Mass balance emulsion phase

Dense emulsion-phase monomer mass-balances Here the mass-balance equation is... 

Heat and mass transfer constitute fundamentally important transport properties for design of a fluidized catalyst bed. Intense mixing of emulsion phase with a large heat capacity results in uniform temperature at a level determined by the balance between the rates of heat generation from reaction and heat removal through wall heat transfer, and by the heat capacity of feed gas. However, thermal stability of the dilute phase depends also on the heat-diffusive power of the phase (Section IX). The mechanism by which a reactant gas is transferred from the bubble phase to the emulsion phase is part of the basic information needed to formulate the design equation for the bed (Sections VII-IX). These properties are closely related to the flow behavior of the bed (Sections II-V) and to the bubble dynamics. 

For the particular case of an irreversible gas solid catalyzed reaction with no accompanying volume change, the mass (mole) balance for a species A in the interstitial gas phase moving through the emulsion phase is frequently simplified assuming axially constant transport parameters (i.e. and kbe) [141, 142, 58] ... 

Species mass balances were developed for the two phases and solved ana-l3dically for first order reactions. Thus, for the case of a completely mixed emulsion phase the concentration of a reactant leaving this phase is given by ... 

In order to develop a continuous separation process, Kataoka et al. [54] simulated permeation of metal ion in continuous countercurrent column. They developed the material balance equation considering back mixing only in the continuous phase and steady-state diffusion in the dispersed emulsion drops which is similar to the Hquid extraction situation. Bart et al. [55] also modeled the extraction of copper in a continuous countercurrent column. They considered only the continuous phase back mixing in the model and assumed that the reaction between copper ions and carrier is slow, so that the differential mass balance equation for external phase in their model is... 

Values for the propagation rate constant can be determined from bulk or solution experiments. Values of k have been published for a wide variety of monomers as a function of temperature. With standard emulsion polymerization recipes the value of [M]p is determined from equilibrium swelling measurements if a free monomer phase is present and by a mass balance if all the monomer is in the polymer particles. One normally assumes that [M] is not dependent on particle size in latexes comprised of different-sized particles. This assumption will be questionable in some systems, especially those involving high-swelling particles. 

The exterior phase was analyzed for phenylalanine concentration and pH. All sample volumes were recorded and used for mass balance determination. Phenylalanine was measured spectrophotometrically at lmax = 257.5 nm. Changes in interior phase volume were calculated using material balances. All material balances closed to within 2%. Interior phase concentrations were estimated by the use of material balances and exterior phase concentrations. The interior phase components of several representative emulsions were measured by analyzing the interior phase components after thermally demulsifying the emulsion samples. These measurements agreed with estimates to within 10%. 

The mass balance of the representative diagram in Figure 22.7 for the gas and emulsion phase, considering continuous and isothermal system, are described below ... 

From the experimental results, the gas exchange rate from bubble-to-emulsion phase can be estimated by analyzing the tracer concentration inside the bubble and solving the mass balance equation for the tracer gas, which eventually yields for a bubble with initial volume Fb.i and with concentration Cco2,i at minimum fluidization conditions (Dang et al (2013)) ... 

Assuming complete mixing in the emulsion phase with respect to gas and solid particles, the mass balance for species A in the emulsion phase can be written as... 

The mass balance equation for species A in the emulsion phase remains essentially the same as Eq. (16). Grace (1986b) further simplified the model by assuming that no net gas flows through the emulsion phase, i.e., /(j = 0. Under this assumption, Eqs. (16) and (19) can be solved analytically for simple reaction kinetics. Elfects of fine particle solids concentration in the bubble phase on the reactor conversion can also be examined analytically. 

In Equation 5.231, the indexes b, c, and e refer to the bubble, cloud, and emulsion phases, respectively. The mass balance for component i is valid in the bubble phase... 

Prediction of the instantaneous chemical composition as well as the rate of polymerisation during an emulsion copolymerisation of monomers 1 and 2 asks for the concentrations of the reacting monomers in the particle phase. Monomers 1 and 2 are only sparsely or moderately water soluble. The amounts of the monomers 1 and 2 in the droplet phase, the water phase and the particle phase are related by mass balances for the monomers. Equation 4.8 gives the mass balance for monomer 1 ... 

Vl stands for the molar volume of pure monomer 1. Note that molar volume changes of the monomers due to mixing with monomer 2 and/or the polymer have been neglected on going from Equations 4.9 to 4.10. For the mass balance of monomer 2 over the three phases analogous equations as 4.8-4.10 can be derived. Note that in the absence of monomer droplets, for example. Interval III for a batch emulsion polymerisation process. Equation 4.10 reduces to Equation 4.11 ... 

Kunii and Levenspiel proposed the following procedure describing the exchange between the gas bubble, the surrounding cloud, and the emulsion. Consider the transfer of species A from the bubble phase through the cloud surrounding the bubble to the emulsion phase, as shown in Fig. 7.35. Denoting the concentration of the transferred species in the bubble, cloud, and emulsion by Ca,b, a,c> a,e respectively, an overall mass balance may... 

Heat transfer between the gas bubbles and the emulsion phase may be calculated in a somewhat similar manner. However, in the establishment of a heat balance about the bubble we shall assume that the rate of transfer between the cloud surrounding the bubble and the emulsion is fast enough so that this process does not contribute a resistance. However, in contrast to the formulation of the mass transfer problem, here too we have to take into consideration the heat capacity of the solids contained in the bubbles. 

Frankenfeld et al. (85) reported a similar study on the recovery of copper with ELM technology. The ELM used had a typical hydrocarbon phase formulation of 2.0 mass % nonionic polyamine surfactant, 2.5 beta hydroxyoxlme carrier, and the balance isoparaffinio hydrocarbon solvent. The internal aqueous phase of the emulsion was approximately 20 mass % HaSO. Using a basis of a 2.7 x 10 liquid membrane plant would save 40 t in capital costs with nearly identical operating costs. 

Chain transfer agents. Emulsion polymerisation may result in an unpractically high molecular mass polymer. To reduce the molar mass, CTAs, usually mercaptans, are frequently used. The mercaptan is introduced into the reactor together with the monomer phase. The consmnption of the mercaptan taking place in the loci should be properly kept in balance with monomer consumption. 

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