Viscosity of the Continuous Phase

Viscosity of the Continuous Phase An increase in the viscosity r of the continuous phase reduces the diffusion coefficient D of the droplets, since, for spherical droplets, 

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The emulsification process in principle consists of the break-up of large droplets into smaller ones due to shear forces (10). The simplest form of shear is experienced in lamellar flow, and the droplet break-up may be visualized according to Figure 4. The phenomenon is governed by two forces, ie, the Laplace pressure, which preserves the droplet, and the stress from the velocity gradient, which causes the deformation. The ratio between the two is called the Weber number. We, where Tj is the viscosity of the continuous phase, G the velocity gradient, r the droplet radius, and y the interfacial tension. 

Viscosity Increase. The flocculation rate of an emulsion is iaversely proportional to the viscosity of the continuous phase and an iacrease of the viscosity from 1 mPa-s (=cP) (water at room temperature) to a value of 10 Pa-s (100 P) (waxy Hquid) reduces the flocculation rate by a factor of 10,000. Such a change would give a half-life of an unprotected emulsion of a few hours, which is of Httle practical use. 

Example. The viscosity of the continuous phase liquid is 20. The viscosity of the dispersed phase liquid is 30. The volume fraction of the dispersed phase liquid is 0.3. The nomograph shows the emulsion viscosity to be 36.2. 

The fluid resistance force acting on the droplet should be taken as that given by Stokes law, that is 3ntidu where /< is the viscosity of the continuous phase, velocity relative to the continuous phase. 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

No matter what the situation, the specific gravity difference is a very, very important variable. Aerstin Street (6) have published the simple decanting equation with viscosity of the continuous phase in cp and time in hours ... 

The above discussion dealt with only that particular situation where the continuous phase approximated to an inviscid fluid. However, the equations thus derived can be easily modified to include the effects of viscosity of the of the continuous phase. Under constant pressure conditions also, viscosity of the continuous phase tends to increase the bubble volume by increasing the drag during both the expansion and detachment stages. 

The model of Null and Johnson (N4) neglects the viscosity of the continuous phase which has been found to be effective (K2). 

Vr Final volume of the bubble, drop, cm3 Me Viscosity of the continuous phase, poise centipoise [Eq. 

In Eq. (6.1), Pw is the density of the external water phase, g is the acceleration due to gravity (9.8 m/s ), and rjc is the viscosity of the continuous phase. Then, it becomes possible to determine the internal droplet volume fraction (/>, inside the globules according to the relation ... 

Calderbank and Korchinski (Cl) showed that the correlations described above are limited in applicability to systems in which the viscosity of the continuous phase is lower than 5 cp. Johnson and Braida (Jl) used an additional parameter in the ordinate of Fig. 7 to extend its range to continuous-phase viscosities of 20 cp. The parameter was (/ / Mwater) Data ou systeffis involving field viscosities up to 400 cp. (Wl) showed that the best correlation would be that of Boussinesq, using an experimental value of e. 

It is very important to note that the range of micron sizes indicated in Fig. 2 for which the four laws of settling apply is valid only for spherical particles having the density of water suspended in air at atmospheric temperature and pressure. When any of the following change, the micron size at which the various laws apply will also change (1) density of the particle (2) density of the continuous phase fluid (3) viscosity of the continuous phase fluid and (4) shape of the suspended particle— to a slight extent. 

To understand the mechanism of polyblending, experiments have been carried out with polymeric solution. W. Borchard and G. Rehage mixed two partially miscible polymer solutions, measured the temperature dependence of the viscosity, and determined the critical point of precipitation. When two incompatible polymers, dissolved in a common solvent, are intimately mixed, a polymeric oil-in-oil emulsion is formed. Droplet size of the dispersed phase and its surface chemistry, along with viscosity of the continuous phase, determine the stability of the emulsion. Droplet deformation arising from agitation has been measured on a dispersion of a polyurethane solution with a polyacrylonitrile solution by H. L. Doppert and W. S. Overdiep, who calculated the relationship between viscosity and composition. 

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