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The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\\boldsymbol{F}_L = {\\rm \\pi}\\rho a^3 (\\boldsymbol{\\varOmega} \\times \\boldsymbol{v}) \\bar{h}_L$, where $\\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\\boldsymbol {\\varOmega }$ is its angular velocity, $\\boldsymbol {v}$ is its velocity and $\\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

Contact angle is a physical quantity used to evaluate the interaction between a solid surface and a liquid. However, many research laboratories or educational institutions with budget constraints have limited access to a commercial contact-angle goniometer with a high-resolution imaging system. In this study, we fabricated a custom-made contact angle goniometer with a smartphone and quantified the contact angles of water on various surfaces. We found that the receding contact angles on the surfaces were sensitive to the change in flow rates. The receding angle sharply decreases when the flow rate exceeds 50 µl/min, indicating that accurate flow control is required in contact angle measurements. The dynamic contact angles could also be quantified by the developed goniometer in an extremely low-capillary number regime. The dynamic advancing and receding contact angles on tested surfaces followed the molecular-kinetic theory.

Kinetic theory and modeling have been proven extremely suitable in computing the flow rates in rarefied gas pipe flows, but they are computationally expensive and more importantly not practical in design and optimization of micro- and vacuum systems. In an effort to reduce the computational cost and improve accessibility when dealing with such systems, two efficient methods are employed by leveraging machine learning (ML). More specifically, random forest regression (RFR) and symbolic regression (SR) have been adopted, suggesting a framework capable of extracting numerical predictions and analytical equations, respectively, exclusively derived from data. The database of the reduced flow rates W used in the current ML framework has been obtained using kinetic modeling and it refers to nonlinear flows through circular tubes (tube length over radius l∈[0,5] and downstream over upstream pressure p∈[0,0.9]) in a very wide range of the gas rarefaction parameter δ∈[0,103]. The accuracy of both RFR and SR models is assessed using statistical metrics, as well as the relative error between the ML predictions and the kinetic database. The predictions obtained by RFR show very good fit on the simulation data, having a maximum absolute relative error of less than 12.5%. Various expressions of the form of W=W(p,l,δ) with different accuracy and complexity are acquired from SR. The proposed equation, valid in the whole range of the relevant parameters, exhibits a maximum absolute relative error less than 17%. To further improve the accuracy, the dataset is divided into three subsets in terms of δ and one SR-based closed-form expression of each subset is proposed, achieving a maximum absolute relative error smaller than 9%. Very good performance of all proposed equations is observed, as indicated by the obtained accuracy measures. Overall, the present ML-predicted data may be very useful in gaseous microfluidics and vacuum technology for engineering purposes.

A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characterize a self-organized structure as a thermal equilibrium on a leaf of foliated phase space. By introducing a model of a grand canonical ensemble, the Casimir invariant is interpreted as the number of topological particles.

The general kinetic theory of coarse-grained systems is presented in the abstract formalism of communication theory developed by Shannon and Weaver, Khinchin and Kolmogorov. The martingale theory shows that, under reasonable, general hypotheses, coarse-grained systems can be approximated by generalized Markov systems. For mixing systems, the Kolmogorov entropy production can be defined for nonstationary processes as Kolmogorov defined it for stationary processes.