Media well-stirred

The dissolution rate of a solid may be defined as dm/dt, where m is the mass of solid dissolved at time t. In a batch dissolution method, the analyzed concentration, cb, in the solution (if well stirred) is representative of the entire volume, V, of the dissolution medium, so that... 

It should be emphasized that Eq. (22) is already based on a number of preconditions. In particular, the intracellular medium may significantly deviate from a well-stirred ideal solution [141 143], While the use of Eq. (22) is often justified, several authors have suggested to allow noninteger exponents in the expression of elementary rate equations [96,142,144] corresponding to a more general form of mass-action kinetics. A related concept, the power-law formalism, developed by M. Savageau and others [145 147], is addressed in Section VII.C. 

The general principle of two-phase catalysis in polar solvents, for example, in water, is shown in the simplified diagram of Fig. 1. The metal complex catalyst, which can be solubilized by hydrophilic ligands, converts the reactants A + B into the product C. The product is more soluble in the second than in the first phase and can be separated from the catalyst medium by simple phase separation. Excellent mixing and contacting of the two phases are necessary for efficient catalytic reaction, and thus the reactor is normally well stirred. 

The net reaction is A I B -> E I F. This reaction scheme has been developed by the Brussels School of Thermodynamics, and consists of a trimolecular collision and an autocatalytic step. This reaction may take place in a well-stirred medium leading to oscillations, or the diffusions of the components A and B may be considered. In the latter case, the system may produce Turing structures. 

In heat-transferring properties, the fluidized bed is equivalent to a well-stirred liquid the interstitial gas serves as a stirring agent and as a heat-transfer medium between adjacent particles and between particles and wall (164). 

The aforesaid situations apply in special cases where diffusion through the material in chamber A is not important (A is well stirred) and where the dissolution rate of the drug particles in A is rapid. A more common situation arises when drug release is both a function of its concentration within a vehicle and its ability to diffusion through it. When placed into a release medium, the drug closest to the surface is released the fastest. Over a period of time, the drug must diffuse from further and further back within the bulk of the device, which progressively slows the release. Systems such as this can be described by solutions to Ficks s second law of diffusion (1). 

In these studies spheroids are exposed to the culture medium at a known drug concentration. If the culture medium is well stirred (in the case of suspension culture), the spheroids are exposed to a symmetric environment. If the culture medium is still and the spheroids rest on some surface, they are exposed to an asymmetric environment, resulting in an asymmetric concentration profile. The methods to measure concentration profiles include microelectrodes (which can be inserted into a spheroid up to various desired radial positions), autoradiography, and fractional disaggregation of various spheroid layers to measure cellular concentration in each layer. Each method has its own advantages and limitations. 

The reduction of thymol or menthone was conducted in a well-stirred autoclave as described in [4]. The catalyst (0.15-0.50 g) suspended in cyclohexane was activated by stirring the mixture for two hours at the temperature of the reaction under 3MPa H2 pressure. Then 0.05 mol of thymol or menthone was Introduced under H2 pressure and the reaction was started by stirring under 3 MPa H2. Gas chromatographic analyses of samples of the reaction medium, withdrawn at regular time intervals were performed on a Durabond Wax (J W) capillary column. 

In the case of short diffusion times (i.e., only near surface penetration), it can be useful to approximate a mineral with a planar boundary as a semi-infinite medium. For the case of diffusion from a well-stirred semi-infinite reservoir at concentration Co into a half space initially at zero concentration, the concentration distribution is given by... 

In a batch dissolution method the analyzed concentration c of a well-stirred solution is representative of the entire volume V of the dissolution medium, so that... 

At this point in our discussion of well-stirred continuous-flow bioreactors it is helpful to consider a straightforward extension of our analysis to encompass the possibility of using more than a single feed stream. Illustration 13.5 considers a situation in which a supplementary feed stream is suppUed to the second CSTBR. This illustration lets us address situations in which it is desirable to include additional components (e.g., inducers) in the growth medium to enhance the selectivity of the cascade for the production of desired product species. Induction enhances the production of secondary metabolites becanse of the presence of particular chemical species in the growth medium. 

Operation of various types of bioreactors in a perfusion mode (21, 22) enables the design engineer to combine several advantages of traditional modes of operation of well-stirred bioreactors (e.g., semibatch operation in a fed batch mode or use of recycle with a chemostat). Perfusion consists of operation in a mode in which a fresh growth medium (possibly together with a recycled growth medium) is fed to a bioreactor containing viable cells that are retained within the bioreactor by permselective membranes, microfllters, immobilization, or by partial separation and recovery from the reactor effluent followed by recycle to the entrance of the reactor. 

Assuming the fluid medium surrounding the catalyst particle is very well stirred, the boundary conditions are... 

Fig. 1.4 a Emergence of chemical waves in unstirred medium [48], b and c The temporal oscillations with respect to optical density, and change in potential in well-stirred BZ reaction medium (Adopted fiom Ref. [1])... 

The MA in BZ reaction has an important drawback which is producing carbon dioxide gas bubbles in the oscillating reaction process. Some attempts have been made to develop gas-free versions of the BZ reactions. The diketonic compound such as cyclohexanedione (CHD) is a well-set example in which the gas-free oscUlations and formation of spatial patterns have been examined. The acetyl acetone (AA) and ethyl acetoacetate (EAA) can also bear an analogue diketonic property. The potential oscillations in these two compounds have been reported in well-stirred medium. Though, the characteristics of an oscillating reaction in stirred reaction may differ from the unstirred reaction medium. Thus, two diketonic compounds, namely AA and EAA, are selected to extend the study of patterns formation and oscillatory behaviors in unstirred BZ conditions. 

Fluoro-3-nitroaniline (4.38 g, 0.028 mole) dissolved in 30 ml of concentrated HCl and 5 ml of water at 45° is filtered and then chilled to —20° in a Dry Ice-acetone bath. Sodium nitrite (2.4 g, 0.034 mole) in 5 ml of water is added slowly to the well stirred acid medium while the flask temperature is kept at —15° to —20°. The reaction mixture after a 10-min stirring is filtered into a flask at —20°. To this filtrate, sodium azide (2.2 g, 0.032 mole) dissolved in 8 ml of water is added drop-wise while the reaction mixture is stirred and kept in the dark at —15°... 

To a well-stirred slurry of a-K9[AlWn039] (5.43 g, 1.80 mmol) in 10 mL of H2O in a 50-mL beaker, vanadyl sulfate trihydrate (V0S04-3H20, 0.39 g, 1.80 mmol), dissolved in 5 mL of H2O, is added dropwise rapidly at room temperature. The color changes immediately to dark purple. The mixture is stirred for 30 min and filtered on a medium-porosity glass frit, then the dark purple filtrate is cooled to 5°C for 2 h. The resulting dark purple crystals are collected on a coarse fritted funnel and recrystallized from a minimum of warm (60 C) H2O. Recrystallized yield 3.5 g (61%). 

Is this dependence valid for other systems In the first place, permeation into cells is ordinarily considered to take place from a relatively large volume of well-stirred medium, so that Co remains essentially constant. Therefore the co/2 of the equation above becomes co. Any deviation from these conditions merits special treatment. 

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