Macro fluids

For an nth order reaction of a macro fluid. Equation 9-16 is substituted into Equation 9-6 to give... 

The nature of the fluid (i.e., whether a micro or macro fluid) in the system... 

Consider two limiting cases to help explain the effect of segregation on a single reaction Feed streams containing reactants A and B are available, each first as a micro-fluid (free to mix) and then as a macro-fluid (segregation maintained) [15]. Micro-fluids A and B behave in the expected manner and reaction occurs. However, upon mixing of macro-fluids, no reaction takes place because molecules of A cannot contact molecules of B (except at the interface, which has a zero volume in this idealization). These two situations are illustrated in Figure 9.20. 

The above are, of course, only a few possible implications of slip at the wall, which extend far beyond tribology into all aspects of micro- and macro-fluid mechanics. 

Fiber dimensions have been studied for hemodialysis. When blood is circulated through the fiber lumen (m vivo), a significant reduction in apparent blood viscosity may occur if the flow-path diameter is below 100 p.m (11). Therefore, current dialy2ers use fibers with internal diameters of 180—250 p.m to obtain the maximum surface area within a safe range (see Dialysis). The relationship between the fiber cross section and the blood cells is shown in Figure 5. In many industrial appUcations, where the bore fluid is dialy2ed under elevated pressure (>200 kPa or 2 atm), fibers may burst at points of imperfection. Failure of this nature is especially likely for asymmetric fibers that display a large number of macro voids within the walls. 

If fluid shear stresses are likely to be involved in obtaining a process result, then one must qualitatively look at the scale at which the shear stresses influence the resiilt. If the particles, bubbles, droplets, or fluid clumps are on the order of 1000 [Lm or larger, the variables are macro scale and average velocities at a point are the predominant variable. 

The overall superficial fluid velocity, mentioned earlier, should be proportional to the settling velocity o the sohds if that were the main mechanism for solid suspension. If this were the case, the requirement for power if the setthng velocity were doubled should be eight times. Experimentally, it is found that the increase in power is more nearly four times, so that some effect of the shear rate in macro-scale turbulence is effec tive in providing uphft and motion in the system. 

Pilot plant experiments represent an essential step in the investigation of a process toward formulating specifications for a commercial plant. A pilot plant uses the microkinetic data derived by laboratory tests and provides information about the macro kinetics of a process. Examples include the interaction of large conglomerates of molecules, macroscopic fluid elements, the effects of the macroscopic streams of materials and energy on the process, as well as the true residence time in the full-scale plant. 

Lattice gases are micro-level rule-based simulations of macro-level fluid behavior. Lattice-gas models provide a powerful new tool in modeling real fluid behavior ([doolenQO], [doolenQl]). The idea is to reproduce the desired macroscopic behavior of a fluid by modeling the underlying microscopic dynamics. 

The Engineering Effects of Fluids Flow on Freely Suspended Biological Macro-Materials and Macromolecules... 

The Engineering Effects of Fluid Flow on freely Suspended Biological Macro-Materials... 

The convective diffusion equations presented above have been used to model tablet dissolution in flowing fluids and the penetration of targeted macro-molecular drugs into solid tumors [5], In comparison with the nonequilibrium thermodynamics approach described below, the convective diffusion equations have the advantage of theoretical rigor. However, their mathematical complexity dictates a numerical solution in all but the simplest cases. 

Fluid loss additives are used are used to reduce the rate of fluid loss from the fracture to the formation and to naturally occurring macro- and micro-fractures within the formation. Silica flour (73,74), oil-soluble resins (75), diesel oil emulsions (5% by volume) (74) have also been used. 

The principle of a lattice gas is to reproduce macroscopic behavior by modeling the underlying microscopic dynamics. In order to successfully predict the macro-level behavior of a fluid from micro-level rules, three requirements must be satisfied. First, the number of particles must be conserved and, in most cases, so is the particle momentum. States of all the cells in the neighborhood depend on the states of all the others, but neighborhoods do not overlap. This makes application of conservation laws simple because if they apply to one neighborhood they apply to the whole lattice. 

These alternative processes can be divided into two main categories, those that involve insoluble (Chapter 3) or soluble (Chapter 4) supports coupled with continuous flow operation or filtration on the macro - nano scale, and those in which the catalyst is immobilised in a separate phase from the product. These chapters are introduced by a discussion of aqueous biphasic systems (Chapter 5), which have already been commercialised. Other chapters then discuss newer approaches involving fluorous solvents (Chapter 6), ionic liquids (Chapter 7) and supercritical fluids (Chapter 8). 

Bloomfield, V. A., Ma, C. and Arscott, P. C. in K. S. Schmitz (ed.), Macro-Ion Characterization from Dilute Solutions to Complex Fluids, American Chemical Society, Washington DC 1994, pp. 195-209. 

---