Initial Events

Processes 1-4 are often grouped in mathematical models as a single process termed deposition.

Preconditioning of the Substratum. In the case of intentional pretreatment of a surface (i.e., adhesion molecules for biomaterials), there is no rate to be considered; the substratum essentially enters the system with a biased sur face chemistry. However, in cases where a clean substratum material is exposed to an aqueous environment, transport of dissolved organic molecules or macromole-cules in laminar flow is basically by molecular diffusion; in turbulent flow, transport must also consider convective transport effects. Once at the surface, adsorption of mac-romolecules occurs almost instantaneously, immediately changing the surface chemistry of the exposed material. Loeb and Neihof (50) and Depalma et al. (51) measured adsorption rates of organic molecules to various solid substrata in seawater, and Bryers (52) reported analogous adsorption rates in a freshwater laboratory system. The net rate of adsorption in these studies can be described by equation 1.

where Radsorption is the rate of net adsorption (ML-2t-1); ka is the adsorption rate constant (Li-1); kS is the surface saturation coefficient (ML-2); and Si is the real concentration of adsorbed species (ML-2). Although experiments indicate the maximum amount of adsorbed material may not exceed 0.10 im in thickness, the surface properties resulting from adsorption of an organic film can significantly bias subsequent microbial events.

Cellular Adsorption and Desorption. The net deposition rate of cells upon a "conditioned" substratum is itself a composite of the individual rates of cell transport to the substratum, cell adsorption, and adherent cell desorption.

Many models exist to describe bacterial transport from the fluid phase to the target surface. Bowen et al. (53) and Beal (54) derive continuity equations describing the transport of suspended particles from a flowing fluid to the surfaces of a surrounding conduit that accounts for both con-vective and molecular transport mechanisms. From their work, the maximum flux of particles transported to the surface, L distance from the inlet, of a rectangular flow cell, with gap height 2h, can be written as


where ktr is the particle transport coefficient ((2/9)K033/ C(4/3)); K = (1 /Pe)(8L/3h); Peis the Peclet number = 4vh/ v is the average velocity of the fluid; C is the gamma function (C(4/3) = 0.89338);and is the diffusivity of cells in the liquid. For nonmotile cells, the Brownian diffusion coefficient can be estimated from the Stokes-Einstein equation,

where kb is the Boltzmann constant (1.38 X 10~23 J/K); T is absolute temperature; i is absolute viscosity; dc is cell diameter. To compensate for cell motility, Jang and Yen (55) propose the following equation,

where vm is the velocity of motility, dr is the free length of a random run, and a is the angle turned by the motile cell.

Once at the substratum interface, cells stick. Observations have indicated that cells can adsorb to a surface for a period of time and then may desorb from the substratum, returning to the bulk liquid. If cells spend sufficient time at the surface, they become permanently bound, initiate within minutes the secretion of extracellular polymer production, and can be removed only by rather aggressive physical or chemical means. One can conceive of this overall process as much like two reaction steps in series, with the reversible adsorption process followed by an irreversible step pertaining to permanent adsorption,

where X is the suspended cells, Xrev is the reversibly adsorbed cells, and Xirr is the irreversibly adsorbed cells. Assuming no cell replication, the total amount of cells observed at a substratum, Xt, at any one time comprises both reversibly and permanently adsorbed cells, that is, Xt = X + X

Cell Attachment. Attachment is the deposition of cells from the fluid phase onto an existing biofilm. This process differs from adsorption in that the target surface is now a developed biofilm. The biofilm itself poses a different type of substratum in that biofilm surface morphology is generally more irregular (perhaps filamentous), very porous, compliant, and gelatinous. Experimental results indicate that the increased attachment of cells to a biofilm-covered substratum may depend on far more subtle mechanisms than mere changes in surface morphology. The local chemistry of a biofilm surface will reflect the composition of the bacterial cell and that of the insoluble polymer matrix, both of which could affect subsequent chemical interactions with incoming cells.

Banks (56) and Banks and Bryers (57) report that the rates of cell deposition increased when cells were exposed to biofilm surfaces versus clean glass (Fig. 4). Two species were investigated, Pseudomonas putida and Hyphomicro-bium ZV620, as to their deposition rates, under laminar flow conditions, onto both clean glass and biofilm-covered surfaces. Pseudomonas putida cells attached to a P. putida biofilm at a rate (zero order in attached cell concentration) that was 3.6 times higher than the cell attachment rate to clean glass. Pseudomonas putida cells attached to a Hy-phomicrobium biofilm (with zero-order kinetics in attached cell concentration) that was 2.4 times higher than to clean glass. Hyphomicrobium illustrated an attachment rate to a Hyphomicrobium biofilm (again a zero dependency on attached cells) that was 3.3 times higher than the Hy-phomicrobium attachment rate to clean glass. Attachment rate of Hyphomicrobium spp. cells to a P. putida biofilm was only 1.3 times that to clean glass. The attachment rate of Hyphomicrobium cells to a Hyphomicrobium biofilm was about half of the rate of Pseudomonas cells attaching to a Pseudomonas biofilm, even though suspended Pseudomonas cell concentrations were three times higher. Results insinuate that species-dependent enhancement of cell attachment may occur by specific rather than nonspecific adhesion mechanisms.

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