We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（...We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.展开更多
Fouling of heat transfer surfaces during subcooled flow boiling is a frequent engineering problem in process industries. It has been generally observed that the deposits in such industrial systems consist mainly of ca...Fouling of heat transfer surfaces during subcooled flow boiling is a frequent engineering problem in process industries. It has been generally observed that the deposits in such industrial systems consist mainly of calcium carbonate （CaCO3）, which has inverse solubility characteristics. This investigation focused on the mechanism to control deposition and the morphology of crystalline deposits. A series of experiments were carried out at different surface and bulk temperatures, fluid velocities and salt ion concentrations. It is shown that the deposition rate is controlled by different mechanism in the range of experimental parameters, depending on salt ion concentration. At higher ion concentration, the fouling rate increases linearly with surface temperature and the effect of flow velocity on deposition rate is quite strong, suggesting that mass diffusion controls the fouling process. On the contrary, at lower ion concentration, the fouling rate increases exponentially with surface temperature and is independent of the velocity, illustrating that surface reaction controls the fouling process. By analysis of the morphology of scale, two types of crystal （calcite and aragonite） are formed. The lower the temperature and ion concentration, the longer the induction period and the higher the percentage of calcite nreciDitated.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos. 10775104 and 10305009
文摘We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.
基金Supported by the Special Funds for Major State Basic Research Projects of China (G2000026304)
文摘Fouling of heat transfer surfaces during subcooled flow boiling is a frequent engineering problem in process industries. It has been generally observed that the deposits in such industrial systems consist mainly of calcium carbonate （CaCO3）, which has inverse solubility characteristics. This investigation focused on the mechanism to control deposition and the morphology of crystalline deposits. A series of experiments were carried out at different surface and bulk temperatures, fluid velocities and salt ion concentrations. It is shown that the deposition rate is controlled by different mechanism in the range of experimental parameters, depending on salt ion concentration. At higher ion concentration, the fouling rate increases linearly with surface temperature and the effect of flow velocity on deposition rate is quite strong, suggesting that mass diffusion controls the fouling process. On the contrary, at lower ion concentration, the fouling rate increases exponentially with surface temperature and is independent of the velocity, illustrating that surface reaction controls the fouling process. By analysis of the morphology of scale, two types of crystal （calcite and aragonite） are formed. The lower the temperature and ion concentration, the longer the induction period and the higher the percentage of calcite nreciDitated.
