Fate and Transport of Nanomaterials in Aquatic Environments - Nanotechnologies for Water Environment Applications - page 508

There is no single model available to describe the biotic transformation
processes. Usually, to ensure the degradation rate not exceeding a maximum value,
biodegradation can be described by a Monod rate model as follows:

R - = f=- (Eq. 15.46)

where Rbd = rate of biodegradation of the NM, M/L 3 -T; r ma x = maximum biodegradation
rate, M/M-T; K s = saturation coefficient, M/L 3 ; and X = biomass concentration, M/L 3 .
Eq. 15.46 can be used to describe biodegradation of NMs by biomass (e.g., bacteria or
mixed population of microorganisms) in either free water or interstice's water (e.g.,
water within porous media, sediments, or bio films). Other rate forms (Metcalf and
Eddy, 2003), such as R b d = -k, -kC, -kCX, or -kXC/C 0 , may also be valid for
biodegradation of NMs, depending mainly on the characteristics of NMs and microbes
involved. The particular rate expression used to define kinetics of NM degradation
needs to be determined by the experimental data available to fit the kinetic equations and
the application of the kinetic model. Usually, these rate expressions are valid in
different aquatic environments, and therefore can be inserted into the mass balance
equations (eqs. 15.1, eq. 15.13).

Bioaccumulation. Bioaccumulation is the net result of competing processes of
uptake and elimination. Factors that affect the rate of one or both processes will affect
the degree of bioaccumulation. Bioaccumulation can be affected by many factors,
including biological factors of aquatic biota, the physical, chemical, and biological
characteristics of NMs, and environmental conditions (Tables 15.8-10). Many of these
factors are interdependent. For example, different species have characteristic lipid
contents, tissue lipid distributions and metabolic capabilities, which depend on
physiological status (e.g., feeding rate, physical stress, growth and spawning) and
environmental conditions (e.g., temperature, habitat, water quality, food availability).

Interaction among these factors can be evaluated more conveniently by
bioconcentration and bioaccumulation models. Bioconcentration refers to NMs obtained
by biota (e.g., fish) directly from water via gill or epithelial tissue. The bioconcentration
process is viewed as a balance between two kinetic processes, uptake and elimination, as
quantified by pseudo-first-order rate constants ki and k2, respectively.
(ir) c = klC » ~ kzC b = ~ R '/ M Tissue

(Eq. 15.47)

where (dC b /dt) 0 = bioconcentration rate in biota, M of NMs/M of tissue-T; ki = uptake

constant, L 3 /M of tissue-T; C w = NM concentration in water, M/L 3 of water; k2 =
elimination constant due to diffusive release, 1/T; Cb = NM concentration in biota, M of
NM/M of tissue; Re = rate of NM decrease in water due to bioconcentration, M/L -T;
and M-Tissue = mass of tissue in water, M of tissue/L 3 of water. Eq. 15.47 assumes that