The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function are needed to capture the main feature of the flow state and the evolution process. Based on the ellipsoidal statistical Bhatnagar–Gross–Krook model, Discrete Boltzmann Models (DBMs) that consider various orders of TNE effects are developed to study flows in various depths of TNE. In numerical tests, DBMs including the first up to the sixth order TNE effects are demonstrated. Specifically, at first, the model's capability to capture large flow structures with zeroth-order TNE effects in two types of one-dimensional Riemann problems is demonstrated. The ability to capture large flow structures with first-order TNE effects is also shown in the Couette flow. Then, a shock wave structure given by Direct simulation Monte Carlo is used to verify the model's capability to capture fine structures at the level of the mean free path of gas molecules. Furthermore, we focus on the TNE degree of two colliding fluids mainly decided by two parameters: the relaxation time τ and relative speeds $\Delta \mathbf{u}$ of two fluids. Consequently, three numerical tests for flows with various depths of TNE are constructed. Due to any definition of the TNE strength is dependent on the perspective of investigation, we propose to use a N-component vector ${\mathbf{S}}_{\mathit{TNE}}$ to describe the TNE system from N perspectives. As specific applications, we use a three-component vector ${\mathbf{S}}_{\mathit{TNE}}=(\tau ,\Delta \mathbf{u},{\mathbf{\Delta }}_2^{*})$ to roughly characterize three cases for numerical tests in this work. Then, we check the system TNE behavior from the perspective of the xx component of the TNE quantity, viscous stress ${\mathbf{\Delta }}_2^{*}$ . It is found that, for the first two cases, at least up to the second-order TNE effects, i.e., the second-order terms in Knudsen number in the CE expansion, should be included in the model construction, while for the third case, at least up to the third-order TNE effects should be included. Similar to ${\mathbf{\Delta }}_2^{*}$ , three numerical tests for flows in various depths of ${\mathbf{\Delta }}_{3,1}^{*}$ are constructed. It is found that from the perspective of ${\Delta }_{3,1,x}^{*}$ , for case 1 and case 3, at least up to the second-order TNE effects should be required, while for case 2, the first-order TNE effects are enough. These findings demonstrate that the inadequacy of focusing only on the few kinetic moments appearing in Navier–Stokes increases with the degree of discreteness and deviation from thermodynamic equilibrium. Finally, a two-dimensional free jet is simulated to indicate that, to obtain satisfying hydrodynamic quantities, the DBM should include at least up to the third-order TNE effects. This study is meaningful for the understanding of the TNE behavior of complex fluid systems and the choice of an appropriate fluid model to handle desired TNE effects.

The two-dimensional Rayleigh-Taylor instability (RTI) in compressible flow with intermolecular interactions is probed via the discrete Boltzmann method. The effects of interfacial tension, viscosity, and heat conduction are investigated. It is found that the influences of interfacial tension on the perturbation amplitude, bubble velocity, and two kinds of entropy production rates all show differences at different stages of RTI evolution. It inhibits the RTI evolution at the bubble acceleration stage, while at the asymptotic velocity stage, it first promotes and then inhibits the RTI evolution. Viscosity and heat conduction inhibit the RTI evolution. Viscosity shows a suppressive effect on the entropy generation rate related to heat flow at the early stage but a first promotive and then suppressive effect on the entropy generation rate related to heat flow at a later stage. Heat conduction shows a promotive effect on the entropy generation rate related to heat flow at an early stage. Still, it offers a first promotive and then suppressive effect on the entropy generation rate related to heat flow at a later stage. By introducing the morphological boundary length, we find that the stage of exponential growth of the interface length with time corresponds to the bubble acceleration stage. The first maximum point of the interface length change rate and the first maximum point of the change rate of the entropy generation rate related to viscous stress can be used as a criterion for RTI to enter the asymptotic velocity stage.

Microfluidic chips have shown their potential for applications in fields such as chemistry and biology, and 3D printing is increasingly utilized as the fabrication method for microfluidic chips. To address key issues such as the long printing time for conventional 3D printing of a single chip and the demand for rapid response in individualized microfluidic chip customization, we have optimized the use of DLP (digital light processing) technology, which offers faster printing speeds due to its surface exposure method. In this study, we specifically focused on developing a fast-manufacturing process for directly printing microfluidic chips, addressing the high cost of traditional microfabrication processes and the lengthy production times associated with other 3D printing methods for microfluidic chips. Based on the designed three-dimensional chip model, we utilized a DLP-based printer to directly print two-dimensional and three-dimensional microfluidic chips with photosensitive resin. To overcome the challenge of clogging in printing microchannels, we proposed a printing method that combined an open-channel design with transparent adhesive tape sealing. This method enables the rapid printing of microfluidic chips with complex and intricate microstructures. This research provides a crucial foundation for the development of microfluidic chips in biomedical research.

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.

A two-fluid discrete Boltzmann model with a flexible Prandtl number is formulated to study the shock–bubble interaction (SBI). This paper mainly focuses on the viscous effects on morphological and thermodynamic non-equilibrium (TNE) characterizations during the SBI process. Due to the rapid and brief nature of the SBI process, viscosity has a relatively limited influence on macroscopic parameters but significantly affects the TNE features of the fluid system. Morphologically, viscosity affects the configuration of the vortex pair, increases both the amplitudes of gradients of average density and average temperature of the fluid field, and reduces circulation of the bubble. As a higher viscosity fluid absorbs more energy from the shock wave, it leads to an increase in both the proportion of the high-density region and the corresponding boundary length for a fixed density threshold. The spatiotemporal features of TNE quantities are analyzed from multiple perspectives. The spatial configuration of these TNE quantities exhibits interesting symmetry, which aids in understanding the way and extent to which fluid unit deviates from the equilibrium state. Theoretically, viscosity influences these TNE quantities by affecting the transport coefficients and gradients of macroscopic quantity. Meanwhile, the viscosity increases the entropy production rate originating from the non-organized momentum flux mainly through amplifying the transport coefficient and enhances the entropy production rate contributed by the non-organized energy flux by raising the temperature gradient. These multi-perspective results collectively provide a relatively comprehensive depiction of the SBI.

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.