Range of scales

Chemical engineers of the future will be integrating a wider range of scales than at r other branch of engineering. For example, some may work to relate the macroscale of the environment to the mesoscale of combustion systems and the microscale of molecular reactions and transport (see Chapter 7). Others may work to relate the macroscale performance of a composite aircraft to the mesoscale chemical reactor in which the wing was formed, the design of the reactor perhaps having been influenced by studies of the microscale dynamics of complex liquids (see Chapter 5). 

The detail signals at the various scales of the tree provide the features of the trend that are distinct to the corresponding range of scales. 

Table 6 presents the range of scaling parameters for tests undertaken by different investigators to verify the scaling relationships for a bubbling bed. 

Cerisier et al examined copper electrodeposits over a range of scales from 6 nm to 10 pm [78], They obtained a = 0.33 and j> = 0.46 for deposition on silicon from pyrophosphate solution, and concluded that growth occurs at three dimensional centers with little surface diffusion. 

A second application of current interest in which widely separated length scales come into play is fabrication of modulated foils or wires with layer thickness of a few nanometers or less [156]. In this application, the aspect ratio of layer thickness, which may be of nearly atomic dimensions, to workpiece size, is enormous, and the current distribution must be uniform on the entire range of scales between the two. Optimal conditions for these structures require control by local mechanisms to suppress instability and produce layer by layer growth. Epitaxially deposited single crystals with modulated composition on these scales can be described as superlattices. Moffat, in a report on Cu-Ni superlattices, briefly reviews the constraints operating on their fabrication by electrodeposition [157]. 

The relative simplicity of the gasification system enables its operation to be within the technical expertise of most operators who are experienced with conventional boilers and furnaces, and results in favorable project economics. Its modular design allows a wide range of scale-up or scale-down possibilities, so the systems can vaiy in size from about one ton per hour of residue to 20 tons per hour or larger, with the size being limited only by biomass availability. 

In conclusion, the pedosphere is an environment of active mineral formation and transformation and exhibits a large variation in formation parameters in space and time over a range of scales. It openly and permanently communicates with neigh-... 

In natural systems there are two types of transport phenomena (1) transport by random motion, and (2) transport by directed motion. Both types occur at a wide range of scales from molecular to global distances, from microseconds to geological times. Well-known examples of these types are molecular diffusion (random transport) and advection in water currents (directed transport). There are many other manifestations such as dispersion as a random process (see Chapters 24 and 25) or settling of suspended particles due to gravitation as a directed transport. For simplicity we will subdivide such transport processes into those we will call diffusive for ones caused by random motions and those called advective for ones resulting from directed motions. 

From what has been stated above it is clear that there is a similarity in concepts over a considerable range of scale as between, on the one hand real crystals where the elements are atoms, through ordered phase materials such as copolymers, where the elements are amorphous but in a crystalline lattice, to macro-crystalline materials such as composites. Since a great deal of work has been done in recent years on the properties of composites, in particular fibre composites, it is worth examing the generality of the results obtained particularly in the respect of molecular composites such as semicrystalline polymers and copolymers. 

Following the above approach, the correlative multi-scale CFD reduces the computation cost by transforming information over a range of scales into meso-scale models. With these works, it seems feasible to establish a numerical experiment facility to consider thoroughly the... 

The first challenge lies in how to sufficiently sweep all the possible states of flow structures over the wide range of scales. As discussed... 

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