Droplet coalescence kinetics: thermodynamic non-equilibrium effects and entropy production mechanism

The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescence are studied in detail via the discrete Boltzmann method. The temporal evolutions of the total TNE strength ($D^*$) and the total entropy production rate ($\dot S$) can both provide concise, effective and consistent physical criteria to distinguish the stages of droplet coalescence. Specifically, when $\bar D^*$ and $\dot S$ reach their maxima, it corresponds to the time when the liquid-vapor interface length changes the fastest; when $D^*$ and $\dot S$ reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. During the merging process, the force contributed by surface tension in the coalescence direction acts as the primary promoting force for droplet coalescence and reaches its maximum concurrently with coalescent acceleration. In contrast, the force contributed by non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as $D^*$. For the coalescence of two unequal size droplets, the smaller droplet exhibits larger values for TNE intensity, merging velocity, driving force contributed by surface tension, and resistance contributed by NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet, are all smaller than those in the larger droplet and gradually decrease with the radius ratio

Thermodynamic non-equilibrium effects in bubble coalescence: A discrete Boltzmann study

The Thermodynamic Non-Equilibrium (TNE) effects in the coalescing process of two initially static bubbles under thermal conditions are investigated by a Discrete Boltzmann Model (DBM). The spatial distributions of the typical none-quilibrium quantity, i.e., the Non-Organized Momentum Fluxes (NOMF) during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological or kinetics characteristics of bubble coalescence. It is found that the $xx$-component and $yy$-component of NOMF are anti-symmetrical; the $xy$-component changes from an anti-symmetric internal and external double quadrupole structure to an outer octupole structure during the coalescing process. More importantly, the evolution of the averaged $xx$-component of NOMF provides two characteristic instants, which divide the non-equilibrium process into three stages. The first instant corresponds to the moment when the mean coalescing speed gets the maximum and at this time the ratio of minor and major axes is about $1/2$. The second instant corresponds to the moment when the ratio of minor and major axes gets $1$ for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence and negative slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. Surface tension and heat conduction accelerate the process of bubble coalescence while viscosity delays it. Both surface tension and viscosity enhance the global non-equilibrium intensity, whereas heat conduction restrains it. These TNE features and findings present some new insights into the kinetics of bubble coalescence

Finite Difference and Sinc-Collocation Approximations to a Class of Fractional Diffusion-Wave Equations

We propose an efficient numerical method for a class of fractional diffusion-wave equations with the Caputo fractional derivative of order α. This approach is based on the finite difference in time and the global sinc collocation in space. By utilizing the collocation technique and some properties of the sinc functions, the problem is reduced to the solution of a system of linear algebraic equations at each time step. Stability and convergence of the proposed method are rigorously analyzed. The numerical solution is of 3-α order accuracy in time and exponential rate of convergence in space. Numerical experiments demonstrate the validity of the obtained method and support the obtained theoretical results

Effect of saline stress on the physiology and growth of maize hybrids and their related inbred lines

Salinity is one major abiotic stress that restrict plant growth and crop productivity. In maize (Zea mays L), salt stress causes significant yield loss each year. However, indices of maize response to salt stress are not completely explored and a desired method for maize salt tolerance evaluation is still not established. A Chinese leading maize variety Jingke968 showed various resistance to environmental factors, including salt stress. To compare its salt tolerance to other superior maize varieties, we examined the physiological and growth responses of three important maize hybrids and their related inbred lines under the control and salt stress conditions. By compar- ing the physiological parameters under control and salt treatment, we demonstrated that different salt tolerance mechanisms may be involved in different genotypes, such as the elevation of superoxide dismutase activity and/ or proline content. With Principal Component Analysis of all the growth indicators in both germination and seedling stages, along with the germination rate, superoxide dismutase activity, proline content, malondialdehyde content, relative electrolyte leakage, we were able to show that salt resistance levels of hybrids and their related inbred lines were Jingke968 > Zhengdan958 > X1132 and X1132M > Jing724 > Chang7-2 > Zheng58 > X1132F, respectively, which was consistent with the saline field observation. Our results not only contribute to a better understanding of salt stress response in three important hybrids and their related inbred lines, but also this evaluation system might be applied for an accurate assessment of salt resistance in other germplasms and breeding material