Solute concentrations, versus

The flux rate is obtained from the slope of the receptor chamber solute concentration versus time plot. The mass transfer coefficient, hh is equal to PA, where A is the surface area of the membrane separating the two subcompartments. 

However, in contrast to Equation 4, the Np solution concentration versus pe+pH (Figure 4) appears to decrease rather than increase with the pe+pH sum. This suggests that at pH values... 

We obtained a measure of the degree of ionization as a function of the total sodium density in the flame by plotting the ratio of the ionization signal to sodium solution concentration versus the latter concentration on double logarithmic scales as shown in Fig. 3. For concentrations in excess of... 

A chromatogram is a plot of some function of solute concentration versus elution time or elution volume. 

Myerson (2002), Mullin (2001), and Mersmann (2001) provide excellent descriptions of methods for crystal growth rate measurements. These methods involve measurements of either single crystals or suspensions. Much information can be gained from the traditional technique of measuring ( grab samples or in-line) solute concentration versus time in batch crystallization on a seed bed. Initial and later slopes on such a plot can provide multiple data points of growth rate versus supersaturation. 

An expression for solute concentration versus angular displacement at the column outlet requires inversion of this solution back to the 0 domain, a procedure which cannot be performed analytically. A fast Fourier transform algorithm was used to perform the inversion numerically (21). Equations 1 and 2 were also solved using a finite difference algorithm. 

All of the direct measurement techniques are time consuming and require a significant number of experiments to obtain sufficient data to obtain kinetic parameters. This has led a number of investigators (Garside et al. 1982 Tavare and Garside 1986 Qiu and Rasmussen 1990 Witkowski et al. 1990) to look at indirect methods for the estimation of both growth and nucleation kinetics. Most of the indirect methods are based on the measurement of the solution concentration versus time in a seeded isothermal batch experiment. This is often called the desupersaturation curve since the concentration and the solubility can be used to calculate the supersaturation of the system versus time. 

Fig. 3.26 Schematic representation of the solute concentration versus time in the nucleation and growth of particles from a solution. Reproduced with permission from [111]. Copyright 1950, American Chemical Society...

Constmction of a molecular model for HPMCAS is complicated by the complex and varied substitution patterns possible as evident in the representative substructure shown along with the variety of R-substituents that may he found at each of the indicated oxygens (Fig. 13.6). As recently observed by Porter in et al. [60], a limited variety of HPMCAS products are available, and they cover a relatively small subspace of the entire allowed compendial space. In particular, they observed that the ratio of acetyl to succinyl substitution may have a dramatic impact on the ability of HPMCAS to form supersatnrated solutions as measured by areas under the solution concentration versus time profiles (AUCs). Supersaturation profiles are highly dependent on the HPMCAS composition and also very dmg specific. MD simulations may ultimately contribute to understanding of the molecular basis for the relationship between HPMCAS molecular structure and dispersion performance. Clearly, HPMCAS polymer assembly in terms of composition and substitution pattern requires careful attention. 

Fig. 3. Solute concentration versus time for albite-acetate experiments as a function of pH. Numbers on the right indicate the initial pH of each solution. Apparent dissolution rate is equal to the slope of each line. Data from Franklin (1991)...

In most cases, we want the release rate of a solute, like a drug, to be constant with time. This constant release rate will often give a constant concentration when in use, as suggested by Fig. 19.0-1. Often, we will test for this type of release rate by placing this solute, or a device containing solute, in a beaker of stirred solvent. We will measure the solute concentration versus time. We hope for a linear variation, for this would mean a constant release rate. Such a variation is called zero-order release, as shown in Fig. 19.1-1. 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

If the solute size is approximately the (apparent) membrane-pore size, it interferes with the pore dimensions. The solute concentration in the permeate first increases, then decreases with time. The point of maximum interference is further characterized as a minimum flux. Figure 4 is a plot of retention and flux versus molecular weight. It shows the minimum flux at ca 60—90% retention. 

FIG. 22-4 Cl irves for progressive freezing, showing solute concentration C in the solid versus fraction-solidified X (Pfann, Zone Melting, 2d ed., Wileij, New York, 1966, p. 12. )... 

Figure 36. Temperature versus solute concentration curve.

Fig. 136. Nb205 concentration versus pH of solutions prepared by dissolution of (NH4)3NbOF6 (1) and (NH4)2NbOF5 (2) in water or Nb in HF solution (3) (after Agulyanskaya et al., [492, 493]).

In the case of tantalum-containing solutions, a sharp drop in Ta205 concentration was observed also at pH > 10. The precipitated material was identified as a pure amorphous powder, which after appropriate thermal treatment was converted into tantalum oxide. Fig. 137 presents isotherms (20°C) of Ta205 concentration versus pH for solutions with compositions close to those of industrial strip solutions. 

Compare these results with those of Equation (2.22) for the same reactions in a batch reactor. The CSTR solutions do not require special forms when some of the rate constants are equal. A plot of outlet concentrations versus t is qualitatively similar to the behavior shown in Figure 2.2, and i can be chosen to maximize bout or Cout- However, the best values for t are different in a CSTR than in a PFR. For the normal case of bi = 0, the t that maximizes bout is a root-mean, t ix = rather than the log-mean of... 

Referring to Fig. 1.4, the solution begins with the initial concentration conditions Aq, Bq, Cq and Dq, defined at time t = 0. Knowing the magnitudes of the kinetic rate constants k], k2, k3 and k4, thus enables the initial rates of change dCA/dt, dCfi/dt, dCc/dt and dCo/dt, to be determined. Extrapolating these rates over a short period of time At, from the initial conditions, Aq, Bq, Cq and Do, enables new values for A, B, C and D to be estimated at the new time, t = t -I- At. If the incremental time step At is sufficiently small, it is assumed that the error in the new estimated values of the concentration. A, B, C and D, will also be small. This procedure is then repeated for further small increments of time until the entire concentration versus time curves have been determined. 

The most common extravascular route is oral. When a solution or a rapidly dissolving solid dosage form is given orally, the absorption process often obeys first-order kinetics. In these cases, absorption can be characterized by evaluating the absorption rate constant, ka, using plasma concentration versus time data. 

When gel sections are analyzed for solute concentration, a value C is obtained, and when the solution bathing the gel is analyzed, a value C0 is obtained. The ratio C7C0 is plotted versus gel section distance, x, on arithmetic probability paper, and the slope of this plot is used to determine the diffusion coefficient, D, in the gel as... 

Carrier-mediated transport is linear with mucosal solute concentration until this concentration exceeds the number of available carriers. At this point the maximal solute flux (7max) is independent of further increases in mucosal solute concentration. In the linear range of solute flux versus mucosal concentration (C), the proportionality constant is the ratio of / to the solute-carrier affinity constant (Km). This description of Michaelis-Menten kinetics is directly analogous to time changes in mass per unit volume (velocity of concentration change) found in enzyme kinetics, while here the appropriate description is the time change in solute mass per unit surface area of membrane supporting the carrier. 

Piel et al. compared the intravenous pharmacokinetics of miconazole in sheep after its administration in a polyoxyl-35 castor oil/lactic acid mixture, a 100 pM hydroxylpropyl-/l-cyclodextrin-50 pM lactic acid solution, and a 50 pM sulfobutyl ether (SBE7)-/i-cyclodextrin 50 pM lactic acid solution. Intravenous administration of 4 mg/kg of miconazole was completed within 5 min [108]. There were no differences of the miconazole blood plasma concentration versus time for the three dosage forms. The half-life of distribution was <2.4 min. Both hydroxylpropyl-/ -... 

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