Half-saturation time

Note that in the notation of Fig. 18.6, CA becomes the aqueous concentration in the pores of the particle aggregate, C, while Cg becomes the time-constant fluid concentration C°. For simplicity we consider only the case where the initial concentration in the sphere is zero (CA = 0). The dissolved concentration in the sphere, C (r,t), follows from Eq. 18-33 by putting CA = 0 and replacing C by C°. The half-saturation time tm is given by Eq. 18-37 (D replaced by the effective diffusivity... 

Development of a conditioning film. This process should depend on surface properties of the substratum and on the charge and polarity of the sorbed matter. It is a relatively fast [half-saturation times of 5-72 s (Armstrong... 

One mol of 2,6-xylidine is dissolved in 800 ml glacial acetic acid. The mixture is cooled to 10°C, after which 1.1 mol chloracetyl chloride is added at one time. The mixture is stirred vigorously during a few moments after which 1,000 ml half-saturated sodium acetate solution, or other buffering or alkalizing substance, is added at one time. The reaction mixture is shaken during half an hour. The precipitate formed which consists of cj-chloro-2,6-di-methyl-acetanilide is filtered off, washed with water and dried. The product is sufficiently pure for further treatment. The yield amounts to 70 to 80% of the theoretical amount. 

After the reaction mixture is cooled to room temperature, 100 mL of half-saturated brine is added to the reaction mixture, which is stirred for 10 min before the layers are separated. The aqueous layer is extracted three times with 200 mL each of... 

In the calculation results, shown in Figure 28.4, phenol concentration decreases with time at a constant rate for about the first 30 days of reaction. Over this interval, the concentration is greater than the value of K, the half-saturation constant, so the ratio m/(m + K ) in Equation 28.9 remains approximately constant, giving a zero-order reaction rate. Past this point, however, concentration falls below K and the reaction rate becomes first order. Now, phenol concentration does not decrease linearly, but asymptotically approaches zero. 

Various criteria have been developed to indicate whether film- or pellet-diffusion will be controlling. In one, proposed by Helffrich and Plesset(15), the times are compared for a pellet to become half-saturated under the hypothetical conditions of either film-diffusion control, f/( 1/2), or pellet-diffusion control, (1/2). 

Vl/2 Time for half saturation assuming film diffusion control s T... 

The best-known exception to exponential kinetics is the elimination of alcohol (ethanol), which obeys a linear time course (zero-order kinetics), at least at blood concentrations > 0.02 %. It does so because the rate-limiting enzyme, alcohol dehydrogenase, achieves half-saturation at very low substrate concentrations, i.e at about 80 mg/L (0.008 %). Thus, reaction velocity reaches a plateau at blood ethanol concentrations of about 0.02 %, and the amount of drug eliminated per unit of time remains constant at concentrations above this level. 

Comparing these results with the half-equilibration time of the aqueous phase, tm (see table above) we conclude that the aqueous concentration reaches its saturation value well before the exchange process switches from the boundary-layer-controlled to the NAPL-diffusion-controlled regime. Thus, diffusive transport of the diesel components from the interior of the NAPL to the boundary never controls the transfer process. Consequently, the simplex box model described in answer (a) is adequate. 

Soderquist and Walton72 showed an overshoot in adsorbed amount as a function of time and a kink or inflection in the isotherm at about half saturation (Fig. 18, see also Fig. 14). They proposed ... 

The results of our two experiments are consistent with these seasonal changes in the availability of light and iron, given the interrelated influences of irradiance and iron availability on phytoplankton growth rate. The data from our laboratory dose-response iron-addition experiment indicate a relatively high iron requirement for colonial Phaeocystis at an irradiance of 20 fiE m 2 s-1, a value that is representative of the mean irradiance in the mixed layer of the southern Ross Sea during early spring (Smith et al. 2000 Smith and van Hilst 2003 Hiscock 2004). At that time, dissolved Fe concentrations are likely to exceed our estimated half-saturation... 

Several studies have examined the P uptake kinetics of Trichodesmium (Table 4.2). McCarthy and Carpenter (1979) first reported a relatively low affinity (Ks = 9 pM) and long P- based doubling times (>200 d) for natural populations of Trichodesmium. More recendy, Fu et al. (2005) determined half saturation values of 0.4-0.6 pM and 0.1—0.2 pM for a strain they isolated from the Great Barrier Reef and for the widely used strain IMS 101 (Prufert-Bebout et al., 1993), respectively. 

Fe concentrations measured at the start of the bioassays, and based on the estimated half-saturation constant fQ of 0.09 nM Fe (by employing MichaeHs—Menten type kinetics), the availability of Fe during that time (ambient dissolved Fe concentration of 0.03—0.04 nM) would appear to limit NO uptake by phytoplankton. These studies aU demonstrate a clear enhancement of specific and absolute NO3 uptake rates by Fe during short-term incubations, and are supported by similar results conducted in other HNLC regions including the equatorial Pacific Ocean (Coale et al., 1996 Cochlan, 2001 Price et al., 1991, 1994) and the eastern (Boyd et al., 1996, 1998 Marchetti et al., 2006) and western (Kudo et al., 2005, in review) subarctic Pacific Ocean. 

The variables and the units are those which have been used since Chapter 1 S(t) is the nutrient concentration at time t, Xx(t) is the concentration of plasmid-bearing organisms at time t, and X2(0 is the concentration of plasmid-free organisms at time t S is the input concentration of the nutrient, and D is the washout rate of the chemostat. These are the operating parameters. The mj term is the maximal growth rate of x, and a, is the Michaelis-Menten (or half-saturation) constant of x,. These are assumed to be known (measurable) properties of the organism that characterize its growth and reproduction. A plasmid is lost in reproduction with probability q, and y is the yield constant. 

---