We use an RDE to continuously quantify the bacterial adhesion under shear at a charged surface. We first plot a dimensionless Levich curve, Fig. 1, which describes the dependence of mass transport on momentum transport. As described in Levich1212. B. G. Levich, Discuss. Faraday Soc. 1, 37 (1947). https://doi.org/10.1039/df9470100037 and put in a dimensionless form, Eq. (2), the ideal Levich curve shows that the Sherwood number, Sh, is proportional to the square root of the Reynolds number, Re, Sh=kmRD0∝(ωR2ν)1/2=Re1/2,(2)where km is the mass-transport coefficient, R is the radius of the disk, D0 is the diffusivity, ω is the rotation rate, and ν is the kinematic viscosity. We modify Sh using Batchelor’s3434. G. Batchelor, J. Fluid Mech. 83, 97 (1977). https://doi.org/10.1017/S0022112077001062 2nd order correction for viscosity of a fluid containing particles with volume fractions ϕ<5%, μ∗=μ(1+52ϕ+7.6ϕ2),(3)to find that Sh∗=Sh⋅(1+52ϕ+7.6ϕ2)1/2∝Re1/2.(4)Sh* accounts for the variation in bacterial density as B. subtilis concentrations were ≈0.10%v/v and E. coli concentrations were ≈0.25%v/v. We find that the Levich curve for ferricyanide in the abiotic buffer maintains an approximate 1/2 power dependence between Sh* and Re, as shown in Fig. 1 and predicted by Eq. (4). We assume a 1/2 power dependence and plot a line using an intercept from a linear best fit to the data. The intercepts of the lines deviate significantly because the bulk of the points are after the inflection. The power dependence for the buffer in the smooth (Sa=2.5) and rough (Sa=3.9) cases is both 0.45, but there is curvature in both the E. coli and B. subtilis cases.Curvature away from a linear dependence in an RDE was demonstrated in the literature for the adhesion of red blood cells by Ficquelmont-Loizos et al.2626. M. de Ficquelmont-Loizos, L. Tamisier, and A. Caprani, J. Electrochem. Soc. 135, 626 (1988). https://doi.org/10.1149/1.2095678 as shown in Fig. 2 using Sh* to account for differences in volume fraction. We also use 1.04μm diameter polystyrene beads at a volume concentration of ≈5% v/v average to the buffer as an abiotic control. The linear dependence is similar to the buffer and does not show adhesion. This is in contrast to E. coli and B. subtilis, which show curvature and adhesion. Our results on polystyrene contrast work by Meinders et al.,3535. J. Meinders, V. H. der Mei, and H. Busscher, J. Colloid Interface Sci. 176, 329 (1995). https://doi.org/10.1006/jcis.1995.9960 who used a channel geometry to show that 0.736μm polystyrene particles adhered to glass at rates similar to those of bacteria. The contrast is likely due to the shear rates in this work being much higher than the 50s−1 used in their work,3636. E. Thormann, A. Simonsen, P. Hansen, and O. Mouritsen, Langmuir 24, 7278 (2008). https://doi.org/10.1021/la8005162 though it could also be a function of the interaction force between polystyrene and Pt. Additionally, their setup allows for sedimentation enhanced adhesion, whereas our flow geometry is more applicable to systems that rely on forced convection to and away from the surface similar to propellers and the upper walls of pipes.The Levich curve shows a transition from a 1/2 power dependence of mass transport and momentum transport for the bacteria. Determining this inflection point of sufficient magnitude in the Levich curve using numerical methods is difficult due to the noise in the nearly flat data. Caprani et al.1616. A. Caprani, M. de Loizos, and M. Nakache, Physicochem. Hydrodyn. 6, 567 (1985). used multiple linear fits to distinguish different slopped regions. We plot the ratios of Sh* for each particle and bacteria to that of the buffer solution to determine the rotation rate that leads to the deviation from linear behavior. As shown in Fig. 3, there is an inflection point at rotation rates of 500 and 600 rpm (613.02s−1, 6.14dyncm−2) for B. subtilis and E. coli, respectively, but not for the beads. Rheological measurements show that viscosity typically does not change upon addition of such a small number of particles, live or dead (Fig. S34949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods. and Ryan et al.3838. S. D. Ryan, B. M. Haines, L. Berlyand, F. Ziebert, and I. S. Aranson, Phys. Rev. E 83, 050904 (2011). https://doi.org/10.1103/PhysRevE.83.050904). The diffusivity would not be expected to appreciably change according to the model developed by Tribollet et al.3333. B. Tribollet, J. Newman, and W. H. Smyrl, J. Electrochem. Soc. 135, 134 (1988). https://doi.org/10.1149/1.2095539 Since the ratio of particle to buffer Sherwood number is stable for the beads, we can assume that the deviation from the Levich dependence is not due to Coulombic reactions of ferri/ferrocyanide or pure hydrodynamics. E. coli can metabolize 5% of the ferricyanide in solution over the 2 h experiment if they also had an electron donor.3939. P. Ertl, B. Unterladstaetter, K. Bayer, and S. R. Mikkelsen, Anal. Chem. 72, 4949 (2000). https://doi.org/10.1021/ac000358d Unlike E. coli that metabolizes ferricyanide through an NADH shuttle, B. subtilis membrane bound cytochromes directly reduce ferricyanide under anaerobic conditions.4040. A. Bisschop, J. Boonstra, H. J. Sips, and W. N. Konings, FEBS Lett. 60, 11 (1975). https://doi.org/10.1016/0014-5793(75)80407-8 This will likely change the physics of interaction between B. subtilis, ferricyanide, and the electrode leaving more to be explored in future work. The only variable unaccounted for in the Levich equation is the area. The results show an inflection point in the change in area around 600 rpm for E. coli and 500 rpm for B. subtilis. Chronoamperometry was run for 2 h at this rotation and at limiting current to determine if limiting current can dynamically measure a change in area over time. As shown in Fig. 4, the ratio of computed Sh with bacteria to the initial Sh of the buffer falls over this time. Each break in the data is a cyclic voltammetry measurement. Cyclic voltammetry describes changes in the electroactive area of a surface for a redox molecule.1515. A. J. Bard and L. R. Faulkner, Electrochemical Methods, 2nd ed. (John Wiley & Sons, Hoboken, NJ, 2001). The smaller the enclosed area of the voltammogram, the smaller the electroactive area, as we see for E. coli in Fig. 5.1515. A. J. Bard and L. R. Faulkner, Electrochemical Methods, 2nd ed. (John Wiley & Sons, Hoboken, NJ, 2001). Quantitative analysis requires knowing the mechanisms of attachment and detachment of the redox molecule on the material used.2929. R. Woods, J. Electroanal. Chem. Interf. Electrochem. 49, 217 (1974). https://doi.org/10.1016/S0022-0728(74)80229-9 In the present case, the mechanisms of ferricyanide/ferrocyanide reacting on platinum have not been reported in the literature. Recognizing that the area in Eq. (5)4949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods. is the surface area and not the electroactive area, the change in the limiting current and corresponding Sh shown in Figs. 1–3 and Fig. S44949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods. is a physical blocking of the electrode. This could be due to bacteria or proteins that block the ferricyanide from reacting at the electrode surface. Assuming that the area a single bacteria occupies is half its surface area, we estimate the number of bacteria adhered as a function of time and the subsequent deposition rate as described in Eq. (5), n=1−A/A00.5⋅SAbacteria,(5)where n is the number of bacteria, A is the measured area, A0 is the initial area, and SAbacteria is the surface area of the bacteria. As shown in Table I, the deposition rate of B. subtilis oscillates over each cycle unlike E. coli, which steadily decreases from the second 30 min cycle, as described in the literature.1111. H. J. Busscher and H. C. van der Mei, Clin. Microbiol. Rev. 19, 127 (2006). https://doi.org/10.1128/CMR.19.1.127-141.2006 The values in this work include any proteins secreted into the media or directly onto the substrate, though the deposition rates for E. coli K12 are close to those found for E. coli O2K2 on glass at a lower shear rate 0–100 s−1 (50–400 cm−2.s−2) in the literature.1010. A. Roosjen, N. P. Boks, H. C. van der Mei, H. J. Busscher, and W. Norde, Colloids Surf. B 46, 1 (2005). https://doi.org/10.1016/j.colsurfb.2005.08.009 Although we did not find a direct comparison, it is reported that B. subtilis forms biofilms as strongly as Pseudomonas aeruginosa, which is reported to maintain a near constant 400 cm−2s−1 deposition rate over shear rates from 0 to 600 s−1.1010. A. Roosjen, N. P. Boks, H. C. van der Mei, H. J. Busscher, and W. Norde, Colloids Surf. B 46, 1 (2005). https://doi.org/10.1016/j.colsurfb.2005.08.009 To compare with traditional methods, we quantify bacteria coverage on the electrode using fluorescence microscopy, following the methods of Shive et al.2121. M. S. Shive, S. M. Hasan, and J. M. Anderson, J. Biomed. Mater. Res. 46, 511 (1999). https://doi.org/10.1002/(SICI)1097-4636(19990915)46:4<511::AID-JBM9>3.0.CO;2-M for measuring adhesion (see Fig. S64949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods.). While common in the literature,1111. H. J. Busscher and H. C. van der Mei, Clin. Microbiol. Rev. 19, 127 (2006). https://doi.org/10.1128/CMR.19.1.127-141.2006 this visual method is not dynamic and relies on imprecise “slight rinsing” or “dipping” prior to imaging.1111. H. J. Busscher and H. C. van der Mei, Clin. Microbiol. Rev. 19, 127 (2006). https://doi.org/10.1128/CMR.19.1.127-141.2006 The results, shown in Table II, are variable with error that is as high or higher than the measured values. Regardless, there is a significant difference between the electrode area that E. coli cells cover relative to B. subtilis visually. We would expect that B. subtilis would have significantly larger area coverage as it forms biofilms more readily than E. coli. Therefore, we propose that the closeness in measured area coverage (Fig. S44949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods.) also captures exopolymeric substance secretion, and our deposition rate for B. subtilis is an upper-bound. The combined coverage measurement is equally important in biofouling studies as these substances allow other micro-organisms to adhere to an otherwise incompatible surface. For example, in the development of novel coatings for medical devices, percent area covered is an important metric. The deposition rates found in this study are likely not translatable to different temperatures, fluids, metals, electrical potentials, or bacteria. On the contrary, the full procedure would need to be followed to quantify the bacterial deposition rate for a particular set of conditions. As noted in Eq. (8) of Ref. 4949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods., the diffusivity and viscosity are temperature dependent. The former should affect adhesion similarly to other methods for determining bacterial adhesion. We have described the independent quantification of how those parameters, and the reaction rate of the tracer chemical, vary and affect the measurement in Eq. (8) of Ref. 4949. See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001585 for sample graphs of cyclic voltamogram of bare platinum, rheological data, EIS based diffusivity calculation, raw current versus rotation rate with error bars, and current versus time with error bars, CFU plate viability tests, picture of reactor and illustration of theoretical mechanism, and differences between this and other methods.. Furthermore, while this technique cannot be applied in vivo, this decoupling can also be used to quantify errors that may occur in interdigitated electrochemical impedance techniques.22,2322. J. B. J. H. V. Duuren, M. Müsken, B. Karge, J. Tomasch, C. Wittmann, S. Häussler, and M. Brönstrup, Sci. Rep. 7, 645 (2017). https://doi.org/10.1038/s41598-017-00488-y23. S. Subramanian, E. I. Tolstaya, T. E. Winkler, W. E. Bentley, and R. Ghodssi, ACS Appl. Mater. Interfaces 9, 31362 (2017). https://doi.org/10.1021/acsami.7b04828As we have described, the deposition rates found in this study account for both protein and bacterial coverage of the total molecular electroactive area. Based upon results in the literature, protein adhesion and protein secretion are functions of bacterial adhesion and biofilm formation.4141. Y. Chao and T. Zhang, Anal. Bioanal. Chem. 404, 1465 (2012). https://doi.org/10.1007/s00216-012-6225-y Noting how proteins are involved in the adhesion process and charge transport processes, future inquiry, including applications of these methods, should be taken to understand how prior biofilm adaptation effects protein expression, protein charge, and adhesion rates similar to what the authors showed in Wang et al. for biofilm adaption and protein expression.4242. Q. Wang, A.-A. D. Jones, J. A. Gralnick, L. Lin, and C. R. Buie, Sci. Adv. 5, eaat5664 (2019). https://doi.org/10.1126/sciadv.aat5664 In this paper, initial adhesion occurs under hydrodynamic shear. While biofilms do not need shear to form and many biofilm experiments in the literature are initiated without shear, we have also found that mature biofilms started under shear have drastically different transport properties from mature biofilms initiated without shear.1414. A.-A. D. Jones and C. R. Buie, Sci. Rep. 9, 1 (2019). https://doi.org/10.1038/s41598-019-39267-2 Due to the necessary assumption of constant tracer chemical, this technique could not be used to monitor adhesion rates under no-flow, no-shear conditions. On the contrary, quartz-crystal microbalance methods would need to be used.