Knudsen Number Effects on Two-Dimensional Rayleigh-Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method

Effects of Inclined Interface Angle on Compressible Rayleigh-Taylor Instability: A Numerical Study Based on the Discrete Boltzmann Method

Rayleigh-Taylor (RT) instability is a basic fluid interface instability that widely exists in nature and in the engineering field. To investigate the impact of the initial inclined interface on compressible RT instability, the two-component discrete Boltzmann method is employed. Both the thermodynamic non-equilibrium (TNE) and hydrodynamic non-equilibrium (HNE) effects are studied. It can be found that the global average density gradient in the horizontal direction, the non-organized energy fluxes, the global average non-equilibrium intensity and the proportion of the non-equilibrium region first increase and then reduce with time. However, the global average density gradient in the vertical direction and the non-organized moment fluxes first descend, then rise, and finally descend. Furthermore, the global average density gradient, the typical TNE intensity and the proportion of non-equilibrium region increase with increasing angle of the initial inclined interface. Physically, there are three competitive mechanisms: (1) As the perturbed interface elongates, the contact area between the two fluids expands, which results in an increasing gradient of macroscopic physical quantities and leads to a strengthening of the TNE effects. (2) Under the influence of viscosity, the perturbation pressure waves on both sides of the material interface decrease with time, which makes the gradient of the macroscopic physical quantity decrease, resulting in a weakening of the TNE strength. (3) Due to dissipation and/or mutual penetration of the two fluids, the gradient of macroscopic physical quantities gradually diminishes, resulting in a decrease in the intensity of the TNE.

Microfluidic Fabrication of Gadolinium-Doped Hydroxyapatite for Theragnostic Applications

Among the several possible uses of nanoparticulated systems in biomedicine, their potential as theragnostic agents has received significant interest in recent times. In this work, we have taken advantage of the medical applications of Gadolinium as a contrast agent with the versatility and huge array of possibilities that microfluidics can help to create doped Hydroxyapatite nanoparticles with magnetic properties in an efficient and functional way. First, with the help of Computational Fluid Dynamics (CFD), we performed a complete and precise study of all the elements and phases of our device to guarantee that our microfluidic system worked in the laminar regime and was not affected by the presence of nanoparticles through the flow requisite that is essential to guarantee homogeneous diffusion between the elements or phases in play. Then the obtained biomaterials were physiochemically characterized by means of XRD, FE-SEM, EDX, confocal Raman microscopy, and FT-IR, confirming the successful incorporation of the lanthanide element Gadolinium in part of the Ca (II) binding sites. Finally, the magnetic characterization confirmed the paramagnetic behaviour of the nanoparticles, demonstrating that, with a simple and automatized system, it is possible to obtain advanced nanomaterials that can offer a promising and innovative solution in theragnostic applications.

Thermodynamic nonequilibrium effects in bubble coalescence: A discrete Boltzmann study

The thermodynamic nonequilibrium (TNE) effects in a coalescence process of two initially static bubbles under thermal conditions are investigated by a discrete Boltzmann model. The spatial distributions of the typical nonequilibrium quantity, i.e., nonorganized momentum fluxes (NOMFs), during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological and kinetics characteristics of bubble coalescence. The results show that the xx component and yy component of NOMFs are antisymmetrical; the xy component changes from an antisymmetric internal and external double quadrupole structure to an outer octupole structure during the coalescence process. Moreover, the evolution of the averaged xx component of NOMFs provides two characteristic instants, which divide the nonequilibrium process into three stages. The first instant, when the averaged xx component of the NOMFs reaches its first local minimum, corresponds to the moment when the mean coalescence speed gets the maximum, and at this time the ratio of minor and major axes is about 1/2. The second instant, when the averaged xx component of the NOMFs gets its second local maximum, corresponds to the moment when the ratio of minor and major axes becomes 1 for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence, and the slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. The surface tension and the heat conduction accelerate the process of bubble coalescence, while the viscosity delays it. Both the surface tension and the viscosity enhance the global nonequilibrium intensity, whereas the heat conduction restrains it. These TNE features and findings present some insights into the kinetics of bubble coalescence.

Growth mechanism of interfacial fluid-mixing width induced by successive nonlinear wave interactions

Interfacial fluid mixing induced by successive waves, such as shock, rarefaction, and compression waves, plays a fundamental role in engineering applications, e.g., inertial confinement fusion, and in natural phenomena, e.g., supernova explosion. These waves bring nonuniform, unsteady external forces into the mixing zone, which leads to a complex mixing process. The growth rate of the mixing width is analyzed by decomposing the turbulent flow field into the averaged field and the fluctuating counterpart. The growth rate is thus divided into three parts: (i) the stretching or compression (S(C)) effect induced by the averaged-velocity difference between two ends of the mixing zone, (ii) the penetration effect induced by the fluctuations which represent the penetration of the two species into each other, and (iii) the diffusive effect, which is induced by the molecular diffusion and is negligible in high-Reynolds-number flows at Schmidt number of order unity. The penetration effect is further divided into the Richtmyer-Meshkov (RM) effect, which is induced by fluctuations that were deposited by earlier wave interactions, and the Rayleigh-Taylor (RT) effect, which is caused by the fluctuations that arise in an overall acceleration of the mixing zone. During the passage of the rarefaction waves, the mixing zone is stretched, while during the passage of the compression waves or shock waves, the mixing zone is compressed. To illustrate these effects, a physical model of RM mixing with reshock is used. By combining the S(C), RM, and RT effects, the entire evolution of mixing width is restructured, which agrees well with numerical simulations for problems with a wide range of density ratios.

Increase in Axial Compressibility in a Spinning Van der Waals Gas

We investigated the adiabatic compression along the axial direction of a spinning Van der Waals gas by applying theoretical analysis and molecular dynamics (MD) simulations. Based on the analytical results, the rotation-induced compressibility increase effect is significant in a Van der Waals gas, while the attraction term in the Van der Waals equation of states (EOS) contributes significantly to the compressibility increase in a spinning system. We conducted MD simulations to the axial compression of a spinning gas, whose state is far from the ideal gas state, and further demonstrated that the rotation-induced compressibility increase effect in a dense state is robust, implying that such a phenomenon can be detected in experiments under high-energy-density conditions.

Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure.

Lattice-Gas-Automaton Modeling of Income Distribution

A simple and effective lattice-gas-automaton (LGA) economic model is proposed for the income distribution. It consists of four stages: random propagation, economic transaction, income tax, and charity. Two types of discrete models are introduced: two-dimensional four-neighbor model (D2N4) and D2N8. For the former, an agent either remains motionless or travels to one of its four neighboring empty sites randomly. For the latter, the agent may travel to one of its nearest four sites or the four diagonal sites. Afterwards, an economic transaction takes place randomly when two agents are located in the nearest (plus the diagonal) neighboring sites for the D2N4 (D2N8). During the exchange, the Matthew effect could be taken into account in the way that the rich own a higher probability of earning money than the poor. Moreover, two kinds of income tax models are incorporated. One is the detailed taxable income brackets and rates, and the other is a simplified tax model based on a fitting power function. Meanwhile, charity is considered with the assumption that a richer agent donates a part of his income to charity with a certain probability. Finally, the LGA economic model is validated by using two kinds of benchmarks. One is the income distributions of individual agents and two-earner families in a free market. The other is the shares of total income in the USA and UK, respectively. Besides, impacts of the Matthew effect, income tax and charity upon the redistribution of income are investigated. It is confirmed that the model has the potential to offer valuable references for formulating financial laws and regulations.