Mixing of Two Miscible Fluids

Thus an element of water 1 micron in size would lose its identity in a very short time, approximately 

In general, then, ordinary fluids behave as microfluids except for very viscous materials and for systems in which very fast reactions are taking place. 

The concept of micro- and macrofluids is of particular importance in heterogeneous systems because one of the two phases of such systems usually approximates a macrofluid. For example, the solid phase of fluid-solid systems can be treated exactly as a macrofluid because each particle of solid is a distinct aggregate of molecules. For such systems, then, Eq. 2 with the appropriate kinetic expression is the starting point for design. 

In the chapters to follow we apply these concepts of micro- and macrofluids to heterogeneous systems of various kinds. 

To help understand what occurs, imagine that we have A and B available, each first as a microfluid, and then as a macrofluid. In one beaker mix micro A with micro B, and in another beaker mix macro A with macro B and let them react. What do we find Micro A and B behave in the expected manner, and reaction occurs. However, on mixing the macrofluids no reaction takes place because molecules of A cannot contact molecules of B. These two situations are illustrated in Fig. 16.4. So much for the treatment of the two extremes in behavior. 

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Figure 16.5 Partial segregation in the mixing of two miscible fluids in a reactor.

Microscopic mixing mixing of individual molecules, like homogenization of two miscible fluids, or dissolution of a solid in a liquid without the formation of any concentration (temperature) gradients. 

MIXING OF TWO MISCIBLE HIGHLY VISCOUS FLUIDS, 479 CONCLUSION, 481 NOTATION, 483 REFERENCES, 484... 

Mixing between two miscible fluids can be broken down into the following steps, where the length scales given are for turbulent mixing of liquids (high Sc) ... 

A few words of explanation are not useless in order to understand this formalism. As a consequence of mixing, the medium is assumed to have a lamellar structure and n is a unit vector which remains normal to the material slices undergoing deformations in the velocity field, n n denotes a dyadic product (the dyadic product of vectors a and b is the tensor a.jbj) and 13 n n denotes the scalar product of the two tensors (the scalar product of tensors i = Tij and W = is the scalar quantity T W = E Z T j wji)- Assume that we start with two miscible fluids A J and B (having for instance different colors). Upon mixing, we obtain a lamellar marbled structure characterized by a striation thickness 6 and a specific "interfacial" area av. If the fluid is incompressible, avS = 1. Then,by application of (7-1)... 

Mixing of two or more miscible fluids in microfluidic systems is important in a variety of applications, e. g., to achieve a homogenized solution of the reagents used in chemical... 

Many of the mixing simulations described in the previous section deal with the modeling of mass transfer between miscible fluids [33, 70-77]. These are the simulations which require a solution of the convection-difliision equation for the concentration fields. For the most part, the transport of a dilute species with a typical diSusion coeflEcient 10 m s between two miscible fluids with equal physical properties is simulated. It has already been mentioned that due to the discretization of the convection-diffusion equation and the typically small diffusion coefficients for liquids, these simulations are prone to numerical diffiision, which may result in an over-prediction of mass transfer efficiency. Using a lattice Boltzmann method, however, Sullivan et al. [77] successfully simulated not only the diffusion of a passive tracer but also that of an active tracer, whereby two miscible fluids of different viscosities are mixed. In particular, they used a coupled hydrodynamic/mass transfer model, which enabled the effects of the tracer concentration on the local viscosity to be taken into account. 

The operation consisting of mixing two miscible fluids of high viscosity remains difficult with two-blade impellers. Correlations obtained from experimental data to estimate the time necessary to get a good homogeneity cannot be found in the literature. 

Miscible Mixable. Describes full mixing of two fluids without dissolution of one into the other. Soluble = dissolves in, miscible = mixes into. The converse, immiscible, refers to a lack of mixing ability, as seen in the case of oil and water. 

A turbine type agitator is commonly used for liquid-solid systems. Mixing rates depend on the forces required to suspend all solid particles. Minimum levels can be determined for (1) lifting the particles, and (2) for suspending them in an homogeneous manner [200]. Similar requirements apply to liquid-liquid systems. For cases where two poorly miscible fluids of about equal volume are used in the reaction, the mixer is placed at the interface. For a bench-scale experimental system of about 2 liters capacity, the minimum rotational speed to obtain well-dispersed system is 300 to 400 rpm [201], depending on the type of mixer. This rotational value decreases as the vessel volume increases. 

FIGURE 5.3 Mixing of miscible fluid elements caused by density differences. 1 = two... 

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