interactions with S. mutans biofilms for dental cleaning applications (Fabbri et al., 2015). HSC videography suggested the formation of migratory ripple-like structures at the biofilm/fluid interface. Considering the intriguing nature of this phenomenon, in the present study we used an identical setup in order to allow these structures to more fully develop.
S. mutans biofilms were grown on glass microscope slides for 72 h in a BHI 1 2% sucrose 1 1% mucin medium. The microfluidic flow channel was created by inserting two biofilm-colonized glass microscope slides in parallel separated by a distance of 1 mm into a specially fabricated holder. S. mutans biofilms were exposed to either a water or an air microspray burst. HSC movies of S. mutans biofilms exposed to a high-velocity water microspray (Supporting Information Video S1) or an air microspray (Supporting Information Video S2) showed the burst rapidly entered the microchannel forcing the biofilm downstream and out of the device as it created a clearance zone through the body of the biofilm. Migratory ripple-like structures developed within ms at the fluid-biofilm interface. The ripple structures travelled with an average velocity of 1.87 6 0.27 m/s and 2.69 6 0.07 m/s during the water microspray and air bursts respectively. Immediately, after the burst, the ripples began to dissipate leaving little trace of their formation (Supporting Information Video S3). Different ripple patterns were observed at different phases of the bursts. The water microspray generated thick crescentshaped ripples (Fig. 1A) with an average wavelength of 1.85 6 0.02 mm and width of 0.31 6 0.03 mm. The air microspray first produced curved ripples protruding from the biofilm into the channel created by the air with an average amplitude of 0.57 6 0.11 mm (Fig. 1B). Then, thicker crescent shaped-ripples developed at the leading edge of the air burst with an average wavelength of 1.12 6 0.04 mm and a width of 0.2 6 0.04 mm (Fig. 1C). We noticed similarities in the ripple morphology of these highvelocity ripples to the slow moving, long-lived ripples observed in previous studies (Stoodley et al., 1999b;Purevdorj et al., 2002) for biofilms grown under steady liquid flows of 1 m/s (Re 5 3000). However, our videos demonstrate that ripples can also form and migrate at extremely fast time scales (ms) when exposed to high velocity fluid flow.
Ripples formation in S. mutans biofilms exposed to air jets at different velocities Microsprays generated from the AF device have very complex flow hydrodynamics (Rmaile et al., 2014), therefore, A-C. S. mutans biofilms exposed to high-velocity air and water microsprays (A) The water microspray burst generated thick crescent-shaped ripples at the front edge of the burst. B. The air microspray generated arcuate ripples (white arrows) at the edges of the clearance zone. C. Crescent-shaped ripples at the front edge of the air microspray. Flow was left to right. Scale bar 5 2 mm. D-G. Three-day old S. mutans biofilms exposed to a compressed air jet of 24.6 m/s (D), 44.9 m/s (E), 68.1 m/s (F), 85.5 m/s (G).The ripples pattern changed as air jet velocity increased. Panel (D) and (E) show thin, parallel ripples appeared during low-velocity air jets (24.6 m/s and 44.9 m/s). F. Transition from parallel to crescent-shaped at 85.5 m/s. G. Complex crescent-shaped at high velocities (110.1 m/s). Scale bar 5 5 mm. H, I. Ripples formed in S. epidermidis biofilm (H) and wrinkles formed in P. aeruginosa biofilm (I) during the exposure to an air jet of 85.5 m/s. Flow was left to right. Scale bars are 2 mm. ripples morphology variation was also caused because of the velocity changes in the flow itself. To study the phenomenon under conditions where flow rate could be controlled we used a well-defined compressed air jet of seven different velocities ( Table 1). The Reynolds number (Re) and the relative wall shear stress (s w ) in the biofilmexposed zones were calculated according to Stoodley et al. (1999a) (Table 1). The transition between laminar and turbulent flow in rectangular channels occurs at Re$2500 (Hanks and Ruo, 1966), therefore, the lowest velocity of 7.2 m/s (Re 5 780) will be laminar, but higher velocity air jets would be in the turbulent regime. Turbulent flow is mainly found in fast moving streams and rivers (Re 5 10 5 -10 6 ), industrial pipelines, ship hulls (Re 5 up to 10 9 ) and water irrigators for oral health and surgical debridement. Using the same microfluidic flow channel system as previously, S. mutans biofilms samples were exposed to the air jets. HSC movies of S. mutans biofilms showed there was no ripple formation at the lowest air flow of 7.2 m/s (Re 5 780) but they did occur at flows greater than 24.6 m/s (Re 5 2667) (Supporting Information videos S4-8). Ripples generated at 24.6 m/s (Fig. 1D) and 44.9 m/s ( Fig. 1E) were thin, straight and parallel to the flow direction whereas ripples formed at 68.1 m/s (Fig. 1F) and 85.5 m/s ( Fig. 1G) had more complex crescentpatterns. The ripple velocity increased exponentially (R 2 5 0.972), with increasing air jet velocity, from u R 5 0.22 6 0.02 m/s at u jet 5 24.6 m/s to u R 5 2.27 6 0.16 m/s at u jet 5 110.1 m/s ( Fig. 2A, black dots), while wavelength decreased exponentially (R 2 5 0.972), from w R 5 1.85 6 0.16 mm at u jet 5 24.6 m/s to w R 5 0.68 6 0.07 mm at u jet 5 110.1 m/s (Fig. 2B, black dots). Anova followed by Tukey-Kramer tests showed statistical difference within the two set of data (velocity and the wavelength) between low velocities and high velocities. The morphology of the generated ripples was similar to the ones discovered in annular thin ($ 147 mm) liquid films exposed to high gas velocities (> 20 m/s) (Asali and Hanratty, 1993) and their formation has been explained by interfacial instability as the fluids flow past each other (Cohen and Hanratty, 1965;Craik, 1966). Although our wavelength values were lower by a factor of $ 10 21 than the ones measured by Asali et al. (Asali and Hanratty, 1993), the same trend was observed.
Fast Fourier Transform (FFT) was also used to determine whether there were dominant frequencies in the ripple pattern. Below an air jet velocity of 68.1 m/s, the spectrum was relatively simple, whereas at the higher velocities of 85.5 m/s and 110.1 m/s there was more fluctuation. Some of this noise could be due to the imaging itself. However, studies showed that a transition to turbulence is bordered by an instability which can increase the randomness of the FFT spectra (Joseph and Renardy, 2013). In addition, similar FFT spectra were found in a computational model on rippling in biofilms colonies subject to external forcing (L. Jian et al., in preparation). Despite this noise distinct peaks are identifiable in the data: the major peaks identified in the FFT spectrum for each air-jet velocity corresponded to wavelengths values were similar to the ones measured using Fiji (Supporting Information Fig. S1).

Ripples and wrinkles formation in S. epidermidis and P. aeruginosa biofilms
We hypothesised that the formation of rippling patterns might likewise be a general phenomenon to bacterial biofilms given the right set of biological and environmental conditions. We tested our hypothesis by exposing biofilms grown from S. epidermidis (a skin isolate and opportunistic biofilm pathogen in orthopaedic device related infections) or P. aeruginosa (a common nosocomial biofilm pathogen infecting wounds, medical devices and the upper respiratory tract) to a steady air jet of velocity u jet 5 85.5 m/s (Re 5 9268). S. epidermidis biofilms formed ripples which were morphologically similar to the S. mutans ripples at the equivalent air jet velocity (Supporting Information Video S9, Fig. 1H) which were crescent-shaped with wavelengths of 1.2 mm 6 0.08 mm and widths of 0.23 mm 6 0.04 mm moving at a velocity of 1.7 m/s (60.5, n 5 5) ( Fig. 2A). In contrast, the P. aeruginosa biofilms were pushed forwards but the air jet did not create a channel through the biofilm. Wrinkle-like structures formed rather than ripples as the biofilm bunched up against the downstream portion which remained attached and was not moved (Supporting Information Video S10 and Fig. 1I). The widths of the wrinkles were 0.18 mm 6 0.03 mm. Unlike the ripples, the wrinkles did not migrate over the surface after they had formed but resisted the air jet for approximately 300 ms. During this time the wavelength of the wrinkles decreased from 1.1 mm 6 0.3 mm to almost 0 mm as the biofilm was increasingly compressed against the biofilm downstream (Fig. 2B). After 300 ms the whole biofilm detached from the surface and was pushed out of the flow cell as a plug. All SDs were below 34% of the means.

Biofilm ripples as Kelvin-Helmotz instabilities
The formation of ripples at the interface of the biofilm and the high velocity air jet occurred within milliseconds, suggesting that the phenomenon was not likely to be a sedimentary-like process of erosion and deposition but more likely a shear flow induced interfacial instability (Tauber et al., 2002). KHI occur when immiscible, incompressible and inviscid fluids are in relative and irrotational motion (Matsuoka, 2014). To test our hypotheses, we performed a classical KHI linear stability analysis to estimate the correlation between the ripple wavelength and air velocity (See Supporting Information Materials and Methods). Classical analysis assumes the fluids are simple Newtonian materials. We considered a two-fluid system formed by a top fluid (air), moving initially horizontally with velocity u a and a bottom fluid (biofilm), initially stationary (Supporting Information Fig. S2). To reflect the biofilm structure, we modelled the second fluid using a widely accepted model for the biofilm material referred to as a multiphase model that assumes that the biofilm is composed of both fluid and solid components (e.g., encapsulated water and EPS/bacterial components) (Cogan and Keener, 2004;Klapper and Dockery, 2006;Winstanley et al., 2010;Seminara et al., 2012). In practice, this allows the theory to focus on a variety of physical, Fig. 2. Comparison between the theoretical predictions (lines) and the experimental measurements (symbols) of ripples' velocity and wavelength as a function of the air jet velocity for S. mutans, S. epidermidis and P. aeruginosa biofilms. Solid line represents the predicted data using a base viscosity (g B 5 2.8 3 10 5 PaÁs) whereas dashed lines a low viscosity value (g/10) and a high viscosity value (10 g) to cover a range of three orders of magnitude. Experimental data of S. mutans (•), S. epidermidis (᭡) and P. aeruginosa () biofilms are represented as means 6 1 SD from three independent replicates. A. The measured ripples' velocity for S. mutans biofilms increased exponentially (R 2 5 0.957 for exponential fit) with the air jet velocity. Predicted values using the base viscosity value agreed well with the experimental data (R 2 5 0.99) for S. mutans biofilm. Ripple velocity for S. epidermidis at u jet 5 85.5 m/s was inside the range of predicted data. The inset plots represent data from u R 5 0-3 m/s. B. The measured ripples wavelength for S. mutans biofilms decreased exponentially (R 2 5 0.989 for exponential fit) with the air jet velocity. Predicted values using the base viscosity value agreed well with the experimental data (R 2 5 0.98) for S. mutans biofilm. Ripple wavelengths for S. epidermidis and P. aeruginosa were inside the range of predicted data. The inset plots represent data from k R 5 0-2.5 m/s. [Colour figure can be viewed at wileyonlinelibrary.com] chemical and biological processes since the model separates the constituent parts of the biofilm. Therefore, rather than using a lumped constitutive relationship, the model allows for a distinction between forces that affect the EPS and those that affect the fluid. Additionally, the multiphase framework allows for natural implementation of non-Newtonian properties via the interaction between the solid and liquid components of the biofilm. We used a baseline biofilm viscosity (g) of 2.8 3 10 5 Pa.s, which was the mean g measured on similar S. mutans biofilms (Vinogradov et al., 2004). From the linear stability analysis (see Supporting Information) we obtained a dispersion curve, that relates the perturbation wavelength, k, and the growth rate, x; of the perturbation: where the coefficients are N 5 2k 2 u 2 1 1 gk 3 : The viscosities are explicit in Eqs.
(1-4). The dispersion curve has a unique maximum (peak) that depends on the air jet velocity in a complicated nonlinear way (Supporting Information Fig. S3). The peak indicates the most unstable mode and is used to estimate the ripples wavelength and velocity. From a pattern formation standpoint, we expect that the observed wavelength will correspond to this maximum since it is growing the fastest. The peak gives a good estimate for the observable wavelength until nonlinear effects such as mixing take over The model predicted an exponential dependence of the ripple velocity and wavelength on the air jet velocity (Fig. 2). An excellent agreement (R-squared$99%) was observed between the experimental measurements of the ripples velocity for S. mutans biofilms and the data obtained from the analysis using g B ( Fig. 2A). Whereas, the experimental measurements of the ripples wavelength for S. mutans biofilms were in good agreement (Rsquared > 98%) with the model using a viscosity in the range 1/10g Bg B (Fig. 2B). The key process involved in the ripple formation is, therefore, a KHI implying viscous fluid behaviour of S. mutans biofilms during rapid high shear stresses. This implies that the rippling phenomenon is likely dominated by physical interactions. The details of the material properties, surface tension, air jet velocities, and so forth serve to scale the predicted pattern. We noted that we need some level of detail regarding the material properties of the biofilm (such as shear thinning or elasticity) to match the observed air jet velocity/wavelength relationship since a simple Stokes fluid approximation of the biofilm had a much poorer match (data not shown). It appears that viscoelasticity does not play a substantial role except possibly at lower velocities, based on the agreement between the model and the data. The wavelength in the theory increases faster than the measurements for low velocities, therefore, is more likely that for low forcing velocities elastic properties might need to be included. However, in the future, modelling viscoelastic behaviour can be included to see any changes in the ripples characteristic.
Whether a biofilm is more likely to flow in ripples or form more solid-like wrinkles is likely a function of a number of factors such as biofilm viscosity. Therefore, we assessed the influence of biofilm viscosity on KHI formation performing the same analysis using biofilm viscosity values of 1/ 10x and 10x the baseline value. Changing the viscosity has the effect of changing the peak of the dispersion curve. Although the relationship is quite complicated, generically the wavelength/velocity curve moves up and right with increasing viscosity (Fig. 2) implying that the wavelengths are typically higher for the same bulk velocity as viscosity increases. S. epidermidis ripple wavelength and velocity values fell within the predicted range for the chosen viscosities, whereas P. aeruginosa wrinkles did not migrate over the surface (u 5 0, Fig. 2). This implies that P. aeruginosa biofilm has a higher viscosity than the ones we had assumed.
Finally, our data supports the hypothesis by Thomas et al. regarding a possible mechanism for ripples formation in Kinneyia fossils (Thomas et al., 2013). Kinneyia are a type of microbially mediated sedimentary structures (MISS) (Noffke et al., 2001; characterised by an undulating ripple-like pattern with a wavelength on the millimetre to centimetre scale. The researchers proposed that the key mechanism involved in the ripples formation is a KH instability induced in a viscoelastic film subjected to flow in the overlying fluid. However, these interfacial instabilities were demonstrated in gels, not living biofilms. In addition, in contrast to our findings, they showed that the ripples wavelength was independent on the viscosity and the flow velocity. Additionally, it should be noted that we assume direct coupling between the surface flow and the biofilm flow via an interface condition (continuity) while they impose a pressure condition. Thus, although their dispersion curve predicts a relation to the height, the form of their pressure dependence obscures other nonlinearities.

Biofilm fluid behaviour
Literature on biofilm mechanics showed a progression of behaviours as shear loading is increased from an elastic solid (no hysteresis), viscoelastic solid (hysteresis but no permanent deformation), viscoelastic liquid (both elastic recoil and viscous flow) and finally viscous liquid (Klapper et al., 2002;Stoodley et al., 2002b). Here, we documented that when exposed to high shear stresses S. mutans biofilm behaved immediately as a liquid and it was only after the flow was removed that the viscoelastic recoil of the biofilm was observed (Supporting Information Video S3). A similar behaviour was seen in S. epidermidis biofilm. However, in P. aeruginosa biofilms the wrinkles structures we observed were similar to those described by Trejo et al. in Bacillus subtilis biofilm pellicles (2013) suggesting cohesive attachment failure at the biofilm-substratum interface resulting in wrinkling rather than true flow. The authors also showed that eps mutant biofilms had no elastic response highlightening the key role of the matrix in providing the elasticity of the pellicle for forming the wrinkling process. We speculate that the differences in the response of P. aeruginosa biofilm to that of S. mutans or S. epidermidis biofilms was due to differences in the EPS chemistry and mechanical properties.

Microscopic structure of ripples and wrinkles
Changes in the EPS composition can considerably change biofilm mechanical behaviour which can affect biofilm detachment and proliferation (Flemming, 2016). Therefore, we went on studying how cell packing and spatial EPS organization through the biofilm change as ripples form using confocal laser scanning microscopy (CLSM) and scanning electron microscopy (SEM). Plan views of confocal images of S. mutans biofilms prior to exposure to water microsprays showed a relatively uniform biofilm covering the surface (Fig. 3A). The cross section showed that cells were evenly distributed and the film was approximately 20 mm thick (Fig. 3B). After exposure to the microspray the remaining biofilm in the area where the ripples had formed adjacent to the clearing zone showed a heterogeneous pattern of cell clusters separated by areas where biofilm was completely removed (Fig. 3C). Cross-sections through the clusters in these areas showed that the cells were more densely packed and the clusters were approximately 5 mm thick (Fig. 3D). The cell-density measured in the ripple area (1.4 3 10 6 6 2.8 3 10 5 cells/mm 2 ) was significantly higher than the cell-density measured in the undisturbed areas (5.7 3 10 5 6 1.6 3 10 3 cells/mm 2 ; p 5 0.01) (Fig. 3E). The fact that the cell density was increased by a factor of 3 but the thickness was reduced by a factor of 4 after the ripple formation suggests that much of the loss in thickness could be attributed to compression rather than detachment of the top layer of biofilm. We hypothesize that the water microspray might have altered the biofilm structure by 'squeezing' water out or by rearranging the EPS matrix structure. Mechanical compression and tensile tests on biofilms formed by S. mutans, P. aeruginosa and S. aureus and mixed species biofilms show that the biofilms become stiffer as they are compressed or pulled (Rupp et al., 2005;Fabbri and Stoodley, 2016) demonstrating a J-shaped stressstrain curve (Klapper et al., 2002). Such a curve can be explained by dewatering, even if the biofilms are fully submerged. As mechanical stresses are applied to the biofilm the squeezing of water out of the matrix would cause the EPS polymer strands to become denser and forced closer together thus becoming increasingly stiffer. Future work will focus on looking at EPS ultrastructure using techniques such as transmission electron microscopy (TEM) or stimulated emission depletion (STED) microscopy. Also, staining the EPS with appropriate lectins and then analysing with CLSM could give further information about spatial EPS organization. SEM images of the S. mutans biofilms not exposed to high velocity fluid flow, showed a structure with an undulating surface interspersed with prominent clusters of cocci ( Fig. 4A) arranged in towers (Fig. 4B). The S. epidermidis biofilm were more compact than the S. mutans biofilms with a dense layer of cocci and less pronounced clusters ( Fig. 4C and D). The P. aeruginosa biofilms showed rod-shaped cells embedded in an undulating EPS matrix (Fig. 3F). Higher magnification revealed that some clusters had cells which were interconnected by fibre-like structures (white arrows, Fig. 4F). Although macroscopically the ripples rapidly dissipated after the fluid flow was removed, SEM showed residual structures. In the S. mutans biofilms the cells had been rearranged in dense parallel ridges ( Fig. 5A and B). The S. epidermidis biofilms showed similar band structures but these were much fainter and appeared to be on the glass surface. Individual cocci were arranged on the bands ( Fig. 5C and D). In the P. aeruginosa biofilms there were a base layer of single cells and intriguing parallel bands. The bands, perpendicular to the flow, were possibly dehydrated EPS, suggesting that the EPS had been concentrated into ridges during the wrinkling. It is known that the dehydration process significantly alters biofilms three-dimensional structure due to EPS polymers collapsing (Fassel and Edmiston, 1999). Therefore, these bands were likely more voluminous than seen in the SEM.

Conclusions
HSC videography on laboratory-grown single-species biofilms exposed to rapid high-velocity fluid (water and/or air) flows allowed the discovery of transient surficial corrugations, which migrated over the biofilm surface. In particular, we documented flowing ripples formed in S. mutans and S. epidermidis biofilms and wrinkles in P. aeruginosa biofilms when exposed to a well-defined compressed air jet. We found that the measured ripples' wavelength and velocity were dependent on the air jet velocity. Using a detailed physics-based model and classical mathematical analysis, we showed that the rippling process is primarily due to physics providing support for the evidence that ripples are KHI and suggesting the onset of turbulence in the biofilm. In addition, the analysis demonstrated that biofilm viscosity modulates KHI formation and, therefore, the type of corrugation.
The agreement among the modelling and the experimental measurements implies viscous fluid behaviour of S. mutans biofilms during rapid high shear stresses. The ability of biofilm to flow and migrate in ripples when exposed to transient high-velocity fluid flows has important consequences for mechanical removal strategies in the medical field or spread of pathogens. Fluid/structure interactions in biofilms are known to modulate the dynamics of biofilm growth, tolerance to antibiotics and virulence. This phenomenon might also explain our recent finding that high-velocity water sprays more effectively delivered microbeads and antimicrobials into in vitro dental biofilms . Interfacial instabilities in biofilms may enhance mass and heat transport (Chen et al., 1997;Vazquez-Una et al., 2000). Finally, our discovery of different observable patterns in biofilms offer the opportunity for theoretical models to be tested against specific and repeatable observations. These models are used, in turn, to   (Picioreanu et al., 2001)], explore aspects of biofilms not available for experimental studies (Cogan, 2010;Friedman, 2015), and to optimize removal protocols (De Leenheer and Cogan, 2009).

Biofilm growth
S. mutans biofilms were grown on autoclaved glass microscope slides (75 mm 3 25 mm, Corning, Sigma-Aldrich). The slides were placed in petri dishes and conditioned with 10 ml of BHI 1 S and 1% type II porcine gastric mucin (Sigma-Aldrich; BHI 1 SM) to simulate salivary proteins and establish a conditioning film. Then the conditioned-slides were inoculated with the S. mutans adjusted-overnight culture and grown under static conditions for 72 h at 378C and 5% CO 2 with medium replacement every 24 h. S. epidermidis and P. aeruginosa biofilms were grown similarly on glass slides (but with no mucin conditioning) for 72 h or 7 days respectively at 378C in a humidified incubator with replacement of their media every 24 h.

Microchannel flow system
Previously we had developed a microfluidic flow channel system (Fabbri et al., 2015) to study the removal of dental biofilms by high velocity jets and sprays. Briefly, the flow channel was created by inserting two biofilm-colonized glass microscope slides in parallel separated by a distance of 1 mm into a specially fabricated holder. The glass slide enabled high-speed imaging [recorded at between 500 and 8000 frames per seconds (fps)] with a HSC MotionPro X3 (IDT) equipped with a Sigma 105 mm f/2.8 EX DG Macro lens. Illumination was provided by two optical fibre light sources (MH-100, Dolan Jenner Industries Inc.). After the growth period, biofilm covered-slides were gently rinsed in 1% phosphatebuffered saline (PBS) solution (Sigma-Aldrich) to remove loosely adhered cells before being placed in the microchannel system.

Biofilm exposure to high-velocity microsprays
First, S. mutans biofilms were exposed to either a water or an air microspray burst delivered from a commercially available oral hygiene device (Philips AirFloss) as previously described (Fabbri et al., 2015). The device was filled either with water to generate a water microspray, as per normal use of the device, or was left empty in order to generate an air microspray. The water microspray lasted 60 ms and dispensed 130 6 0.03 ml (n 5 11) of water dispersed as a discrete burst of micro drops in air. The device was convenient since it could generate high velocity fluid flow and the generation of liquid waste was minimized (Fabbri et al., 2015).

Biofilm exposure to air-jets
An air piston compressor was used to generate a velocitycontrolled air-jet (ClassicAir 255, Metabo). The average air jet velocities (u jet ) entering the microchannel (Table 1) were determined from the volumetric air flow rate (Q jet ), measured using a rotameter (FR2000, Key Instruments), from: where D h is the hydraulic diameter, A* and P are the area (1.92 3 10 23 m 2 ) and the perimeter (5.57 3 10 23 m) of the nozzle (Supporting Information Fig. S4). The air jet, as it passed through S. mutans biofilms, generated a clearance area where the biofilm was removed. The Reynolds number (Re) and the relative wall shear stress (s w ) in the clearance area were calculated according to Stoodley et al. (1999a) (Table 1). In this case D h was derived from the depth of the microchannel (distance between the slides, D 5 1 mm) and the width (W) of the clearance area, measured 10 mm far from the inlet (W 5 4.5 6 0.4 mm). Re has been calculated according to the following equation: where q and g are the density and viscosity of air at 208C and 1 atm. Assuming fully developed laminar flow through the microchannel, the associated wall shear stress (s w ) was measured using: Instead for turbulent flow, the following equation was used: where f is the fanning friction factor (f 5 0:0791 Re 0:25 , for turbulent flow).
S. epidermidis and P. aeruginosa biofilms were exposed to u jet 5 85.5 m/s (Re 5 9268).

High-speed camera image-processing
Videos were analysed with the image-processing package Fiji (Schindelin et al., 2012). The videos were converted to tiff stacks with each frame in the stack being a different time (T) so that the stack could be represented in XYT co-ordinates. Ripples wavelength (k R ) and width (w R ) were measured using the plot profile function (Supporting Information Fig. S5A and B). The ripples' velocity (u R ) was measured using the reslice function which creates a time-trace along a line drawn across the ripple (Supporting Information Fig. S5C). Fast Fourier Transform (FFT) was used to determine whether there were dominant and secondary frequencies in the ripple pattern formed during the S. mutans biofilm exposure to air jets. First profile plots were obtained from individual frames. This produced a graph showing peaks (dark pixels) and valleys (light pixels) corresponding to ripples and the spaces between them. Next, FFT analysis was performed on the plot profile data. The major peaks corresponding to dominant frequencies were identified by eye. Wavelengths were obtained from the inverse of the relative peak frequencies.
Confocal microscopy S. mutans biofilms were fixed with 4% Paraformaldehyde (PFA) solution to preserve structure (von Ohle et al., 2010) and the cells were stained with the nucleic acid stain Syto 63 (Invitrogen). Following a rinse in 1% PBS solution for 5 secs, the slides were gently covered with a cover slip and inverted. Confocal laser scanning microscopy (CLSM) was performed using an inverted Leica DMI600 SP5 (Leica Microsystems). In order to assess the influence of the high velocity flow on internal restructuring, we measured cell-density from confocal stacks of biofilm exposed to the water microspray using the Fiji software. First, we selected a region of interest (ROI) where there was remaining biofilm in the region adjacent to the cleared zone where the HSC showed ripples had formed. Then we measured the area of a single bacterium (A 5 0.52 6 0.09 mm 2 , n 5 6) and, using the threshold function, we measured the biofilm area coverage. To estimate the density of cells, we divided the area of the biofilm by the area of a cell and divided this again by the area of the ROI (452.8 mm 2 ) to give cells per surface area. For comparison, the cell-density was also measured from confocal images in peripheral regions of the slide unaffected by the air jet.

Scanning electron microscopy
SEM (FEI Quanta-200) was used to qualitatively assess the structures of the biofilms of the three species in high resolution. Biofilm slides were processed by first immersing in 200 ll of fixative solution (3% glutaraldehyde, 0.1 M sodium cacodylate and 0.15% alcian blue). After 1 h of incubation in the fridge the samples were washed with 0.1 M sodium cacodylate and incubated for 1 h at room temperature. Next, the samples were incubated for 1 h with 200 ll of secondary fixative solution (0.1 M osmium tetroxide and 0.1 M sodium cacodylate). The solution was then replaced with 0.1 M sodium cacodylate and the samples were incubated for 1 h at room temperature. Finally, the samples were placed though an ethanol series (30, 50, 70, 95 and (two times) 100%), adding and replacing 1 ml of each concentration. All the concentrations were incubated at room temperature for 15 min, except for 100% which was incubated for 20 min. After processing, the samples were critical point dried and then sputter coated with gold.

Mathematical model
The system being studied is sketched in Supporting Information Fig. S1. The top fluid (air) is moving initially horizontally with velocity u a ! while the bottom fluid (biofilm) is initially stationary. We assume that the dynamics of the air layer can be described using Euler equations: r Á u a ! 50: where the velocity is denoted u a ! , the pressure in the upper layer is denoted p a and the air density is denoted q a . To reflect the biofilm structure, we modelled the second fluid using a widely accepted model for the biofilm material referred to as a multiphase model that assumes that the biofilm is composed of both fluid and solid components (e.g., encapsulated water and EPS/bacterial components) (Cogan and Keener, 2004;Klapper and Dockery, 2006;Winstanley et al., 2010;Seminara et al., 2012).The underlying assumption is that any infinitesimal volume of the biofilm can be separated into solid, occupying a fraction of the volume u s . Since the biofilm consists entirely of either solid or fluid, the fluid volume fraction (u f ) and the solid volume fraction must sum to one. Therefore, u f 512u s . We also assume that the solid and liquid components of the biofilm have the same density, allowing us to neglect buoyancy forces within the biofilm. This also implies that conservation of mass is equivalent to conservation of volume fraction. The governing dynamical equations are derived from conservation of mass/volume and momentum, where the latter assumes that the biofilm material is in force balance. The equations of motion are: ou s ot 1r Á u s ru s ! À Á 50; (12) u s 2u f 51; We used the standard Bernoulli matching condition that incorporates surface tension that arises between the materials (Funada and Joseph, 2001). Then, we carried out linear stability analysis for the two-fluid model of a biofilm by perturbing the interface that separates the two materials (See Supporting Information Materials and Methods). As the shear forces drag the biofilm, certain wavelengths grow while the growth of others are suppressed by surface tension and other forces. We used a baseline biofilm viscosity (g) of 2.8 3 10 5 Pa.s, which was the mean g measured on similar S. mutans biofilms (Vinogradov et al., 2004). We also performed the analysis using values of 1/10th and 103 the baseline value.

Statistical analysis
Data were analysed by analysis of variance (One-way ANOVA) followed by the Tukey-Kramer multiple comparisons test.

Supporting information
Additional Supporting Information may be found in the online version of this article at the publisher's web-site: 110.1 m/s (e). The peaks in a FFT spectrum represent periodicities in the data. In this case, the periodicity is the distance between the ripples (i.e., wavelength). Black arrows indicate the position of the peak frequency relative to the wavelength measured experimentally. while the bottom fluid (biofilm) is initially stationary. Fig. S3. Representative sketch of the dispersion curve that relates the perturbation wavelength, k, and the growth rate, x of the perturbation. Fig. S4. Schematic representation of the air jet entry geometry in the IP space. The air compressor nozzle (a) was positioned in the middle of the IP channel created by two microscope glass slides (b). The calculated area of the entry geometry is shown in yellow.  Table S1. Parameters used in the mathematical analysis. a Fitting, b Assumed, c Reference (Vinogradov et al., 2004). Video S1. High-speed camera video of three day old S. mutans biofilm colonized slide exposed to a high-velocity water microspray showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar55 mm. Video S2. High-speed camera video of three day old S. mutans biofilm colonized slide exposed to a high-velocity air microspray showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar55 mm. Video S3. High-speed camera video of three days old S. mutans biofilm colonized slide exposed to a high-velocity air microspray showing biofilm recoil after the micro spray has ended. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar52 mm.
Video S4. High-speed camera video of three days old S. mutans biofilm colonized slide exposed to a compressed air jet of velocity524.6 m/s showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar55 mm. Video S5. High-speed camera video of three days old S. mutans biofilm colonized slide exposed to a compressed air jet of velocity544.9 m/s showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar55 mm. Video S6. High-speed camera video of three days old S. mutans biofilm colonized slide exposed to a compressed air jet of velocity568.1 m/s showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar55 mm. Video S7. High-speed camera video of three days old S. mutans biofilm colonized slide exposed to a compressed air jet of velocity585.5 m/s showing ripples structures forming at the biofilm/fluid Video S8. High-speed camera video of three days old S. mutans biofilm colonized slide exposed to a compressed air jet of velocity5110.1 m/s showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar55 mm Video S9. High-speed camera video of three days old S. epidermis biofilm colonized slide exposed to a compressed air jet of velocity585.5 m/s showing ripples structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar52 mm. Video S10. High-speed camera video of seven days old P. aeruginosa biofilm colonized slide exposed to a compressed air jet of velocity585.5 m/s showing wrinkles structures forming at the biofilm/fluid interface. The nozzle tip was located at the left edge of the slide. Flow was left to right. Scale bar52 mm.