Surface area minimization

As a result of surface area minimization, a surface will assume the smoothest shape it can. Since any curvature in the surface shape results in greater area, a higher energy will also result. Consequently the surface will push back against any curvature in much the same way as a ball pushed uphill will roll back to minimize its gravitational potential energy. 

Catalyst particles are usually cylindrical in shape because it is convenient and economical to fonii tliem by extmsion—like spaghetti. Otlier shapes may be dictated by tlie need to minimize tlie resistance to transport of reactants and products in tlie pores tlius, tlie goal may be to have a high ratio of external (peripheral) surface area to particle volume and to minimize the average distance from tlie outside surface to tlie particle centre, witliout having particles tliat are so small tliat tlie pressure drop of reactants flowing tlirough tlie reactor will be excessive. 

The available surface area of the catalyst gready affects the rate of a hydrogenation reaction. The surface area is dependent on both the amount of catalyst used and the surface characteristics of the catalyst. Generally, a large surface area is desired to minimize the amount of catalyst needed. This can be accomphshed by using either a catalyst with a small particle size or one with a porous surface. Catalysts with a small particle size, however, can be difficult to recover from the material being reduced. Therefore, larger particle size catalyst with a porous surface is often preferred. A common example of such a catalyst is Raney nickel. 

Maintenance of isothermal conditions requires special care. Temperature differences should be minimised and heat-transfer coefficients and surface areas maximized. Electric heaters, steam jackets, or molten salt baths are often used for such purposes. Separate heating or cooling circuits and controls are used with inlet and oudet lines to minimize end effects. Pressure or thermal transients can result in longer Hved transients in the individual catalyst pellets, because concentration and temperature gradients within catalyst pores adjust slowly. 

Types of air strippers include packed towers, tray towers, and spray towers. Packed towers are packed or filled with small forms made of polyethylene [9002-88-4] stainless steel, poly(vinyl chloride) (PVC) [9002-86-2] or ceramic that provide large surface area to volume ratios which increase transfer rates into the air stream. Packed towers operate in countercurrent mode, that is, the aqueous stream enters at the top of the tower while air is blown in from the bottom. An example of this type of unit is shown in Figure 1. Channeling or short circuiting of the aqueous stream is minimized by... 

Color Concentrates. Color concentrates have become the method of choice to incorporate colorants into resins. Color concentrates have high ratios of colorant to a compatible vehicle. The colorant may be added at 70% colorant to 30% vehicle in a titanium dioxide mixture whereas the ratio may be 15% colorant to 85% vehicle in a carbon black mixture. The amount of colorant that can be added is dependent on the surface area and the oil absorption of the colorant and the wetting abiHty of the vehicle. The normal goal is to get as much colorant in the concentrate as possible to obtain the greatest money value for the product. Furthermore, less added vehicle minimizes the effect on the physical or chemical properties of the resin system. 

Nucleation is initiated by secondary mechanisms involving the seed crystals or low super-saturation and high surface area of seed crystals eliminate or minimize nucleation seed crystals grow... 

Large surface area-to-volume ratio to minimize heat leak. 

Example 4 Calculation of Sample Weight for Surface Moisture Content An example is given with reference to material with minimal internal or pore-retained moisture such as mineral concentrates wherein physically adhering moisture is the sole consideration. With this simphfication, a moisture coefficient K is employed as miiltipher of nominal top-size particle size d taken to the third power to account for surface area. Adapting fundamental sampling theory to moisture sampling, variance is of a minimum sample quantity is expressed as... 

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