Migration Mass balance

Uncharged reaction components are transported by diffusion and convection, even though their migration fluxes are zero. The total flux density Jj of species j is the algebraic (vector) sum of densities of all flux types, and the overall equation for mass balance must be written not as Eq. (4.1) but as... 

It was shown in Section 1.8 that in addition to ion migration, diffusion and convection fluxes are a substantial part of mass transport during current flow through electrolyte solutions, securing a mass balance in the system. In the present chapter these processes are discussed in more detail. 

Note that for the summation the second term is quite small. Because the mass balance for migration out of plastic into a liquid (Eq. 7-47) shows itil.x. = mp.0 ... 

Then calculating the fraction migrated using the mass balance equation ... 

With equations (7-38) and (7-50), taking the mass balance into account, the migrated amount mL.i through the contact surface A during time t can be calculated as follows [if the dimension of cPjo is w/w (mg/g), then cp0 p means w/v (mg/cm3)] ... 

The maximum amount of migration derived from the mass balance is ... 

An important quantity which can be calculated at equilibrium conditions is the amount of substance migrated into the food or food simulant at equilibrium, mF,e. Provided that the migration potential in the polymer, i.e. the initial amount of migrant dissolved in the polymer, mP0, is known then from mass balance calculations the following equation can be derived ... 

Mass balance estimation of worst case styrene migration... 

The simplest estimation of migration is to use the mass balance calculation shown in Eq. (14-1) below. This equation assumes that all of the styrene found in the polymer will migrate into the food instantly. This is of course not realistic but the estimation gives an upper limit to the possible migration that could occur at the end of the product s shelf life. 

It is possible that styrene will never reach the mass balance migration limit specified by Eq. (14-1) in certain foods because of partitioning effects. The systems most likely to have partitioning effects, i.e. when K 1, are those for styrene between aqueous foodstuffs and PS. Migration is usually highest into fats and oils since styrene is readily soluble in both the fats and polymers so that K < 1. 

Interpretation of result The calculated migration values here are realistic since results calculated using Eq. (14-4) cannot be larger than the mass balance result (Example 14-1). The calculated amount of styrene is still above the assumed sensory threshold limit of 0.1 mg/kg in the product for the worst case in step 4 but is equal to the estimation using the experimental diffusion coefficient in step 5. 

Diffusion controlled migration results in step 3 compared to the results in step 4 assuming a mass balance, show that the diffusion of the styrene in the polymer acts to slow down mass transfer into the product. These calculations also show that the relationship in Eq. (14-1) is still valid (mass balance calculations represent the maximum possible amount of migration). 

In this context, to describe the position dependence of the model species, it is important to take in mind that, in electrochemical wastewater-treatment processes, it can be assumed that in the treated wastewater there is always enough supporting electrolyte to minimize the migration of electroactive species. Hence the primary mass-transport mechanisms are diffusion and convection. Hence, the mass balance of a volume element assuming that reactions are restricted to the electrode surface takes the form of (4.2). 

One of the most important migration problems occurs if a liquid food or food simulant F with the volume Vp and density pp comes in contact with a plastic layer P of thickness dp and density pp. The mass transfer takes place across an interface with area A between two different media with different characteristics, e.g., with different diffusion coefficients Dp and Z>p of the migrant. If the value of a quantity is desired, for example, the concentration of the substance transported across the interface in one of the two media, then a mass balance must be considered that takes into account the ratio of the contact surface area and the volume of the corresponding medium. The model describing this process is based on the following assumptions ... 

For migration from P into F the total amount mpo of the migrant is contained in P at time t = 0 and the mass balance is expressed as ... 

Shown in Figure 8.3 is the opposing reactants geometry in which the two reactants enter the membrane from its opposite sides. A reaction plane is formed inside the catalytically active membrane. This implies that the flow front of either reactant is fairly uniform due to the well-engineered microstructure of inorganic membranes. The reactants arrive at the reaction plane in a stoichiometric ratio. Thus undesirable side reactions are reduced. It is noted that as any of the reactant flow rate or concentration changes, the reaction plane will migrate to a new position inside the membrane so that mass balance is maintained. 

Jones, R.W. 1980. Some mass balance and geological constraints on migration mechanisms. Am. Assoc. Pet. Geol. Studies Geol., 10 47-68. 

In this case, the concentration distribution at a given time in a band migrating along the column depends on the position, z, and the distance, r, from the column axis. It does not depend on the azimuthal angle around the column axis. The differential element of the column is a ring of axial thickness dz, limited by the cylinders of radii r and r + dr [60,61], In this element, the mass balance is written... 

King MWG, Barker JF, Devlin JF, et al. 1999. Migration and natural fate of a coal tar creosote plume 2. Mass balance and biodegredation indicators. J Contain Hydrol 39 281-307. 

Here, we use the Bear Creek Uranium example discussed in 6.2 to calculate the acidity of contaminated groundwater and tailings fluids. If the total acidity of groundwater and contaminated sediments, as well as the neutralization capacity of the aquifer matrix are known, the distance that the acid plume will migrate can be estimated based on mass balance. 

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