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Mass balance condition

The simplest approach considers a perfectly mixed bioturbated layer of thickness L and homogeneous concentration C. If v is the sedimentation rate, the mass balance condition for element i reads... [Pg.408]

Next, the parameter a needs to be found using the mass balance condition. [Pg.382]

The following mass balance condition may be applied to relate and other parameters ... [Pg.392]

If the diffusion of a minor or trace element can be treated as effective binary (not uphill diffusion profiles) with a constant effective binary diffusivity, the concentration profile may be solved as follows. The growth rate u is determined by the major component to be n D ff, and is given, not to be solved. Use i to denote the trace element. Hence, w, and Dt are the concentration and diffusivity of the trace element. Note that Di for trace element i is not necessarily the same as D for the major component. The interface-melt concentration is not fixed by an equilibrium phase diagram, but is to be determined by partitioning and diffusion. Hence, the boundary condition is the mass balance condition. If the boundary condition is written as w x=o = Wifl, the value of Wi must be found using the mass balance condition. In the interface-fixed reference frame, the diffusion problem can be written as... [Pg.409]

The solubility is usually a complicated function of Pg (e.g., Liu et ah, 2005). (5) Mass balance condition at the bubble-melt interface ... [Pg.414]

At the a/p phase boundary, an equivalent mass balance condition in terms of the boundary velocity is... [Pg.267]

Such diagrams of course contain the same information as used in numerical calculations—i.e., equilibrium conditions for the various reactions, and the mass balance conditions. Their advantage is in giving in a single glance a clear picture of the situation. [Pg.52]

The brute force method is the classical approach where mass action expressions are substituted directly into the mass balance conditions and solved for total concentrations which are then compared to the analytical values. In the continued fraction method, the non-linear equations are rearranged to solve for free ion concentrations which are initially assumed to be equal to the total concentrations, as detailed by Wigley (42). These two methods are best illustrated by a simple example. Assume a solution which contains free Ca2+ ions, free CQ ions, and only one ion pair CaCO. The mass balance s conditions are given by... [Pg.862]

Now suppose the system in fact exists as N separate phases, with K = 1,2,.. ., N the phase index let be the number of moles of phase K per mole of the system. The a f s must satisfy the mass balance condition... [Pg.15]

Let X (x) be the mole fraction distribution in phase K. The X s must satisfy the mass balance condition... [Pg.15]

One could still, of course, insist that.J lj ) be a gamma distribution (t>(a,x) and, correspondingly, that X (x) = gamma distribution, but only a linear combination of those. It is the mass balance condition in Eq. (24) that causes the problem (Luks et al, 1990 Sandler and Libby 1991 Shi-hat etal., 1987). [Pg.19]

The flash problem is of course still subject to the mass balance condition in Eq. (35). The bubble point pressure (a = 0) is , and this is relatively easy to calculate because the activity coefficients t(x) are those at the feed composition X Ij ) and they are at worst very weak functions of pressure. The situation is different for the dew point pressure (a = 1), which is 1/. [Pg.19]

The difficulty illustrated above has been discussed by Sandler and Libby (1991), who propose an alternate procedure for the method of moments as applied to a flash calculation. First, one chooses a functional form for one of the two distributions, with which one to choose being suggested by the particular problem one is trying to address. Next, one uses the mass balance condition, Eq. (35), to calculate the functional form for the mole fraction distribution in the other phase. The method of moments (or other solution procedures) can then be used to determine the parameters from the equilibrium condition. Following this procedure, no mass conservation problem arises. [Pg.21]

It is important to realize that any distribution of chemical potentials satisfying Eq. (51) (in the discrete case) or Eq. (60) corresponds to an equilibrium composition. Of course, given an initial value M or M(y), infinitely many of such equilibrium compositions will not satisfy the mass balance condition [Eq. (40) or its equivalent continuous form]. [Pg.25]

Modify Example C.4 to use the array OBS directly, ignoring the mass-balance condition i yiu.adj =" 1- The full set of experimental data is given in the table below ... [Pg.169]

Using this value of k, we may now find the least-squares approximate solution p to equation 7.4 giving the outlet molar contents subject to the mass balance condition in equation 7.3. The solution turns out to be... [Pg.146]

All mass balance conditions must be met (the concentrations of each component or element contained in all species must equal the total concentration of that component in the system). [Pg.522]

A simple attempt to estimate the composition in mixed micelles from surface tension data at the CMC was made by Funasaki and Hada using a mass balance condition [57]. Indeed the composition of micelles and the bulk solution containing two surfactants can be related to the surfaee tension values at the CMC. The material balance for this system takes the form... [Pg.437]

A possible interpretation of the shape of the surface tension isotherm at the CMC was given by Rusanov and Fainerman in the framework of a quasichemical approach to micellisation [62]. The general idea is as follows the total surfactant concentration is related to the concentrations of micelles and monomers by the mass balance condition (5.18) and the mass action law in form of Eq. (5.23). From these conditions, one of two quantities can be expressed as a function of the other. For a single non-ionic surfactant this gives (see also Eq. (5.40))... [Pg.439]

The conditions at the bubble surface are more intricate. Among them is the mass balance condition for component 1 ... [Pg.149]

In order to obtain the integrated form in terms of B, it is necessary to use the mass balance conditions. For a 1 1 stoichiometry, the changes in concentration are related by... [Pg.5]

Application of mass balance conditions to the total moles of G in the gas and liquid phases at any time and at the end of the process, along with the ideal gas law gives... [Pg.392]

The second part on the right is zero due to eq. (10). The first term can be expressed by the mass balance condition eq. (9). This yields eq. (22). [Pg.244]

During the fast process, the only relations between the E and E are the mass balance condition eq. [Pg.244]

Equation (19) under the conditions (23) and (24) has a solution only if Cm = constant, which corresponds to / = K j t, the law of spontaneous imbibition. The following mass-balance condition on the moving meniscus surface will be used in this case ... [Pg.346]

Let us consider first the case of high concentration of the surfactant solution, Co > Cc (curves 3-5). A sharp decrease in the penetration rate at I = Iq (Fig. 18) corresponds to the transition from Cm > Co to Cm < Q, where Cm is the surfactant concentration at the meniscus. The length /q may be estimated from the mass-balance condition on the meniscus surface [18,20,21] ... [Pg.349]

The last two reactions are also required because acid-base equilibria occur. The combination of the charge balance with both mass balance conditions gives the simpler relation (called the proton condition relation)... [Pg.467]


See other pages where Mass balance condition is mentioned: [Pg.196]    [Pg.43]    [Pg.366]    [Pg.428]    [Pg.429]    [Pg.384]    [Pg.167]    [Pg.858]    [Pg.861]    [Pg.422]    [Pg.408]    [Pg.241]    [Pg.248]   
See also in sourсe #XX -- [ Pg.407 , Pg.409 , Pg.419 , Pg.437 ]




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