Definition continuous phase

The subscripts m, L, S, and G will represent the local two-phase mixture, liquid phase, solid phase and gas phase, respectively. The definitions below are given in terms of solid-liquid (S-L) mixtures, where the solid is the more dense distributed phase and the liquid the less dense continuous phase. The same definitions can be applied to gas-liquid (G-L) flows if the subscript S is replaced by L (the more dense phase) and the L by G (the less dense phase). The symbol

volume fraction of the more dense phase, and s is the volume fraction of the less dense phase (obviously (p = 1 — e). An important distinction is made between ([Pg.444]

Alternatively, the dispersed phase is chosen because, by definition, it will not contain droplets of the continuous phase. In this way the dispersed phase, after settling, will not entrain the continuous phase and entrainment losses from the settler will be reduced. 

From the definition of a particle used in this book, it follows that the motion of the surrounding continuous phase is inherently three-dimensional. An important class of particle flows possesses axial symmetry. For axisymmetric flows of incompressible fluids, we define a stream function, ij/, called Stokes s stream function. The value of Imj/ at any point is the volumetric flow rate of fluid crossing any continuous surface whose outer boundary is a circle centered on the axis of symmetry and passing through the point in question. Clearly ij/ = 0 on the axis of symmetry. Stream surfaces are surfaces of constant ij/ and are parallel to the velocity vector, u, at every point. The intersection of a stream surface with a plane containing the axis of symmetry may be referred to as a streamline. The velocity components, and Uq, are related to ij/ in spherical-polar coordinates by... 

A similar definition is frequently used for the continuous phase Sherwood number... 

Careful reading of papers is required to determine which definition has been used. Measurements of the continuous phase resistance around bubbles frequently use photographic, volumetric, or pressure change techniques to yield instantaneous rates of mass transfer, and thus kA. Here too, both definitions of the Sherwood number, Eqs. (7-43) and (7-45), have been used. 

In terms of the analytic solutions for flow around rigid and circulating particles, the effect of containing walls is to change the boundary conditions for the equations of motion and continuity of the continuous phase. In place of the condition of uniform flow remote from the particle, containing walls impose conditions which must be satisfied at definite boundaries. 

Emulsions are colloidal dispersions of liquid droplets in another liquid phase, sometimes stabilized by surface active agents. Emulsions thus consist of a discontinuous phase, dispersed in a continuous phase. The most common types of emulsions are water-in-oil (W/O) in which oil is the continuous phase, and oil-in-water (OAV) in which water forms the continuous phase. However, this traditional definition of an emulsion is too narrow to include most food emulsions. For example, in foods the dispersed phase may be partially solidified, as in dairy products or the continuous phase may contain crystalline material, as in ice cream. It may also be a gel, as in several desserts. In addition to this, air bubbles may have been incorporated to produce the desired texture. 

It is possible to define an evaluation index for the mixing state by using the definition of multi-component mixedness in the previous section. The following discussion focuses on the mixing state of the continuous phase and the dispersed phase with a particle size distribution. 

The distribution of the dispersed particle size is divided into m - 1 groups in the order of size, and each group is considered to be individual component. Additionally, the continuous phase is treated as another component. From this consideration, the mixing can be treated as m-component mixing, and the multi-component mixedness defined by Eq. (2.43) in the previous section can be applied. The extended definition of mixedness for the mixing of the continuous phase and dispersion phase can be expressed as... 

Table 1 summarizes the relation between the hydrophilic-lipophilic balance (HLB) of surfactants and their ability to form concentrated emulsions. Because the continuous phase is that phase in which the surfactant is soluble, it is expected from the definition of HLB [17,18] that surfactants with low HLB values are oil-soluble and can therefore generate w/o concentrated emulsions, while those with high HLB values are water-soluble and can lead to o/w concentrated emulsions. Span 20, whose HLB is 8.6, can generate both w/o and o/w concentrated emulsions. 

Definition and Classification of Emulsions. Colloidal droplets (or particles or bubbles), as they are usually defined, have at least one dimension between about 1 and 1000 nm. Emulsions are a special kind of colloidal dispersion one in which a liquid is dispersed in a continuous liquid phase of different composition. The dispersed phase is sometimes referred to as the internal (disperse) phase, and the continuous phase as the external phase. Emulsions also form a rather special kind of colloidal system in that the droplets often exceed the size limit of 1000 nm. In petroleum emulsions one of the liquids is aqueous, and the other is hydrocarbon and referred to as oil. Two types of emulsion are now readily distinguished in principle, depending upon which kind of liquid forms the continuous phase (Figure 2) ... 

In (3.427) the dispersed phase velocity occurs as an undetermined variable. The phasic velocities are related to the mixture velocity through the mixture velocity definition (3.421). The dispersed phase velocity is computed from the continuous phase velocity Vc and a relative (slip) velocity v fc, in accordance with the definitions ... 

As expected from the definition of the HLB value, materials with high HLB values are O/W emulsifiers and materials with low HLB value are W/O emulsifiers. An HLB value of 3-6 is the recommended range for W/O emulsification 8-18 is recommended for O/W emulsification. Since the requirements for emulsification of a particular ingredient differ markedly, depending on whether the ingredient is the dispersed phase (O/W emulsion)or the continuous phase (W/O emulsion), each ingredient has a different HLB value, depending on which phase of the final emulsion it will become. Thus, paraffinic mineral oil has an HLB value of 11 for emulsification as the dispersed phase in an O/W emulsion and a value of 4 as the continuous phase in a W/O emulsion. 

The official definition (FDA Standard of Identity) describes mayonnaise as a semi-solid food prepared from vegetable oil (no less than 65%), egg yolk and vinegar. Most mayonnaise in the US contains 75-82% oil which is usually soybean oil. Other salad oils that have undergone winterization (including partially hydrogenated soybean oil) can also be used in mayonnaise. The production of mayonnaise is partly an art due to the difficulty of producing the o/w emulsion in which the dispersed phase is seven times more than the continuous phase. Egg solids and processing conditions play critical roles in mayonnaise quality. 

An emulsion polymerization requires the mechanism of polymer particle nudeation to reside outside the monomer droplets. This physical-chemical process involves a series of radical reactions in the continuous phase followed by homogeneous or micellar particle formation. Either of these mechanisms require the initiator to be insoluble in the monomer phase, such as a water soluble initiator and an organically soluble monomer, or vice versa. If, in contrast, the initiator is soluble in the monomer phase, all the components of the reaction are contained in the dispersed phase and the continuous phase serves only to decrease the viscosity and dissipate heat Such polymerizations are categorized as suspensions. The second definition, however, makes no statement as to the magnitude of n and therefore the two criteria are mutually exclusive. 

---