Uptake equation

The solutions for moisture uptake presented in this section are based on the experimental condition of a pure water vapor atmosphere. In the next section a derivation of moisture uptake equations is based on both heat and mass transport that are characteristic of moisture uptake in air. The final section of this chapter presents the results of studies where heat transport is unimportant and mass transport dominates the process. Thus, we will have a collection of solutions covering models that are (1) heat transport limited, (2) mass transport limited, (3) heat and mass transport limited, and (4) mass transport limited with a moving boundary for the uptake of water by water-soluble substances. 

The competition between diatoms and coccolithophorids can be easily modeled by a resource acquisition model based on nutrient uptake (Equation (9)). In such a model, diatoms dominate under highly turbulent conditions, when their nutrient storage capacity is maximally advantageous, while coccolithophorids dominate under relatively quiescent conditions (Tozzi et al., 2003). 

The relative deutraium uptake is determined by the dififa-ence in the average mass at each time point and the undeutraated control. To determine the absolute deuterium uptake. Equation 1.14 is used where the deutraium uptake is adjusted according to the back-exchange during HX-MS analysis ... 

Biological significance of °I, 31 Blocking by iodine, 33 Effects in rats, 33 Specific activity, 31 Uptake equation, 32... 

An elegant alternative method to measure sorption into polymers is the Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) method. It allows in situ acquisition of the kinetic data and at the same time records the changes that occur in the polymer matrix due to the influence of the diffusant. Effects such as swelling, changes in morphology and polymer solvent interactions can all be simultaneously monitored. To calculate the diffusion coefficients from ATR-FTIR data, the mass uptake equation used in gravimetric diffusion experiments has to be modified to take into account the convolution of the evanescent field with the diffusion profile. 

The foregoing equation reveals that essentially the concentration distribution ratio for trace concentrations of an exchanging ion is independent of the respective solution of that ion and that the uptake of each trace ion by the resin is directly proportional to its solution concentration. However, the... 

As may be seen from Table 2.14, the uptake of nitrogen at p/p° = 0-4 was 15-5junolm", so that. (reference) when y4(reference) = 1 m was 15-5pmolm. Insertion of these values in Equation (2.38) gives... 

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

Thus, as pointed out by Cohan who first suggested this model, condensation and evaporation occur at difi erent relative pressures and there is hysteresis. The value of r calculated by the standard Kelvin equation (3.20) for a given uptake, will be equal to the core radius r,. if the desorption branch of the hysteresis loop is used, but equal to twice the core radius if the adsorption branch is used. The two values of should, of course, be the same in practice this is rarely found to be so. 

Equation (3.52) is applied in succession to all steps from step 1 onwards, commencing from the uptake n, where all pores are deemed full (often at p/p° = 0-95 cf. p. 132), to obtain the values of 5 4, 6A2 etc. If no correction is made for the thinning of the multilayer as the emptying process continues, the core volumes will be given by Svf = ( — and the uncorrected... 

Any interpretation of the Type I isotherm must account for the fact that the uptake does not increase continuously as in the Type II isotherm, but comes to a limiting value manifested in the plateau BC (Fig. 4.1). According to the earlier, classical view, this limit exists because the pores are so narrow that they cannot accommodate more than a single molecular layer on their walls the plateau thus corresponds to the completion of the monolayer. The shape of the isotherm was explained in terms of the Langmuir model, even though this had initially been set up for an open surface, i.e. a non-porous solid. The Type I isotherm was therefore assumed to conform to the Langmuir equation already referred to, viz. 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

For a step change in sorbate concentration at the particle surface (r = R) at time 2ero, assuming isothermal conditions and diffusion control, the expression for the uptake curve maybe derived from the appropriate solution of this differential equation ... 

A tracing of the electrode signal during a cycle of turning aeration off and on is shown in Fig. 24-15. The rate of supply is zero (after bubbles have escaped) in the first portion of the response curve thus, the slope equals the uptake rate by the organisms. When aeration is resumed, both the supply rate and uptake rate terms apply. The values for C — C can be calculated from the data, the slope of the response curve at a given point is measured to get dC/dt, and the equation can be solved for K a because all the other values are known. 

In these equations, [L = specific growth rate coefficient, v = specific rate of substrate uptake, t = time, x = biomass concentration, Sj = intracellular substrate, and Cj = concentration of intracellular substrate. Several examples where these equations can be applied include nitrogen hmitations in M. citrifolia cultures and phosphate hmited growth in C. roseus, N. tahacum, a.nd Papaver. somniferum. 

Notice diat we have five unknown coefficients (a, b, c, d and e) but four equations. This means we need an additional equation to solve a system of five equations widi five unknowns. An important and measurable parameter in a living system is the respiration quotient (RQ), which is defined as moles of C02 produced per mole of 02 uptake.1,2... 

It was concluded [734] from visual inspection and chemical analysis of partially decomposed dolomite, that reaction was initiated at the outer surfaces of the crystallites and the interface established advanced thereafter into the bulk. The deceleratory a—time curves obeyed the contracting volume equation [eqn. (7), n = 3] and the values of E determined were between 206 and 232 kJ mole-1. These values of E were generally greater than those reported for other studies ( 190 kJ mole-1) which are in the range mentioned [121] for CaC03 dissociation and slightly larger than the enthalpy of that reaction. On exposure of the residue from vacuum decomposition of dolomite to C02, the gas uptake at 1070 K was... 

The free-radical reaction may be equally initiated by photoactivated sulfur dioxide (3S02)442 (equation 79). On the other hand, polysulfones are obtained by radical copolymerization of appropriate olefins with sulfur dioxide443-449, and similarly, uptake of sulfur dioxide by a radical-pair formed by nitrogen extrusion from an azo compound yields the corresponding sulfone450 (equation 80). Correspondingly, alkylbenzenes, dibenzoyl peroxide, and sulfur dioxide yield sulfones under thermal conditions451... 

Biomagnification along terrestrial food chains is principally due to bioaccumulation from food, the principal source of most pollutants (Walker 1990b). In a few instances, the major route of uptake may be from air, from contact with contaminated surfaces, or from drinking water. The bioaccumulation factor (BAF) of a chemical is given by the following equation ... 

For cellular models, a more compUcated form of the above equation is needed, to factor in paracellular, facilitated uptake and effiux transport, etc. [22].)... 

Traditionally, nutrient uptake from solution culture was taken to depend on the concentration of the external mineral nutrient, C , the amount of nutrientabsorbing surface, and the kinetics of uptake per unit surface area or unit length of root (22). The flux of nutrients into the roots, J, is described by one of two functionally equivalent equations. ... 

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