Droplet volume density distribution

Figure 13.9 gives an example of droplet volume density distributions of emulsions obtained by pressing an emulsion premix through a membrane at transmembrane pressure differences varying from 3 bar to 11 bar. These pressure differences are 7.5- to 27.5-fold the minimum pressure difference required (capillary pressure). A hydrophilic polyamide membrane with a mean pore size of 0.8 pm was used. The emulsion premix consisted of 20% dispersed phase (vegetable oil). As continuous phase water containing emulsifier Tween 80 at a concentration of 2% was used. The Sauter diameter of the emulsion premix was X3,2 = 25 pm. 

Droplet size distributions are, as are all particle size distributions, either represented as volume density distributions 3(dp) or as cumulative volume distributions Qi (dp) ... 

Influence of Repeated Processing Repeated processing results in smaller droplets and narrower droplet size distributions of the fine emulsions. Figure 13.10 depicts an example of the volume density distributions of an emulsion with a dispersed phase of 30% after the first, second and third pass at 9 bar through a membrane with a mean pore size of 0.8 pm. In this case, at least two passes through the membrane are required in order to obtain a monomodal droplet size distribution. 

Influence of Emulsifier Concentration Emulsions of small droplet sizes and narrow droplet size distributions can be obtained at high emulsifier concentration. Figure 13.12 shows the volume density distributions of emulsions of a disperse phase fraction of cp = 72% and two different emulsifier (Tween 80) concentrations, 2.4% and 4.6%. The production parameters were trans-membrane pressure difference of 12 bar, three passes and membrane mean pore size of 0.8 pm. In both cases the emulsifier concentration is above the critical micelle concentration (CMC). 

Equations (12.40) to (12.45) describe the velocities u, v, w, the temperature distribution T, the concentration distribution c (mass of gas per unit ma.ss of mixture, particles per volume, droplet number density, etc.) and pressure distribution p. These variables can also be used for the calculation of air volume flow, convective air movement, and contaminant transport. 

The characteristics of a spray depend on the atomization process. The state of each spray element is characterized by its statistical quantities such as droplet number density and radial distribution function, which generally vary both spatially and temporally. We may consider that each spray element (corresponding to the physically infinitesimal volume when the spray is described in the framework of continuum theory) consists of statistically uniformly distributed identical droplets with number density o and droplet radius aq in a gas of uniform state (density pQ, oxygen concentration 7o,o, and temperature Tq in particular) at an initial time. We assume that the evaporation before atomization is negligible. Then, we have the following expression... 

The molecular weight and density of the solvent influence the volume of the evaporated sample and hence the pressure wave. Solvent volatility nay Influence the distribution of sample between the vapor and droplet phases. The same sample amount dissolved in different solvents may produce different peak areas. 

A multicomponent gas flow contains a uniform distribution of small droplets of an organic solvent called A. The droplets have a diameter d and a number density Q [m-3]. The solvent evaporation rate m"k (kg/s-m2) depends on the gas-phase concentration of A. It may be assumed that the volume occupied by the droplets is negligible. 

When two liquids are immiscible, the design parameters include droplet size distribution of the disperse phase, coalescence rate, power consumption for complete dispersion, and the mass-transfer coefficient at the liquid-liquid interface. The Sauter mean diameter, dsy, of the dispersed phase depends on the Reynolds, Froudes and Weber numbers, the ratios of density and viscosity of the dispersed and continuous phases, and the volume fraction of the dispersed phase. The most important parameters are the Weber number and the volume fraction of the dispersed phase. Specifically, dsy oc We 06(l + hip ), where b is a constant that depends on the stirrer and vessel geometry and the physical properties of the system. Both dsy and the interfacial area aL remain unaltered, if the same power per unit volume (P/V) is used in the scale-up. 

The final step in the analysis is to obtain the combustion efficiency for a chamber of length x from the size distribution at position x. Let Qj denote the heat released per unit mass of material evaporated from a droplet of kind j, and let Pi j represent the density of the liquid in droplets of kind j. The mass of the spray of kind j per unit volume of space is therefore lo corresponding mass flow rate (mass per second) is... 

The population balance equation is employed to describe the temporal and steady-state behavior of the droplet size distribution for physically equilibrated liquid-liquid dispersions undergoing breakage and/or coalescence. These analyses also permit evaluation of the various proposed coalescence and breakage functions described in Sections III,B and C. When the dispersion is spatially homogeneous it becomes convenient to describe particle interaction on a total number basis as opposed to number concentration. To be consistent with the notation employed by previous investigators, the number concentration is replaced as n i,t)d i = NA( i t)dXi, where N is the total number of particles per unit volume of the dispersion, and A(xj t) dXi is the fraction of drops in increment X, to X( + dxi- For spatially homogeneous dispersions such as in a well-mixed vessel, continuous flow of dispersions, no density changes, and isothermal conditions Eq. (102) becomes... 

The separation ofa formulation decreases with increase in E, as will be discussed in Chapter 21. The value of E required to stop complete separation depends on the particle or droplet size distribution, the density difference between the particle or droplet and the medium, as well as on the volume fraction of the dispersion. 

The droplet average size (DS) and droplet size distribution (DSD) of the macroemulsion so obtained depend on the volume fraction of the dispersed phase, the geometry of the vessel and impeller, stirring speed, as well as on physical properties of the continuous and dispersed phases, such as density and viscosity, and on interfacial properties [34-39]. 

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