Ratio of surface area to volume

An important characteristic of solvents is rate of evaporation. Rates of solvent loss are controUed by the vapor pressure of the solvent(s) and temperature, partial pressure of the solvent over the surface, and thus the air-flow rate over the surface, and the ratio of surface area to volume. Tables of relative evaporation rates, in which -butyl acetate is the standard, are widely used in selecting solvents. These relative rates are deterrnined experimentally by comparing the times required to evaporate 90% of a weighed amount of solvent from filter paper under standard conditions as compared to the time for -butyl acetate. The rates are dependent on the standard conditions selected (6). Most tables of relative evaporation rates are said to be at 25°C. This, however, means that the air temperature was 25°C, not that the temperature of the evaporating solvent was 25°C. As solvents evaporate, temperature drops and the drop in temperature is greatest for solvents that evaporate most rapidly. 

Gas flows are encountered in many microsystems like micro-motors, micro-turbines, micro-sensors, and microfluidic systems in the presence of air or gas environment. Since the ratio of surface area to volume increases in such microsystems, surface forces become dominant over the body forces, and gas flows have great affects on the performance and reliability of many microdevices. 

Because of ESE, and because of the real forces acting on the particles in the surface layer, there is a tendency for spontaneous contraction of the interfacial area. In practice, such a contraction can be realized only in the case of liquid phases, where the particles can move freely relative to each other. Hence, liquids tend to assume spherical shape with a minimum ratio of surface area to volume (liquid drops), at least when the volume is small and gravitation does not interfere, and when they are not in contact with solid surfaces. 

A packed bed is composed of crushed rock with a density of 175 lbm/ft3 of such a size and shape that the average ratio of surface area to volume for the particles is 50 in.2/in.3. The bed is 6 ft deep, has a porosity of 0.3, and is covered by a 2 ft deep layer of water that drains by gravity through the bed. Calculate the flow rate of water through the bed in gpm/ft2, assuming it exits at 1 atm pressure. 

The transfer hydrogenation methods described above are sufficient to carry out laboratory-scale studies, but it is unlikely that a direct scale-up of these processes would result in identical yields and selectivities. This is because the reaction mixtures are biphasic liquid, gas. The gas which is distilled off is acetone from the IPA system, and carbon dioxide from the TEAF system. The rate of gas disengagement is related to the superficial surface area. As the process is scaled-up, or the height of the liquid increases, the ratio of surface area to volume decreases. In order to improve de-gassing, parameters such as stirring rates, reactor design and temperature are important, and these will be discussed along with other factors found important in process scale-up. 

Because of the slow permeation of water, a method is standardised in BS 903 Part 18 [18] for rubbers, in which the material is cut into small particles by cutting, rasping or grinding. This results in a large ratio of surface area to volume and a relatively short time to equilibrium. The same approach could be applied to plastics. 

The principal iron oxides used in catalysis of industrial reactions are magnetite and hematite. Both are semiconductors and can catalyse oxidation/reduction reactions. Owing to their amphoteric properties, they can also be used as acid/base catalysts. The catalysts are used as finely divided powders or as porous solids with a high ratio of surface area to volume. Such catalysts must be durable with a life expectancy of some years. To achieve these requirements, the iron oxide is most frequently dis-... 

The fibrous bed must be closely packed and possess a high ratio of surface area to volume (Tl, V2). 

Nanoparticles have an exceptionally high ratio of surface area to volume—unlike bulky forms of matter, most of the material in nanoparticles is exposed rather than hidden inside the interior. This feature of nanoparticles can drastically alter the material s properties, which is another example of the changes that occur at the small end of the scale. Gold, for instance, is usually not very chemically active in its bulk form, yet gold nanoparticles are quite reactive. An example of this phenomenon will be described in the following section. 

If the velocities of deposition are averaged over all the surfaces, and S (m 1) is the ratio of surface area to volume in a room, the rate constants for removal by deposition are... 

To create explants, dormant Jerusalem artichoke tubers are typically cut into 25-mm-thick slices, from which cylinders of tissue are fashioned. Cylindrical shapes are favored because they can be uniformly reproduced and have a high ratio of surface area to volume that optimizes gas and nutrient exchange, and facilitates callus formation. A small size is desirable to maximize the number of explants obtained from the same tissue source. Jerusalem artichoke tuber explant size is typically around 2.4 by 2.0 mm. The minimum size is usually 8 mg and approximately 20,000 cells (Yeoman, 1973), although some reports have used smaller explant sizes (e.g., Caplin, 1963). 

CZE is high voltage, free-solution electrophoresis carried out in a capillary. The capillary is filled with the running electrolyte (a buffer solution), and the ionic analytes are separated on the basis of the differences in their electrophoretic mobilities. The favorable ratio of surface area to volume allows the dissipation of the Joule heat from the capillary and the application of high electric fields with rapid and efficient separations. Also, the anticonvective characteristic of the capillary limits the process of zone diffusion, maintaining the efficiency of separation without the need of further anticonvective media such as gels. 

BaP. The importance of reaction losses in film for only BaP (and other low-volatility, high molecular weight PAHs) was ascribed to its tendency to partition into condensed phases (e.g. soil, PM, film), an order of magnitude greater ratio of surface area to volume of films on impervious surfaces (10 ) versus surface films on PM (10 ), and least important, the faster reaction rate in film versus PM. 

Since the ratio of surface area to volume is large, viscous heating is an important factor in microchannels. It is especially important for laminar flow, where considerable gradients exist. The Brinkman number, Br, indicates this effect. A decrease in Nu for Br > 0 and an increase for Br < 0 have been observed. This is due to the fact that for different cases, Br may increase or decrease the driving mechanism for convective heat transfer, which is the difference between the wall temperature and the average fluid temperature. 

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