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Particle Deposition to Protruding Local Sinks Adhering on a Collector Surface R. Bos,* H. C. van der Mei, and H. J. Busscher Laboratory for Materia Technica, University of Groningen, Bloemsingel 10, 9712 KZ Groningen, The Netherlands Received January 15, 1996X In this paper, we measured the local initial deposition rates of streptococci to adhering actinomyces, acting as protruding local sinks on a glass collector, as a function of the actinomyces density in a parallel plate flow chamber. The local initial deposition rates, i.e., deposition in the vicinity of actinomyces, j0,l compared well with values predicted by a model based on convective diffusion perpendicular to the collector surface and convection parallel to the collector surface when the seeding density of adhering actinomyces was below 0.5 × 106 cm-2 (0.03% surface coverage). However, at higher sink densities the model breaks down due to particle depletion of the suspension downstream of a protruding sink.
Introduction Particle deposition from flowing suspensions onto collector surfaces is of importance in a broad field of applications ranging from chromatographic separation to microbial deposition onto carrier materials in bioreactors. Several flow devices, such as the stagnation-point flow chamber,1,2 the rotating disk system,3,4 and the parallel plate flow chamber,5,6 have been designed in order to study particle deposition to solid surfaces under controlled mass transport conditions. In a parallel plate flow chamber, mass transport is mainly through convective diffusion.6 An exact analytical solution of the convective-diffusion equation for the parallel plate flow chamber is difficult to obtain, especially, because the interaction potentials are usually hard to estimate. Therefore, approximate solutions, like the Smoluchowski-Levich approximation,7 have been proposed. In the Smoluchowski-Levich approach it is assumed that the collector surface acts as a perfect sink, i.e., all particles sufficiently close to the surface immediately adhere irreversibly. In general therefore, experimentally observed deposition rates are smaller than those predicted by the Smoluchowski-Levich approach.8,9 All theoretical descriptions of particle deposition onto collector surfaces assume ideally smooth and homogeneous surfaces. Such conditions are never met, and these assumptions may result in large deviations from theoretically expected values.10 Song et al., for instance, demonstrated that surface charge heterogeneity is of key importance in controlling the kinetics of colloidal particle * Corresponding author: tel, 31-50-3633140; fax, 31-50-3633159; e-mail,
[email protected]. X Abstract published in Advance ACS Abstracts, June 1, 1996. (1) Adamczyk, Z. Colloid Surf. 1989, 35, 283. (2) Chari, K.; Rajagopalan, R. J. Chem. Soc., Faraday Trans. 2 1985, 81, 1345. (3) Hull, M.; Kitchener, J. A. Trans. Faraday Soc. 1969, 65, 3093. (4) Marshall, J. K.; Kitchener, J. A. J. Colloid Interface Sci. 1966, 22, 342. (5) Bowen, B. D.; Levine, S.; Epstein, N. J. Colloid Interface Sci. 1976, 54, 375. (6) Adamczyk, Z.; Van de Ven, T. G. M. J. Colloid Interface Sci. 1981, 80, 340. (7) Adamczyk, Z.; Czarnecki, J.; Dabros, T.; Van de Ven, T. G. M. Adv. Colloid Interface Sci. 1983, 19, 183. (8) Sjollema, J.; Busscher, H. J. J. Colloid Interface Sci. 1989, 132, 382. (9) Meinders, J. M.; Busscher, H. J. Colloid Polym. Sci. 1994, 272, 478. (10) Elimelech, M. Sep. Technol. 1994, 4, 186.
S0743-7463(96)00039-X CCC: $12.00
deposition in porous media.11 Besides being heterogeneous, real life, collector surfaces are often rough, sometimes even with adhering objects or protruding uneventies.10 In oil pipe lines, e.g., microorganisms, sand, and rock particles may deposit on the pipe walls or onto each other, while in the oral cavity, microorganisms can adhere directly to the tooth surface, but also to more rapidly adhering, already present initial colonizers or adhering microorganisms not removed by tooth brushing. Recently, we observed that certain micrometer-sized actinomyces, adhering on negatively charged glass, act as local sinks for depositing streptococci.12 An adhering actinomyces, protruding in the flow, can barrierlessly accommodate three to five depositing streptococci through attractive Lifshitz-van der Waals interactions in the presence of minor electrostatic repulsion.13 Initial deposition rates of streptococci to adhering actinomyces were far greater than those predicted by the SmoluchowskiLevich solution of the convective diffusion equation. Obviously, mass transport of streptococci to actinomyces protruding in the flow is through convective-diffusion for its component perpendicular to the collector surface, but in addition, a mass transport component parallel to the surface exists as well, due to collisions between flowing streptococci and adhering actinomyces, acting as protruding local sinks.12,13 For a low density of protruding local sinks (1.4 × 106 cm-2), mass transport to these local sinks could be described by
j0,l* ) j0* + j0,|*
(1)
in which j0,l* is the theoretical total local initial deposition rate of streptococci to the adhering actinomyces, j0* the theoretical initial deposition rate due to convective diffusion according to Smoluchowski-Levich and j0,|* the theoretical initial deposition rate of streptococci to adhering actinomyces due to convective mass transport parallel to the substratum surface in the diffusion boundary layer.12,13 One major assumption in the above model is that the disturbance of the fluid stream lines due to protruding local sinks does not extend beyond the effective grab radius of the sink. However, since blocked areas can become as high as 18 cross sections for polystyrene (11) Song, L.; Johnson, P. R.; Elimelech, M. Environ. Sci. Technol. 1994, 28, 1164. (12) Bos, R.; Van der Mei, H. C.; Busscher, H. J. J. Microbiol. Methods 1995, 23, 169. (13) Bos, R.; Van der Mei, H. C.; De Vries, J.; Busscher, H. J. Colloids Surf., B, in press.
© 1996 American Chemical Society
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particles depending, among others, on the flow conditions,14 this model is doomed to fail at higher protruding local sink densities. The aim of this paper is to determine the influence of protruding local sink density on the initial local deposition rate of flowing particles and to compare the results with predictions from a simple mass transport model accounting for convective-diffusion perpendicular to the collector and convective mass transport parallel to the collector surface. To this end, deposition of Streptococcus oralis J22 was determined from a flowing suspension (wall shear rate 10 s-1; Reynolds number 0.6) in a parallel plate flow chamber using glass as a collector. Protruding local sinks on the collector surface were constituted by adhering Actinomyces naeslundii 5951. Both microbial strains are Gram positive in character and can, for the present purpose, be considered to possess essentially rigid cell walls. Adhering actinomyces were seeded evenly on the glass in densities ranging from 0.36 × 106 cm-2 to 3.86 × 106 cm-2 (surface coverage from 0.02 to 0.30%).
j0,|* )
6Qc (10brh,a4 - 7rh,a5) 4w(2b)3rh,a2δd
(5)
in which Q is the flow rate, w is the width of the flow chamber, and δd is the thickness of the diffusion boundary layer which can be obtained from16
δd ≈
( ) D∞ ν
1/3
δf
(6)
in which ν is the kinematic viscosity (10-6 m2 s-1) and δf is the boundary layer thickness for flow16
( )
δf ≈ 5.2
νx Vm
1/2
(7)
For the calculations in the present manuscript, with adhering actinomyces and flowing streptococci, rh,f and rh,a are taken to be 0.49 and 1.32 µm, respectively.
Theory
Materials and Methods
The local initial deposition rate of particles, to protruding local sinks adhering on a collector surface, is a combination of convective diffusion perpendicular to the collector surface and convective mass transport parallel to the surface and can be written as eq 1. For barrierless deposition, the Smoluchowski-Levich solution of the convective-diffusion equation is valid and accordingly
Bacterial Strains, Culture Conditions, Harvesting, and Suspending Fluids. Streptococcus oralis J22 (kindly provided by Dr. P. E. Kolenbrander, NIH, Bethesda, MD) was cultured in Todd Hewitt Broth. Actinomyces naeslundii 5951 (kindly provided by Dr. J. O. Cisar, NIH, Bethesda, MD) was cultured in Schaedler’s broth supplemented with 0.01 g L-1 hemin. The streptococcal strain was cultured at 37 °C in ambient air, while the actinomyces was grown in an anaerobic cabinet (DW Scientific, West Yorkshire, U.K.) in an atmosphere of 10% H2, 85% N2, and 5% CO2 at 37 °C. For each experiment strains were inoculated from blood agar plates in a batch culture for 24 h. This culture was used to inoculate a second culture which was grown for 16 h prior to harvesting. Bacteria were harvested by centrifugation (5 min at 10000g), washed twice with demineralized water, and resuspended in buffer (2 mM potassium phosphate, 0.5 mM calcium chloride and 50 mM potassium chloride, pH 6.8) for dynamic light scattering and coadhesion experiments. To break bacterial chains and aggregates, cells were sonicated for 30 s at 30 W (Vibra Cell model 375, Sonics and Materials Inc., Danbury, CT). Dynamic Light Scattering. Dynamic light scattering measures the intensity of light scattered by suspended microorganisms as a function of time. Intensity fluctuations are due to Brownian motion of the organisms and can be expressed in a so-called correlation function from which the diffusion coefficient of the organisms can be directly calculated.17 Experiments were done on microbial suspensions in buffer (pH 6.8) with a density of 5 × 106 cells mL-1. Diffusion coefficients were measured with a ALV-5000 (Germany) operated at a constant temperature of 295.8 K. The wavelength of the incident light was 632.8 nm and the detection angle was set to 90°. Two experiments were done using separately cultured bacteria. Parallel Plate Flow Chamber and Image Analysis. The parallel plate flow chamber (length × width: 16 × 8.0 cm) and image analysis system have been described in detail.18 Briefly, glass substrata (5.0 × 7.6 cm) constituting the top and bottom plates of the flow chamber, separated by two Teflon spacers yielding a separation distance of 0.06 cm, were cleaned thoroughly to yield a water contact angle of zero degrees and zeta potential of -20 mV in buffer. Deposition on the bottom glass plate of the parallel plate flow chamber was observed continuously as a function of time (time interval between images 60 s) with a CCD-MXR camera (High Technology, Eindhoven, The Netherlands) mounted on a phase contrast microscope (Olympus BH-2) equipped with a 40× ultralong working distance objective (Olympus ULWD-CD Plan 40 PI). The camera was coupled to an image analyzer (TEA,
j0* )
D∞c
2bPe ( r Γ(4/3) 9x )
1/3
(2)
h
in which rh is the hydrodynamic radius of the depositing particle, b the flow chamber half depth, c the particle concentration in suspension at the flow chamber entrance, x the longitudinal distance from the flow chamber entrance, D∞ the Stokes-Einstein diffusion coefficient, and Pe is the Peclet number, defined as the ratio between convective and diffusion controlled mass transport. For the parallel plate configuration, Pe can be written as6
Pe )
3Vmrh3 2b2D∞
(3)
in which Vm is the mean fluid velocity. The local initial deposition rate component due convective transport of particles toward objects protruding in a flow, j0,|*, can be expressed as
j0,|* )
1 πrh,a2
∫r2r
h,a+rh,f
h,f
c(z) ν(z) b(z) dz
(4)
in which rh,f and rh,a are the hydrodynamic radii of the flowing and the adhering particle, respectively, c(z) is the concentration, and ν(z) velocity of flowing particles at a height z above the surface is assumed to obey the Poiseuille law, while b(z) is the length of the chord b at height z parallel above the surface. Assuming that c(z) varies linearly over the thickness of the diffusion boundary layer, which is a reasonable assumption for small Pe numbers,15 and that flowing particles can be regarded as point masses, eq 4 can be solved using polar coordinates, yielding (14) Meinders, J. M.; Busscher, H. J. Langmuir 1995, 11, 327. (15) Kamiti, M.; Dabros, T.; Van de Ven, T. G. M. J. Colloid Interface Sci. 1995, 172, 459.
(16) Levich, V. G. In Physico Chemical Hydrodynamics; PrenticeHall: NJ, 1962. (17) Lyklema, J. In Fundamentals of Interface and Colloid Science, Vol. 1, Fundamentals; Academic Press: London, 1991; p A11.1. (18) Sjollema, J.; Busscher, H. J.; Weerkamp, A. H. J. Microbiol. Methods 1989, 9, 73.
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lower than the local initial deposition rates and show only a minor decrease with increasing seeding density. At low seeding densities, the nonlocal initial deposition rate equals the initial deposition rate as observed for streptococci to a glass collector, i.e., 1120 cm-2 s-1. Dynamic light scattering yielded a diffusion coefficient for S. oralis J22 of 4.4 × 10-13 m2 s-1. This measured diffusion coefficient for S. oralis J22 has been employed to calculate the theoretical deposition rates in Figure 2, j0,l* and j0*. Note that only at low seeding densities do the experimental values for local and nonlocal initial deposition rates correspond well with theoretical deposition rates. At higher seeding densities major deviations occur, especially for local deposition. Discussion Figure 1. Examples of kinetics of coadhesion of S. oralis J22 deposited from buffer at a wall shear rate of 10 s-1 to glass with a low (0.45 × 106 cm-2) and high (2.20 × 106 cm-2) density of adhering A. naeslundii 5951: 0, locally, in a shell of 1.1 µm around the adhering actinomyces; 4, non-locally, for the area outside these shells; O, for the entire surface. Difa, Breda, The Netherlands). Image acquisition and processing were done as previously described.12,18 Briefly, live images were Laplace filtered after subtraction of an out of focus image. To increase the gray value difference between flowing and adhering bacteria, the first step in the image analysis was the multiplication of four consecutively taken images. Thereafter, adhering bacteria were discriminated from the background by single gray value thresholding. This yields binary black and white images which were subsequently stored on disk. In this setup, one image covers a surface area of 0.017 mm2. Deposition Protocol and Data Analysis. Before each deposition experiment, buffer was circulated through the system by hydrostatic pressure for at least 30 min. Subsequently, the actinomyces suspension (1 × 108 cells mL-1) was circulated through the system until the desired density of evenly distributed, adhering local sinks was reached. Thereafter, the flow was switched to buffer to remove all unattached bacteria from the flow chamber and tubes. Then the flow was switched to the streptococcal suspension (3 × 108 cells mL-1) and image acquisition was set in progress. All experiments were done at a wall shear rate of 10 s-1 in a temperature controlled room at 22 °C with separately cultured bacteria. Data analysis was done as previously described12 distinguishing adhering streptococci from actinomyces on the basis of their times of arrival. In order to study the kinetics of coadhesion, the total streptococcal initial deposition rate, j0, is written as
j0 ) φj0,l + (1 - φ)j0,nl
(8)
in which j0,l and j0,nl represent the initial deposition rates in shells immediately around the adhering actinomyces (local initial deposition rate) and outside these shells on bare substratum (nonlocal initial deposition rate), respectively. φ is the fraction of the collector surface contained within the shells around the adhering actinomyces. For the present experiments, the radius of the shells was chosen to be 1.1 µm, which effectively restricts the streptococci denoted to adhere “locally” to coadhering streptococci.
Results Figure 1 presents examples of the deposition kinetics of S. oralis J22 to glass with a low (0.45 × 106 cm-2) and high (2.20 × 106 cm-2) density of adhering actinomyces. Note that the initial local deposition rate of streptococci is much higher with a low density of adhering actinomyces. Figure 2 shows the local initial deposition rate, j0,l, as a function of the density of adhering actinomyces together with the nonlocal initial deposition rate, j0,nl. The local initial deposition rates j0,l are extremely high at low seeding densities and decrease rapidly with increasing seeding densities. The nonlocal initial deposition rates are much
In this paper, we studied the local initial deposition rate of streptococci to adhering actinomyces, acting as protruding local sinks in the flow, as a function of the density of protruding local sinks. In addition, experimentally observed local initial deposition rates were compared with theoretical values, obtained using a simple mass transport model accounting for convective diffusion perpendicular to the collector surface and collisions with protruding sinks by convection parallel to the collector. The theoretical model overestimates the local initial deposition rates in a seeding density dependent fashion, as can be seen in Figure 2. Figure 3 quantitatively presents this deviation as a function of the seeding density, while excluding the mass transport component perpendicular to the collector surface, employing a factor defined as
)
j0,|* j0,l - j0*
(9)
For low seeding densities, is close to unity, indicating that theoretical and experimental results correspond well. For intermediate seeding densities (see Figure 3), deviations are limited to a factor of 2. At intermediate seeding densities, the distance between the adhering actinomyces varies between 40 and 25 µm and the deviations observed can most likely be explained by so-called particle depletion of the suspension downstream of a protruding local sink. Assuming that a cylinder downstream of a sink with a diameter of 2.5 µm will be completely depleted of particles, it can be calculated that it takes 1.6 s before convectivediffusion has replenished this cylinder with streptococci. Thus, on the basis of the flow velocity 2.5 µm above the collector surface the length of such cylinders can be estimated to be approximately 50 µm, which is within the range of lowest seeding densities. For higher seeding densities (see Figure 3), the simple mass transport model given by eq 5 fully breaks down and deviations becomes as high as a factor of 10. In this seeding density range, distances between protruding sinks (10-20 µm) are too small for replenishment to occur and mass transport by convective transport parallel to the collector surface becomes absent. Consequently, mass transport of streptococci to the adhering actinomyces is by convective diffusion perpendicular to the collector surface only, which explains why at high seeding densities the experimentally observed local initial deposition rates approximate the Smoluchowski-Levich initial deposition rate j0* (see Figure 2). At this point it is emphasized, that hydrodynamic blocking, i.e., the simple disturbance of the flow lines due to the presence of adhering actinomyces is probably less important than particle depletion, as estimates of blocked
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Figure 2. The local (b) and nonlocal (O) initial deposition rates of S. oralis J22 to glass as a function of the seeding density of adhering actinomyces. In addition, the theoretical local initial deposition rate j0,l* based on eq 5 and theoretical initial deposition rate j0* based on the Smoluchowski-Levich approach for convective diffusion are shown.
Figure 3. The ratio between the theoretically calculated and experimentally observed local initial deposition rates, while excluding convective diffusion perpendicular to the collector surface, as a function of the seeding density of adhering actinomyces.
areas seldom exceed 10 particle diameters under conditions of minor electrostatic repulsion and low wall shear rates.14 This indicates that pure hydrodynamic blocking only becomes a factor, contributing to the breakdown of the validity of eq 5 once distances between adhering actinomyces are less than 10 µm. Tentatively, therefore, we propose to name the “depletion factor”. In addition, the nonlocal initial deposition rates are also influenced by the seeding density of the adhering
actinomyces, although only to a minor extent. In the low seeding density range, streptococcal deposition is slightly higher than the Smoluchowski-Levich solution of the convective-diffusion equation for inert particles, most likely because surface appendages on the bacteria assist deposition.19,20 Hydrodynamic blocking, in addition to particle depletion, is responsible for the decrease in nonlocal initial deposition rates with the seeding densities of the adhering actinomyces. Summarizing, we have demonstrated that the density of protruding local sinks on a collector surface greatly affects local deposition of particles. A model is proposed which adequately describes local deposition at low sink densities, but which fails at higher density, presumably due to particle depletion of the suspension downstream of a protruding sink. Acknowledgment. The authors are greatly indebted to Dr. Martien Cohen Stuart, Department of Physical and Colloid Chemistry, Agricultural University of Wageningen, The Netherlands, for the use of the dynamic light scattering equipment and Dr. T. G. M. van de Ven, Paprican and Department of Chemistry, Pulp and Paper Research Centre, McGill University, Montreal, Canada, for helpful discussions. LA960039A (19) Willcox, M. D.; Drucker, D. B. Microbios 1989, 59, 19. (20) Sjollema, J.; Van der Mei, H. C.; Uyen, H. M. W.; Busscher, H. J. J. Adhes. Sci. Technol. 1990, 4, 765.
