Tubes closed growth

For closed tube-growth, numerous unsolved problems remain requiring further investigation. Quantitative experiments have shown that these tubes essentially conserve the volume of injected solutions within their expanding structures. In addition, semiquantitative models have been proposed by Thouvenel-Romans et al. [42] and Pantaleone et al. [38] to account for specific features of popping and budding tube growth, respectively. However, there are no quantitative models available today that address tube formation based on detailed reaction and transport processes. A major obstacle toward the study of such models relates to the involved free-boundary problems that affect fluid motion, transport, and possibly reaction rates in a nontrivial fashion. 

J Mercier. Recent developments in chemical vapor transport in closed tube. J Cryst Growth 56 235, 1982. 

T Nishinaga, H Ogawa, H Watanabe, T Arizumi. Vapor growth of boron monophosphide using open and closed tube processes. J Cryst Growth 13/14 346, 1972. 

In a tube Im long [49], fundamental frequency is close to 100 Hz, the reduced frequency is less than unity, so Re[Z] 3 and we can take F 0.5. From Equation 5.17, it can be seen that the expected growth rate is... 

This process of filament growth is closely related to the synthesis of single walled carbon nano-tubes. Here the aim is to selectively produce a single layer of carbon in a tube that is as long as possible. Owing to their extreme mechanical strength and interesting electronic behavior these materials have recently attracted substantial interest in materials science. 

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