Dispersion of Immiscible Fluids

Mixing involves a reduction of length scales. Let us now consider a typical mixing process as it progresses from large to small scales, as illustrated in 

The problem of following the interface for Newtonian fluids can be described by the Stokes equations, 

In addition, the velocity field is continuous across the interface 

= [VVj + (Vv,)T]/2. The mean curvature of the interface is given by Vs n, where the local normal n is directed from the dispersed phase to the continuous phase and Vs denotes the surface gradient. 

If the length scales associated with changes in velocity are normalized by Vv (characteristic length scale for Stokes flow), length scales associated with changes in curvature are normalized by Ss (typical striation thickness) and velocities normalized by V (a characteristic velocity), then the normal stress condition becomes, 

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Most methods of separating molecules in solution use direct contact of immiscible fluids or a sohd and a fluid. These methods are helped by dispersion of one phase in the other, fluid phase, but they are hindered by the necessity for separating the dispersed phase. Fixed-bed adsorption processes overcome the hindrance by immobilizing the solid adsorbent, but at the cost of cyclic batch operation. Membrane processes trade direct contact for permanent separation of the two phases and offer possibilities for high selectivity. 

Tubular flow reactors (TFR) deviate from the idealized PFR, since the applied pressure drop creates with viscous fluids a laminar shear flow field. As discussed in Section 7.1, shear flow leads to mixing. This is shown schematically in Fig. 11.9(a) and 11.9(b). In the former, we show laminar distributive mixing whereby a thin disk of a miscible reactive component is deformed and distributed (somewhat) over the volume whereas, in the latter we show laminar dispersive mixing whereby a thin disk of immiscible fluid, subsequent to being deformed and stretched, breaks up into droplets. In either case, diffusion mixing is superimposed on convective distributive mixing. Figure 11.9(c) shows schematically the... 

The T-junction, depicted in Fig. 4, is one of the most common geometries used in microfluidic chips to create discrete segments of immiscible fluids. The design of the apparatus is extremely simple - a main, straight channel, that carries the continuous fluid is joined from the side, usually at a right angle, by a channel that supplies the fluid-to-be-dispersed. 

An understanding of the droplet size distribution created during flow mixing of immiscible fluids has long been of importance to the chemical engineering industry. The nature of both the size distribution of dispersed droplets and... 

Droplets distribution of the dispersed phase in size to the formation of fine homogeneous systems in the confiisor-diffuser channels is narrowed by increasing speed of immiscible fluid streams. Increase in volumetric flow velocity co and the number of diffuser confused sections 1 to 4 leads to reduction of the volume-surface diameter of droplets of the dispersed phase and, consequently, to increase in the specific surface of the interface, which in the case of fast chemical reactions intensify flie total process. Inadvisability of using the apparatus with the number of diffuser sections iV confused over 5 1, making these devices simple and inexpensive to manufacture and operate as well as compact, for example, length does not exceed 8-10 caliber (L/d ). 

A surfactant, or surface-active agent, is a molecule that will localize at the interface between two immiscible fluids. This behavior gives rise to a huge diversity of interesting phases when the molecules are combined with different fluids. Surfactants can act to stabilize droplet dispersions of one fluid in another, they can form their own complex phases as a function of concentration in a solvent, and they can even form incredibly thin stable monolayers at a fluid interface. 

The only way significant amounts of immiscible fluids can be mixed together is if the interfacial layer surrounding the dispersed droplets is occupied by an adsorbed layer of molecules that keep the droplets from coalescing. Figure 1.1 shows the importance of the interfacial layer in emulsion systems for the two main classes of surface-active molecules, surfactants and proteins, that stabilize them. Low molecular weight surfactants, lipids, and emulsifiers self-assemble at interfaces with the appropriate part of the molecule associating with the appropriate hydrophilic or hydrophobic phases. Proteins, on the other hand. 

In this chapter, we present an overview of the transport of fluids in microchannels with a focus on the formation and manipulation of emulsion droplets. The next section deals with defining terminology and describing the physics of fluid flow in small channels. We briefly summarize approaches that are used to drive the fluid flow in the microchannels and dispersion of immiscible phases (oil and water) to create well-defined droplets. In the last section, we focus on the applications of droplet-based microfluidics. In particular, we review microparticle formation and biochemical reactions in small droplet reactors. 

Emulsions. Emulsions are formed when one liquid is dispersed as small droplets in another liquid with which the dispersed liquid is immiscible. Mutually immiscible fluids, such as water and oil, can be emulsified by stirring. The suspending liquid is called the continuous phase, and the droplets are called the dispersed (or discontinuous) phase. There are two types of emulsions used in drilling fluids oil-in-water emulsions that have water as the continuous phase and oil as the dispersed phase, and water-in-oil emulsions that have oil as the continuous phase and water as the dispersed phase (invert emulsions). 

Grace, H. P., Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. 3rd Eng. Found. Conf. Mixing, Andover, N. H. Republished in Chem. Eng. Commun. 14, 225-227 (1982). 

H.P. Grace Dispersion Phenomena in High Viscosity Immiscible Fluid Systems and Application of Static Mixers as Dispersion Devices in Such Systems. Chem. Eng. Commun 14, 225 (1982). 

In the extruder, not only shear flow is present, but also extensional flow occurs as well. This is illustrated in Fig. 3.20 for the deformation of a fluid element. Wherever cross-sections narrow, such as at the tips or between kneading blocks and the wall, the fluid elements are compressed and extended. This effect is particularly relevant for non-homogenous polymer melts, e.g., immiscible blends, in which the disperse phase can be split by extensional deformation. For more details, see Chapter 9. 

Figure 8.1. Schematic illustration of dispersion polymerization reactor, (a) two layers of immiscible liquids - monomer and dispersion fluid (e.g. water), and (b) monomer dispersion achieved by agitation (37).

The membrane in a contactor acts as a passive barrier and as a means of bringing two immiscible fluid phases (such as gas and hquid, or an aqueous hquid and an organic hquid, etc.) in contact with each other without dispersion. The phase interface is immobilized at the membrane pore surface, with the pore volume occupied by one of the two fluid phases that are in contact. Since it enables the phases to come in direct contact, the membrane contactor functions as a continuous-contact mass transfer device, such as a packed tower. However, there is no need to physically disperse one phase into the other, or to separate the phases after separation is completed. Several conventional chemical engineering separation processes that are based on mass exchange between phases (e.g., gas absorption, gas stripping, hquid-hquid extraction, etc.) can therefore be carried out in membrane contactors. 

In the second group, the solid-phase concentration is high, and solids particles are either loose but in contact, or consolidated. In this case, the solid phase is the matrix, while the liquid phase is the dispersed phase. In this group, electrical conductivity is used to measure the effective porosity of the porous medium (64, 65). Also, if two immiscible fluids, for example, oil and water, are present in a porous medium, the electrical conductivity can be employed to measure the relative saturations of the two fluids and to give an indication of the wettability of the porous medium (66, 67). 

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