Microscopic Material Balance

FIGURE 4.2 Differential volume element for the microscopic material balance. 

In typical polymer membrane-gas systems, the term l/(l - coa) is approximately equal to 1, so that Eq. 4.16 is further simplified. However, in polymer membrane-solvent systems, coa can be significant, and it cannot be neglected in Eq.4.16.  

Microscopic material balance is based on the conservation of mass. The law of conservation of mass for material A flowing in and out of a differential volume element dx dy dz (Fig. 4.2) in its rate form states that 

This mass balance is similar to Eqs. 2.15 and 5.15, which contain the momenrnm and energy balances, respectively. 

The rate of generation and consumption (net rate of mass production) of material A in Eq. 4.17 refers to chemical reactions, and it will be denoted as 7a (dimensions mass/volume-time). If we consider that the volume element 

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No chemical reactions occur within the control volume, therefore there is no generation. Material balances can be either microscopic or macroscopic. Which to use is primarily... 

Microchemical or ultramicrochemical techniques are used extensively ia chemical studies of actinide elements (16). If extremely small volumes are used, microgram or lesser quantities of material can give relatively high concentrations in solution. Balances of sufficient sensitivity have been developed for quantitative measurements with these minute quantities of material. Since the amounts of material involved are too small to be seen with the unaided eye, the actual chemical work is usually done on the mechanical stage of a microscope, where all of the essential apparatus is in view. Compounds prepared on such a small scale are often identified by x-ray crystallographic methods. 

Macroscopic and Microscopic Balances Three postulates, regarded as laws of physics, are fundamental in fluid mechanics. These are conservation of mass, conservation of momentum, and con-servation of energy. In addition, two other postulates, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use. The conservation principles may be applied either to material systems or to control volumes in space. Most often, control volumes are used. The control volumes may be either of finite or differential size, resulting in either algebraic or differential consei vation equations, respectively. These are often called macroscopic and microscopic balance equations. 

The living microbial, animal, or plant cell can be viewed as a chemical plant of microscopic size. It can extract raw materials from its environment and use them to replicate itself as well as to synthesize myriad valuable products that can be stored in the cell or excreted. This microscopic chemical plant contains its own power station, which operates with admirably high efficiency. It also contains its own sophisticated control system, which maintains appropriate balances of mass and energy finxes through the links of its internal reaction network. 

One of the most promising applications of enzyme-immobilized mesoporous materials is as microscopic reactors. Galameau et al. investigated the effect of mesoporous silica structures and their surface natures on the activity of immobilized lipases [199]. Too hydrophilic (pure silica) or too hydrophobic (butyl-grafted silica) supports are not appropriate for the development of high activity for lipases. An adequate hydrophobic/hydrophilic balance of the support, such as a supported-micelle, provides the best route to enhance lipase activity. They also encapsulated the lipases in sponge mesoporous silicates, a new procedure based on the addition of a mixture of lecithin and amines to a sol-gel synthesis to provide pore-size control. 

The microscopic approach looks at heterogeneous properties of the tissue and has been developed for plant material on the basis of plant physiology studies on the effect of osmosis on water balance and transport in growing plants. 

At present analytical solutions of the equations describing the microscopic aspects of material transport in turbulent flow are not available. Nearly all the equations representing component balances are nonlinear in character even after many simplifications as to the form of the equation of state and the effect of the momentum transport upon the eddy diffusivity are made. For this reason it is not to be expected that, except by assumption of the Reynolds analogy or some simple consequence of this relationship, it will be possible to obtain analytical expressions to describe the spatial variation in concentration of a component under conditions of nonuniform material transport. 

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