Wave-controlled bacterial attachment and formation of biofilms
Sung-Ha Hong, Jean-Baptiste Gorce, Horst Punzmann, Nicolas Francois, Michael Shats, Hua Xia
WWave-controlled bacterial attachment and formation of biofilms
Sung-Ha Hong, Jean-Baptiste Gorce, Horst Punzmann, Nicolas Francois, Michael Shats and Hua Xia a) Research School of Physics, The Australian National University, Canberra ACT 2601,Australia (Dated: 30 October 2019)
The formation of bacterial biofilms on solid surfaces within a fluid starts when bacteria attach to the substrate.Understanding environmental factors affecting the attachment and the early stages of the biofilm developmentas well as the development of active methods of biofilm control are crucial for many applications. Here weshow that biofilm formation is strongly affected by the hydrodynamics of flows generated by surface waves inlayers of bacterial suspensions. Deterministic wave patterns promote the growth of patterned biofilms whilewave-driven turbulent motion destroys the patterns. The location of the attached bacteria on a solid substratediffers from the settlement location of inactive bacteria and of the passive micro-particles: strong biofilms formunder the wave antinodes while passive particles and inactive bacteria settle under nodal points. By controllingthe wave lengths and horizontal mobility of the wave patterns, one can either shape the biofilm formationand enhance the biofilm growth, or discourage the formation of biofilm patterns. The results suggest thatthe deterministic wave-driven transport, rather than hydrodynamic forces, determine the preferred locationfor the bacterial attachment.
I. INTRODUCTION
The motion of particles on the fluid surface perturbedby waves is a challenging theoretical and mathemat-ical problem with only a handful of exact solutions.The prediction of transport of particles on and undersuch surfaces has numerous applications, from spread-ing of the pollutants to clustering and settlement ofliving microorganisms. In recent years, experimentalprogress on understanding wave-driven particle motionhas been impressive. Faraday waves, or parametricallyexcited surface waves have been well characterised andunderstood due to a large body of laboratory experi-ments and numerical simulations. At low excitation am-plitude, these nonlinearly generated waves form stablepatterns which, as the forcing is increased, become un-stable and eventually create turbulent motion of fluid inthe horizontal direction . Such turbulence reproducesin detail the statistics expected in ideal two-dimensionalturbulence . The description of disordered Faradaywaves as ensembles of quasi-particles, or oscillons allows to characterise transitions from linear regime toturbulence, via the introduction of horizontal mobility ofoscillons. The oscillon motion turns into a random walkwhich determines the diffusive transport of fluid particleson the surface . Since waves also generate fluid motionbelow free surfaces, such motion also affects transport ofparticles and sedimentation near the solid bottom in thinlayers. One would expect that the wave-driven trans-port should be essential for the process of settlement andattachment of microorganisms, such as bacteria, duringearly stages of the formation of biofilms.Though many bacterial species are very efficient swim-mers, they prefer to colonise submerged surfaces by build-ing biofilms which are self-produced aggregates of mi- a) Electronic mail: [email protected] croorganisms in which bacteria are embedded in a com-plex three-dimensional matrix of extracellular polymericsubstances. While bacterial biofilms are often associ-ated with their adverse effects on surrounding organismsor hosts (medical implant surfaces, water pipes, etc.),many bacteria are beneficial for a variety of environmen-tal, engineering and medical applications such as watertreatment and biotechnologies aiming at creation of newmaterials . Some applications will benefit from theability to control and shape the growth of biofilms, for ex-ample for the development of bacterial scaffolds for tissueengineering or for growing bacterial cellulose whichis a structural component of some biofilms .The microbial consortia can be shaped using differ-ent patterning techniques. Biofilm lithography has beenused to pattern biofilms using optically controlled mi-crobial gene expression. Patterned substrate modifica-tion together with specific antibodies were used to im-mobilise and pattern live bacterial cells . Communitiesof different bacterial species have been constructed us-ing microfluidic devices to control spatial structure andchemical communication . Bacteria are also sensitive tophysical stimuli and mechanical cues such as hydrody-namic forces, adhesive forces, and the rheology of theirsurroundings . For example, it was shown recentlythat fluid flows control the microscopic structure andthree-dimensional morphology of biofilms . Other me-chanical factors, such as mechanical vibration of the sub-strate, also affect bacterial attachment leaving a footprinton the biofilms .The motion of a liquid must play important roles inthe process of bacterial attachment to the solid substrateand on the biofilm development. On one hand, hydro-dynamic forces may encourage the settlement of bacte-ria at particular spots. On the other hand, the flowsmay create favourable conditions for the biofilm develop-ment by establishing the delivery of nutrients, oxygen orother essential components to the biofilm location. Re-cent progress in understanding the motion of particles in a r X i v : . [ phy s i c s . a pp - ph ] O c t stable pattern (3g)linear stage (120 Hz, 2g) turbulence (7g)unstable pattern (5g) μ m s u r f a c e e l e v a t i onb i o f il m ( C V s t a i n ) (a) (b) (c) (d) (e) (f) (g) (h) μ m 300 μ m300 μ m300 μ m 300 μ m 300 μ m300 μ m-5 μ m 5 μ m0 -150 μ m 150 μ m0 -200 μ m 200 μ m0 -200 μ m 200 μ m0 FIG. 1. (a-d): Measured instantaneous contour plots of the surface elevation. Red/blue colors correspond to peaks/troughsof the waves. (e-h): corresponding images of the crystal violet stain of the biofilm attached to the bottom of the fluid cell afterexposure of the bacterial suspension to the waves for 24 hours. Darker colours correspond to thicker biofilms. Fluid cells arevibrated at f s = 120 Hz at the vertical accelerations of (left to right) a = 2 g, g, g and 7 g . fluids whose surface is perturbed by hydrodynamic wavesoffers new ideas on how such flows can be used to controland shape the formation of biofilms.Here we report the development of bacterial biofilms atthe bottom of vertically vibrated containers. To uncoverfactors affecting bacterial attachment, we image surfacewaves, visualise sedimentation of passive microparticlesand inactive bacteria, vertical mixing by the surfacewaves, and study biofilms developing at the bottom.We find that structured, deterministic wave-drivenflows encourage the development of strong biofilms at-tached to the bottom of the microplates. Such biofilmsare characterised by regular periodic patterns whichare correlated with the patterns of the surface waves.Biofilms are formed under the wave antinodes (the peak-trough locations) while inactive bacteria and passive par-ticles accumulate under nodal points where the surfaceelevation is constant in time. The biofilm patterns arescalable: the characteristic spatial period of a patterncan be adjusted by changing the wave frequency and itsamplitude. At higher wave amplitudes, the wave fieldbecomes disordered, leading to turbulent transport andintense mixing in the fluid. In this regime, the biofilmmass is reduced and a pattern does not develop. II. RESULTSA. Biofilm formation under surface waves
Surface waves induce motion of fluid particles on thesurface of a liquid and in the bulk. For linear small am-plitude waves, the velocities of fluid particles exponen-tially decrease as a function of the distance from thesurface. The depth of the liquid is an important fac-tor affecting both the wave dispersion relation and tra-jectories of particles settling at the bottom, and thus,the sedimentation efficiency . The dispersion rela-tion of waves in the finite-depth fluid layer is given by ω = ( gk + σρ k ) tanh( kh ), where ω is the wave frequency, h is the layer depth, k = 2 π/λ is the wavenumber, σ isthe surface tension coefficient, and g is the accelerationof gravity. If a fluid container is vertically vibrated at thefrequency f s with sinusoidal acceleration above a certainthreshold, Faraday waves at the frequency of f F = f s / f s from 45 to 120 Hz in a broad range of verticalaccelerations. Detailed studies are performed at f s = 120Hz ( f F = 60 Hz) which corresponds to the Faraday wavelength of λ F ≈ h = 2 mm for all the experiments to allowwaves to affect the motion of the fluid at the bottom.Thicker layers of fluids do not show strong patterning ofbiofilms.Figure 1 shows the results from four experiments in antinode node(a) surface elevationbiofilm (c)(b) FIG. 2. (a) A profile of the surface elevation produced bythe Faraday wave at the vertical acceleration of a = 2 g , and(b) corresponding profile of a crystal violet density (approxi-mately proportional to the biofilm thickness). (c) A schematicof the fluid motion under standing surface waves . Blue areasat the bottom indicate the locations of the biofilm growth. which a fluid cell filled with the bacterial suspension of Escherichia coli is vertically vibrated at the frequencyof 120 Hz at different vertical accelerations a . The wavepatterns, measured using synthetic Schlieren technique (see Methods), show circular wave fronts for standingwaves at a = 2 g , stable flower-shaped pattern at a = 3 g ,unstable but ordered square pattern at a = 5 g , and a con-stantly evolving in time turbulent wave field at a = 7 g .Biofilms that develop during 24 hours exposure to suchwaves are illustrated in the bottom row. The biofilms (vi-sualised using crystal violet stain) have the spatial struc-ture similar to that of the Faraday waves at lower accel-erations of a = (2 − g , while in the turbulent wave fieldat a = 7 g no clear biofilm pattern is observed.The comparison between the biofilm strength (derivedfrom the crystal violet intensity) and the amplitude of thesurface elevation, Fig. 2, shows that thicker biofilms formunder the locations of the wave antinodes. Note that inFig. 1 the number of rings in the biofilm at a = 2 g is twicethe number of the wave periods of the wave. The biofilmpattern corresponds to two antinodes per wave period.The fluid motion at the antinodes in a standing wave isvertical, while at the positions of the wave nodes, the fluidparticles move almost horizontally, as illustrated in theschematic of Fig. 2(c). As discussed below, the positionof the biofilm under standing waves does not coincide OD600CV(550) stable patternlinear stage turbulenceunstable patternnormalized absorption (a) μ m (b) (d)(c) μ m 20 μ m 30 μ m0 μ m FIG. 3. (a): Total mass of the biofilms (measured as the nor-malised absorption, or the optical density of the crystal violetstain at 550 nm) generated in a microplate well (35 mm di-ameter) at four different vertical accelerations (the vibrationfrequency is 120 Hz) - violet bars. The optical density of thebacterial suspension was approximately the same (measuredat 600 nm) as shown by the orange bars. (b): A fluorescentimage of the biofilm formed in a well exposed to vibrationat the vertical acceleration of 3 g . (c, d): Reconstructed 3Dsurface of the biofilm using the Confocal Laser Scanning Mi-croscopy at two regions of interest. with the expected locations of the sediment of the passivemicroparticles. Generally, a higher wave amplitude at aparticular location leads to a thicker biofilm underneathit, as seen in Fig. 2(a,b).The total mass of the biofilm within a microplate de-pends not only on the wave amplitude, but also on thestability of the wave pattern, Fig. 3(a). The biomassis estimated from the measurements of the optical den-sity (OD) of the crystal violet stain in the biofilm mea-sured at the wavelength of 550 nm. The light absorp-tion in the crystal violet solution (OD550) is comparedwith the control sample to obtain the normalised biofilmgrowth. Similarly, the OD at the wavelength of 600 nmis measured and compared with the control sample toevaluate the planktonic bacteria growth. For approxi-mately constant density of the bacterial suspension, theOD of the crystal violet is noticeably (3-6 times) higherin the samples exposed to the surface waves in compar-ison with the control (non-vibrated) samples. The massof the biofilm has a maximum at the vertical accelera-tion of a = 3 g . This corresponds to a reasonably intensewaves still showing stable patterns. At higher acceler- oscillon trajectories (a)(b) (c) (d)wave field development 10 -9 -8 -7 -6 -5 unstable patternturbulencestable pattern ~ D osc t (e) MSD (m ) μ m300 μ m300 μ m stable pattern (3g) turbulence (7g)unstable pattern (5g) FIG. 4. (a) The development of the measured surface wave field in time, (b-d) trajectories of the wave maxima at differentvertical accelerations 3g, 5g and 7g. (e) MSD of the wave maxima at different vertical accelerations. ation, the mass is decreased in the presence of movingunstable pattern ( a = 5 g ), while for a turbulent wavefield at a = 7 g , the biofilm mass is comparable to thatin the control sample. In other words, the biofilm de-velopment is the strongest in the presence of stationarywave patterns, while the pattern mobility reduces the ef-ficiency of the pattern formation and the biofilmMeasurements of the biofilm thickness are also per-formed using the Confocal Laser Scanning Microscopy(CLSM). Fig. 3(b) shows the fluorescent image of thestrongest biofilm corresponding to a = 3 g . CLSM im-ages of two regions of interest indicate that at the thickerspot, the biofilm thickness is about 20-25 µ m, Fig. 3(c),while at the minimum it is a monolayer (Fig. 3(d)) whosethickness is similar to that of the control (non-vibrated)sample: 2-5 µ m. B. Wave amplitude and horizontal mobility determine thebiofilm growth
Parametrically excited waves in vertically vibratedcontainers become disordered at higher verticalacceleration . A wave in a circular cell develops atthe first subharmonic of the vibration frequency f F = f s / . This process is illus-trated in Fig. 4(a) during the first few seconds of the de-velopment of the parametrically excited waves. The mo-tion of individual oscillons becomes random, they chaot-ically move, collide and merge, as illustrated in the Sup-plementary Video 1. Such wave fields can be analysedby viewing oscillons as quasi-particles. It was shown that the diffusion coefficient characterising the random walkmotion of the oscillons (derived from the mean-squareddisplacement of the maxima of the local surface eleva-tion) is directly related to the fluid particle dispersion atthe fluid surface . In a stable wave pattern, such as theone in Fig. 1(b), oscillons move very slowly around theirequilibrium positions, but as the vertical acceleration isincreased (Fig. 1(c-d)), the horizontal motion of oscillonsbecomes essential for the wave dynamics. Figures. 4(b-d) show trajectories of oscillons in the horizontal planefor three vertical accelerations, corresponding to the wavefields shown in Fig. ?? (b-d). Figure 4(e) shows the mean-squared displacement (MSD) of oscillons as a function oftime, (cid:104) δr (cid:105) = (cid:104) r ( t ) − r (0) (cid:105) . At long times, the MSDis proportional to time which indicates the diffusive na-ture of the process: (cid:104) δr (cid:105) = 2 D osc t . At the low verticalacceleration ( a = 3 g ), corresponding to the case of thestable pattern of Fig. 1(b), the MSD is small, while athigher a it is increased by up to four orders of magnitude,Fig. 4(e).The diffusion coefficient D osc is a measure of the os-cillon horizontal mobility and it is proportional to theirroot-mean-squared velocity (cid:104) ˜ u osc (cid:105) rms . This velocity islinearly proportional to the rms velocity of the fluid par-ticles at the fluid surface : (cid:104) ˜ u (cid:105) rms ≈ (cid:104) ˜ u osc (cid:105) rms . In thinfluid layers, such as those in the reported experimentswhere the fluid thickness is less than the wave length( h/λ ≈ . µ m) sedimented at the bottom of the microplate. Pat-terns formed by the sedimented particles are similar tothe patterns of biofilms, Fig. 1(e-h). The main differenceis that the passive TiO particles are accumulated under (e) ~ D sed t
3g 5g 7g μ m300 μ m300 μ m300 μ m stable pattern (3g)linear stage (2g) turbulence (7g)unstable pattern (5g)(a) (b) (c) (d)MSD (m )0.01 0.1 1 t (s)1010 -9 -8 -7 -6 -5 -4 antinodenode sedimentbiofilmsediment (f) FIG. 5. (a-d) TiO sedimentation pattern at different vertical accelerations at 120Hz: 2g, 3g, 5g and 7g. (e) A schematicof the streaming pattern under standing surface waves . Blue and grey areas at the bottom indicate the locations of thebiofilm growth and TiO sediment, respectively. (f) The corresponding MSD of the sedimentation patterns at different verticalaccelerations at 120 Hz. the wave nodes, in contrast to the maxima of the biofilmswhich correspond to antinodes.The sedimentation of passive particles under waves isbelieved to be due to a wave streaming effect, or the gen-eration of the time-averaged motion due to the rectifica-tion of the fluctuations of the fluid velocity (for examplethe Reynolds stress). The streaming motion was firstconsidered by Rayleigh for acoustic waves and it waslater termed ’steady streaming’ in incompressible flows .Figure 2(c) illustrates the fast oscillating fluid motion in-duced by the wave. In addition to these oscillations, thesurface wave induces a steady streaming motion as shownin Fig. 5(e). The streaming moves fluid down from theantinodes and up at the nodal points. Such a stream-ing pattern has been confirmed experimentally in theFaraday waves . In our experiments, the sedimentationof passive TiO particles is also observed at the nodalpoints, in agreement with previous observations andconsistent with the streaming motion.The increased horizontal mobility of the surface wavesleaves a footprint on the sedimentation patterns. Thesepatterns become blurry at higher accelerations a = (5 − g . We track the sedimented particles near the bottomof the cell. The MSD of the sediment as a function oftime is shown in Fig. 5(f) for the vertical acceleration inthe range of a = (3 − g . The MSD is rather low in thepresence of the stable wave pattern ( a = 3 g ), while in the presence of the unstable pattern ( a = 5 g ) and turbulence( a = 7 g ), the diffusion coefficient D sed is higher by a feworders of magnitude. It was shown that on the surface ofthe fluid perturbed by steep Faraday waves, the horizon-tal diffusion coefficient is given by D = (cid:104) ˜ u (cid:105) rms L f , where L f = λ F / L f ≈ . f F = 60 Hz. From thediffusion coefficient D sed of the sedimented particles ofFig. 5(f), we estimate the rms particle velocity at thebottom (cid:104) ˜ u sed (cid:105) rms to be about 10 − mm/s for the caseof a stable pattern ( a = 3 g ) and about 1 mm/s in theturbulent regime at a = 7 g . The former velocity (10 µ m/s) is less than the motility of active E. coli bacte-ria which is in the range of 15 to 70 µ m/s . Thusthe microorganisms can overcome the wave-induced fluidmotion at lower wave amplitudes ( ≤ g ), while in theturbulent regime, the wave-driven flow dominates overtheir motility. III. SUMMARY AND DISCUSSION
Faraday waves in thin layers of media generate flowswhich affect the attachment of bacteria to the microplatebottom and the overall growth of biofilms. The patternsof mature biofilms (48 hours incubation time) reproducepatterns of the surface waves: the maximum thicknessof biofilms is correlated with the locations of the peaks-troughs of the waves. The settlement of passive TiO particles, in contrast, occurs under the wave nodal pointswhere the surface elevation does not change in time.The sediment pattern of the TiO particles agrees withthe streaming patterns and with recent experimentalobservations . To exclude the possibility that the sizeand the density of the sedimented TiO particles play arole in their settlement locations, we performed experi-ments with inactive E. coli bacteria in the suspensions ofphosphate buffer saline with no nutrient. In such solu-tions, bacteria show substantially reduced motility andthus should sediment similarly to passive microparticles.Indeed, the settlement of inactive microorganisms is ob-served at the wave nodes (see Supplementary Fig. S1).This suggest that the ability of active E. coli to overcomethe wave-produced flows is an important factor which de-termines the selection of the attachment location at thebottom. When the fluid velocities exceed the swimmingspeed of the bacteria, no clear biofilm patterns are ob-served.Other factors which determine the location of thebiofilm, can be the wave-driven transport routes, deliv-ering, for example, oxygen. It has been found that inthe nutrient broth,
E. coli cells use oxygen very quicklyand once oxygen is exhausted, the average velocity of thebacteria dramatically decreases . It is thus possible thatthe transport routes connecting the fluid surface with thebottom of the container, due to the wave streaming, isthe main factor determining the locations of the biofilmdevelopment.To test how the streaming transport is affected by thehorizontal mobility of the waves, we visualise the mixingof the fluorescent dye (initially placed at the fluid surface)into the bulk (see Supplementary Information, Fig. S2.).In the presence of stable wave patterns ( a = (2 − g ), themixing occurs in the form of well defined stationary ver-tical plumes penetrating from the antinodes at the freesurface to the bottom of the microplate. At higher accel-erations, intense horizontal mixing of the fluid destroysvertical plumes and deterministic transport routes of, forexample, oxygen from the fluid surface.The maximum production of biofilm mass is observedat the intermediate wave intensity and at vertical ac-celerations corresponding to stable wave patterns andlow horizontal transport of a fluid. Fig. 6(a) shows thepeak-to-peak wave amplitude of the surface elevation andthe inverse diffusion coefficient of the sedimented parti-cles (1 /D sed ) as a function of vertical acceleration. Thestrongest biofilm is observed at a finite wave height andrelatively low horizontal mobility ( ∝ D sed ) of the mi-croparticles near the bottom. In the fully turbulent flowat a = 7 g , no patterns are observed and the biofilm massis the lowest.The above results are scalable. By changing the fre- b i o f il m b i o m a ss vertical acceleration (g) 0.10.20.30.40.50 s u r f a c e e l e v a t i on ( mm ) (m -2 s) 10 pk-pk1/D sed FIG. 6. (a) Maximal surface elevation of the surface wavefield (solid line ) and the inverse of the diffusion coefficient ofthe oscillon (dashed line), and (b) the total mass of attachedbiofilm, as a function of the vertical accelerations at 120Hz. quency of the vertical vibration and the Faraday wavelength in the range of f s = (45 − f s , the larger the scale of the biofilm patterns.Presented results offer a simple yet efficient method ofshaping biofilms on a solid substrate and allow increasingthe biofilm development by inducing waves on the surfaceof the media. IV. METHODS
Experimental setup . The sample holders housed in atemperature-controlled incubator (37 ◦ C ), are verticallyvibrated by an electrodynamic shaker. The vertical accel-eration of the microplates is accurately monitored. Thefrequency of the vertical vibration can be changed in therange of (0-1.2) kHz, the maximum acceleration is upto 20 g . Most of the results presented in this paper areconducted at 120 Hz, with vertical acceleration from 2 g to 7 g , which corresponds to a vertical displacement of0.07 mm (2 g ) to 0.24 mm (7 g ). Experiments are alsoconducted at f s = 60 Hz at a = 0 . g (0.11 mm verticaldisplacement) to 3 g (0.4 mm displacement). Polystyrenemicroparticles (1 µ m) and TiO particles (200 nm) areused as tracers in the sedimentation studies. The imagesof the sediment are captured using Andor Zyla cameramounted above the fluid plates.A synthetic Schlieren technique developed in Ref. isused to measure wave fields on the water surface. Themethod is based on the analysis of the refracted image(above the surface) of a random dot pattern placed un-der the transparent bottom of the fluid plate. When thesurface is flat, a reference image is obtained. The appar-ent displacement field between the refracted image andthe reference image is determined, which is then used forthe reconstruction of the instantaneous surface elevationmeasurements. The surface elevation is used to identifyand track the horizontal motion of the oscillons. Afterpreprocessing the images using ImageJ software, the iso-lines of the surface elevation are analyzed to identify theoscillons. A particle tracking algorithm is applied to fol-low trajectories of the oscillons using a nearest neighboralgorithm. Bacteria culture . Microplates (six-well) containing 2ml of media (Tryptic Soy Broth +100 µg/ml ampicillin)are inoculated with 20 µl of overnight culture of Es-cherichia coli
GFP (ATCC 25922 GFP) diluted to 0.1OD. The microplates are vibrated for 24 hours. Thesamples are further incubated for another 24 hours at37 ◦ C . The control samples are incubated for 48 hoursin a non-vibrated incubator. At least six measurementsare performed each time for two overnight growths, eachrepeated three times. At the end of each experiment, thetop solution from the microplates is collected to mea-sure the OD600 to characterise the planktonic bacterialgrowth. The attached bacteria and biofilms are washedbefore they are stained using 0.1 % crystal violet (CV)and incubated for 20 minutes. After the developmentof the stain, the samples are washed several times toremove unabsorbed CV. Then the absorbed CV is dis-solved in 2 ml of ethanol solution (20 % acetone and 80% ethanol) to measure the OD of CV absorbed by theattached biomass. All optical density measurements areperformed using a Varioskan Lux multimode reader. 3Dstructures and movies of biofilms were obtained using anupright Zeiss LSM780 UV-NLO confocal microscope. ACKNOWLEDGMENTS
This work was supported by the Australian Re-search Council Discovery Projects and Linkage Projectsfunding schemes (DP160100863, DP190100406 andLP160100477). H.X. acknowledges support fromthe Australian Research Council’s Future Fellow-ship (FT140100067). N.F. acknowledges supportby the Australian Research Council’s DECRA award(DE160100742).The authors acknowledge the technicalassistance of Centre for Advanced Microscopy (ANU).Author contributions:H.X and M.S designed the project. S.H.H and H.X.conducted the experiments. J.B.G. conducted the wavemeasurements. H.P. designed the experimental setup. N.F. analyzed the sedimentation of passive particles. H.Xand M.S wrote the paper. All authors reviewed the pa-per. Faraday, M. ”On a peculiar class of acoustical figures; and oncertain forms assumed by a group of particles upon vibratingelastic surfaces”,
Philosophical Transactions of the Royal Society(London) , , 299-318(1831). Douady, S. Experimental study of the Faraday instability.
J.Fluid Mech. , 383(1990). Binks, D. J. & van de Water, W. Nonlinear pattern formation ofFaraday waves.
Phy. Rev. Lett. , 4043-4046(1997). Kudrolli, A. & Gollub, J.P. Patterns and spatiotemporal chaosin parametrically forced surface waves: a systematic survey atlarge aspect ratio.
Physica D , , 133 (1996). Arbell, H. & Fineberg, J. Spatial and temporal dynamics of twointeracting modes in parametrically driven surface wave.
Phys.Rev. Lett. , 4384(1998). Zhang, W. & Vi˜nals, J. Square patterns and quasipatterns inweakly damped Faraday waves.
Phys. Rev. E , R4286 (1996). Goldman, D.I., Swift, J.B. & Swinney, H.L. Noise, coherent fluc-tuations, and the onset of order in an oscillated granular fluid.
Phys. Rev. Lett. , , 174302 (2004). Shani, I., Cohen, G. & Fineberg, J. Localized instability onthe route to disorder in Faraday waves.
Phys. Rev. Lett. , ,184507(2010). von Kameke, A., Huhn, F., Fern´andez-Garc´ıa, G., Mu˜nuzuri,A. P. & P´erez-Mu˜nuzuri, V. Double cascade turbulence andRichardson dispersion in a horizontal fluid flow induced by Fara-day waves. Phys. Rev. Lett. , 074502 (2011). Francois N., Xia H., Punzmann H. & Shats M. Inverse energycascade and emergence of large coherent vortices in turbulencedriven by Faraday waves,
Phys. Rev. Lett. , 194501 (2013). Francois N., Xia H., Punzmann H., Ramsden S. & Shats M.,Three-dimensional fluid motion in Faraday waves: Creation ofvorticity and generation of two-dimensional turbulence,
Phys.Rev. X , 021021 (2014). Xia H., Francois N., Punzmann H. & Shats M. Lagrangianscale of particle dispersion in turbulence,
Nat. Commun. , 2013(2013). Xia H., Francois N., Punzmann H.& Shats M. Taylor particledispersion during transition to fully developed two-dimensionalturbulence,
Phys. Rev. Lett. , 104501 (2014). Lioubashevski, O., Hamiel, Y., Agnon, A., Reches, Z. & FinebergJ. Oscillons and propagating solitary waves in a vertically vi-brated colloidal suspension.
Phys. Rev. Lett. Shats, M., Xia, H. & Punzmann, H. Parametrically excited watersurface ripples as ensembles of oscillons.
Phys. Rev. Lett. ,034502(2012). Xia H., Maimbourg T., Punzmann H. & Shats M. Oscillon dy-namics and rogue wave generation in Faraday surface ripples,
Phys. Rev. Lett. , 114502 (2012). Francois, N., Xia, H., Punzmann, H. & Shats, M. Wave-particleinteraction in the Faraday waves.
The European Physical JournalE , 106 (2015). Costerton, J.W., Lewandowski, Z., Caldwell, D.E., Korber, D.R.& Lappin-Scott, H.M. Microbial biofilms.
Annu. Rev. Microbiol. , 711(1995). Costerton, J.W., Stewart, P.S. & Greenberg, E.P. Bacterialbiofilms: A common cause of persistent infections.
Science ,1318(1999). Flemming, H.C. Biofouling in water systems: cases, causesand countermeasures.
Appl. Microbiol. Biotechnol. , 629-640(2002). Singh, R. et al. Biofilms: implications in bioremediation.
TrendsMicrobiol. , 389-397 (2006). Wuertz, S. et al. Biofilms in wastewater treatment: an interdis-ciplinary approach,
IWA Publishing , (2003). Grady, C.P.L., Daigger, G.T., Love, N.G. & Filipe, C.D.M. Bio-logical Wastewater Treatment,
CRC Press , 3rd Ed (2011). Nguyen, P.Q., Botyanszki, Z., Tay P.K.R. & Joshi, N.S. Pro-grammable biofilm-based materials from engineered curli nanofi-bres.
Nat. Commun. , 4945(2014). Wood, T.L. et al. Living biofouling-resistant membranes as amodel for the beneficial use of engineered biofilms.
Proc. Natl.Acad. Sci. U.S.A. , E2802-E2811(2016). Bottan, S., et al, Surface-structured bacterial cellulose withguided assembly-based biolithography (GAB).
ACS Nano , , Serpooshan,V., et al, Bioacoustic-enabled patterning of humaniPSC-derived cardiomyocytes into 3D cardiac tissue,
Biomateri-als , , 47(2017). Svensson, A., Nicklasson, F., Harrah,T., Panilaitis, B., Kaplan,D.L., Brittberg, M. & Gatenholm, P. Bacterial cellulose as apotential scaffold for tissue engineering of cartilage,
Biomaterials , 419 (2005). Suo, Z., Avci, R., Yang, X., Pascual, D.W. Efficient im-mobilization and patterning of live bacterial cells.
Langmuir ,4161(2008) . Kim, H.J., Boedicker, J.Q., Choi, J.W. & Ismagilov, R.F. De-fined spatial structure stabilizes a synthetic multispecies bacte-rial community.
Proc. Natl. Acad. Sci. U.S.A. ,18188-18193(2008). Persat, A., Nadell, C.D., Kim, M.K., Ingremeau, F., Sirya-porn A., Drescher, K., Wingreen, N.S., Bassler, B.L., Gitai,Z. & Stone, H.A. The mechanical world of bacteria.
Cell ,988(2015). Even, C., Marliere, C., Ghigo, J-M., Allain, J-M., Marcellan, A.& Raspaud, E. Recent advances in studying single bacteria andbiofilm mechanics.
Advances in Colloid and Interface Science , 573(2017). Kannan, A., Yang, Z., Kim, M.K., Stone, H.A. & Siryaporn,A. Dynamic switching enables efficient bacterial colonization inflow,
Proc. Natl. Acad. Sci. U.S.A. , , 5438(2018). Yan, J, et al. Bacterial biofilm material properties enable re-moval and transfer by capillary peeling.
Advanced materials , ,1804153(2018). Hartmann, R., Singh, R.K., Pearce, P., Mok, R., Song, B., Diaz-Pascual, F., Dunkel, J. & Drescher, K. Emergence of three-dimensional order and structure in growing biofilms,
NaturePhysics , 252(2019). Murphy, M.F., Edwards, T., Hobbs, G., Shepherd, J., & Be-zombes, F. Acoustic vibration can enhance bacterial biofilm for- mation.
J. Bioscience and Bioengineering , 765 (2016). Kundu, P.K. & Cohen, I.M. Fluid Mechanics, Elsevier (2004). Saylor, J.R. & Kinard, A.L. Simulation of particle depositionbeneath Faraday waves in thin liquid films.
Phys. Fluids ,047106 (2005). Perinet, N., Gutierrez, P., Urra, H., Mujica, N. & Gordillo,L. Streaming patterns in Faraday waves,
J. Fluid Mech. ,285(2017) . Moisy, F., Rabaud, M. & Salsac, K. A synthetic Schlieren methodfor the measurement of the topography of a liquid interface.
Exp.Fluids , , 1021 (2009). Umbanhowar, P. B., Melo, F. & Swinney, H. L. Localized exci-tations in a vertically vibrated granular layer.
Nature , , 793(1996). Purcell, E.M., Life at low Reynolds number.
American Journalof Physics , , 3(1977). Guasto, J.S., Rusconi, R. & Stocker, R. Fluid mechanics of plank-tonic microorganisms.
Annu. Rev. Fluid Mech. , 373 (2012). Wallet, A. & Ruellan, F. Trajectoires Internes Dans un ClapotisPartiel,
La Houille , (1950). Rayleigh Lord. On the circulation of air observed in Kundt’stubes and some allied acoustical problems.
Philos. Trans. R. Soc.London Ser. A , ,1 (1883). Lighthill, J. Acoustic streaming.
J. Sound and Vibration , ,391(1978). Riley, N. Steady streaming.
Annu. Rev. Fluid Mech. , 43(2001). Liao, C.H. & Shollenberger, L.M. Survivability and long-termpreservation of bacteria in water and in phosphate-bufferedsaline.
Letters in Applied Microbiology , , 45(2003). Schwarz-Linek, J., Arlt, J., Jepson, A., Dawson, A., Vissers, T.,Moroli, D., Pilizota, T., Martinez, V.A. & Poon, W.C.K. Es-cherichia coli as a model active colloid: a practical introduction.
Colloids and surfaces B: Biointerfaces ,137