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External flows
Published in Zhigang Li, Nanofluidics, 2018
In the free molecular regime, e.g., a small particle in a rarefied gas, the thermophoretic force is mainly the consequence of a large number of molecular collisions between gas molecules and the particle. At the high temperature side of the particle, gas molecules carry relatively high kinetic energies and the gas–particle collision frequency is higher than that at the low temperature side. These usually lead to a strong momentum transfer between gas molecules and the particle at the high temperature side and consequently the thermophoretic force causes the particle to move from high to low temperature. However, the gas density at the high temperature side is lower than that at the low temperature side, which tends to reduce the momentum transfer. Therefore, under certain situations, the thermophoretic force can drive the particle to travel from low to high temperature area, which is referred to as negative thermophoresis. For nanoparticles, as discussed in Section 7.2, molecular interactions are important and the thermophoretic force and velocity also depend on the molecular nature of the gas and particle.
Chemical Reaction Optimization
Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017
The most important part of the reaction mechanism is the energy requirements, where energy is consumed for a reaction to happen. The actual course that any reaction should follow is the one that requires least activation energy. The minimum amount of energy required for a chemical reaction to occur is known as the activation energy denoted as Ea, discussed in the earlier section. For a reaction to occur, molecules must collide. The collision frequency describes how many times a particular molecule collides with others per unit of time. Collision theory is an aspect of kinetic molecular theory and was proposed by Max Trautz (1916), which explains how chemical reactions occur and why reaction rates differ for different reactions. In order for molecules to react, a physical chemist named Svante Arrhenius explained in 1889 (Arrhenius, 1889) that colliding molecules must possess enough kinetic energy. Energetic collisions are collisions between molecules with enough kinetic energy to cause the reaction to occur. Not all collisions are energetic collisions because they do not provide the necessary amount of Ea, so not all collisions lead to reactions and product formation. The higher the Ea of a reaction, the smaller is the amount of energetic collisions present, and the slower is the reaction. In contrast, the lower the Ea of a reaction, the greater is the amount of energetic collisions present, and the faster is the reaction. The molecular orientation of the energetic collision has to be right to generate the activated complex in the transition state that leads to the product.
Chemical Kinetics of Combustion
Published in Kenneth M. Bryden, Kenneth W. Ragland, Song-Charng Kong, Combustion Engineering, 2022
Kenneth M. Bryden, Kenneth W. Ragland, Song-Charng Kong
To further understand the nature of these reactions, it is necessary to examine the quantum mechanical processes that give rise to them. Put simply, in each case, the rate of reaction is proportional to the collision frequency. The collision frequency is in turn proportional to the product of the reactant concentrations. Only a small fraction of the molecular collisions results in a reaction. Those collisions that are energetic enough and in which the molecular orientation is favorable break a chemical bond. More information about molecular collision theory may be gained by studying the kinetic theory of gases.
Preparation of diamond on GaN using microwave plasma chemical vapor deposition with double-substrate structure
Published in Functional Diamond, 2023
Yurui Wang, Deng Gao, Tong Zhang, Hao Zhang, Yu Zhang, Qiuming Fu, Hongyang Zhao, Zhibin Ma
Figure 1 shows the Schematic diagram of different cavity structures. Unlike the traditional single-substrate structure, the upper and lower cavity of the double-substrate structure is symmetrical, and the plasma state can be regulated by adjusting the short-circuiting plunger. In our previous study [27], it has been found that the double-substrate cavity structure can aggregate the plasma at medium and high pressure (10 ∼ 25 kPa). By adopting the double-substrate structure, the radical concentration of Hα, Hβ, C2 and CH can be significantly increased, which is more beneficial for diamond deposition. However, compared with single-substrate structure, the electron temperature of the plasma generated by double-substrate structure is much lower. This is mainly because the average free path of the particles is smaller under high pressure. Meanwhile, the plasma is more concentrated in the double-substrate structure. So the particle motion is more intense, resulting in higher collision frequency. The collisions between electrons and other particles become more frequent, leading to the loss of electron energy and the decrease of electron temperature.
Numerical investigation of diesel spray flame structures under diesel engine-relevant conditions using large eddy simulation
Published in Combustion Science and Technology, 2018
Haiqiao Wei, Wanhui Zhao, Lei Zhou, Gequn Shu
Figure 15 compares the predicted and measured ID and LOL for different ambient densities with various oxygen concentrations. It can be seen that at higher ambient densities, the reactivity of the mixing is enhanced. The IDs and LOLs are shorter than the cases with initial density of 14.8 kg/m3. Even the low oxygen concentration case still has a shorter ID. For example, the measured ID for the case with an initial oxygen concentration of 10% and ambient density 30.0 kg/m3 is shorter than 0.62 ms. The ID for14.8 kg/m3 ambient density case with the same oxygen concentration is nearly twice as long as the 30.0 kg/m3 ambient density case. At the same time, the LOL drops significantly by increasing the ambient density from 14.8 to 30.0 kg/m3. The collision frequency increases leading to the increase of the reaction rates. With high levels of EGR, the calculated ID is underprediction. Because the combustion temperature at low oxygen concentration is so low that both the computed and measured results may get large errors in ID (Zhou et al., 2015b). Figure 16 presents the lifted flame structures and OH distributions for 30.0 kg/m3 ambient density under 10% and 15% oxygen concentration conditions. For the cases with initial densities of 30.0 kg/m3, the combustion temperature in the whole combustion domain is relatively lower than the high oxygen concentration case. At the same time, the LOL is shorter for the cases with initial ambient densities of 30.0 kg/m3 compared to the cases shown in Figure 8 (a) with the same oxygen concentration.
Effective temperature scaled dynamics of a flexible polymer in an active bath
Published in Molecular Physics, 2020
Xiuli Cao, Bingjie Zhang, Nanrong Zhao
The local exponent is presented in Figure 6(b). Evidently, this parameter monotonously increases with , which provides an evidence that increasing of active particle size can induce a strengthened degree of superdiffusivity of the chain's CM motion. In addition, it is obvious that as is larger, the probed chain enters into the normal diffusion regime at longer times. These non-trivial size effects we observed can be attributed to the key factor of the particle size-dependent characteristic rotational time scale . As already mentioned, . Namely, the rotational time scale grows cubically as a function of . That is to say, for larger , the bath active particle takes longer average time before the direction of particle motion is randomised. As a consequence, the probed chain equivalently experiences stronger collisions with the active particles, and therefore is subject to a more pronounced superdiffusive behaviour. Besides, Figure 6(b) shows a remarkable enhancement of transition time from superdiffusion to normal diffusion with an increase in active particle size. Such size effect on transition time closely relates to the modulated effective collision between bath particles and the probed polymer. As becomes larger, the particle number density decreases, resulting in lower collision frequency in the system. The momentum relaxation of the chain is then retarded, and thus the chain will inevitably undergo diffusion process with longer transition time.