In this series of talks, I will discuss the fluid-dynamic-type equations that is derived from the Boltzmann equation as its the asymptotic behavior for small mean free path. The study of the relation of the two systems describing the behavior of a gas, the fluid-dynamic system and the Boltzmann system, has a long history and many works have been done. The Hilbert expansion and the Chapman–Enskog expansion are well-known among them. The behavior of a gas in the continuum limit, however, is not so simple as is widely discussed by superficial understanding of these solutions. The correct behavior has to be investigated by classifying the physical situations. The results are largely different depending on the situations. There is an important class of problems for which neither the Euler equations nor the Navier–Stokes give the correct answer. In these two expansions themselves, an initialor boundaryvalue problem is not taken into account. We will discuss the fluid-dynamic-type equations together with the boundary conditions that describe the behavior of the gas in the continuum limit by appropriately classifying the physical situations and taking the boundary condition into account. Here the result for the time-independent case is summarized. The time-dependent case will also be mentioned in the talk. The velocity distribution function approaches a Maxwellian fe, whose parameters depend on the position in the gas, in the continuum limit. The fluid-dynamictype equations that determine the macroscopic variables in the limit differ considerably depending on the character of the Maxwellian. The systems are classified by the size of |fe− fe0|/fe0, where fe0 is the stationary Maxwellian with the representative density and temperature in the gas. (1) |fe − fe0|/fe0 = O(Kn) (Kn : Knudsen number, i.e., Kn = `/L; ` : the reference mean free path. L : the reference length of the system) : S system (the incompressible Navier–Stokes set with the energy equation modified). (1a) |fe − fe0|/fe0 = o(Kn) : Linear system (the Stokes set). (2) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(Kn) (ξi : the molecular velocity) : SB system [the temperature T and density ρ in the continuum limit are determined together with the flow velocity vi of the first order of Kn amplified by 1/Kn (the ghost effect), and the thermal stress of the order of (Kn) must be retained in the equations (non-Navier–Stokes effect). The thermal creep[1] in the boundary condition must be taken into account. (3) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(1) : E+VB system (the Euler and viscous boundary-layer sets). E system (Euler set) in the case where the boundary is an interface of the gas and its condensed phase. The fluid-dynamic systems are classified in terms of the macroscopic parameters that appear in the boundary condition. Let Tw and δTw be, respectively, the characteristic values of the temperature and its variation of the boundary. Then, the fluid-dynamic systems mentioned above are classified with the nondimensional temperature variation δTw/Tw and Reynolds number Re as shown in Fig. 1. In the region SB, the classical gas dynamics is inapplicable, that is, neither the Euler

Kinetic Theory and Fluid Dynamics

THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

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The Kinetic Theory of Gases

Electrode processing plays an important role in advancing lithium-ion battery technologies and has a significant impact on cell energy density, manufacturing cost, and throughput. Compared to the extensive research on materials development, however, there has been much less effort in this area. In this Review, we outline each step in the electrode processing of lithium-ion batteries from materials to cell assembly, summarize the recent progress in individual steps, deconvolute the interplays between those steps, discuss the underlying constraints, and share some prospective technologies. This Review aims to provide an overview of the whole process in lithium-ion battery fabrication from powder to cell formation and bridge the gap between academic development and industrial manufacturing.

From Materials to Cell: State-of-the-Art and Prospective Technologies for Lithium-Ion Battery Electrode Processing.

Conventional techniques of extracting oil using organic solvents pose health, safety, and environmental concerns. In modern extraction methods, green solvents such as water, ethanol, ethyl acetate, carbon dioxide, ionic liquids, and terpenes are currently gaining prominence. These green solvents present no signs of pollution and remain in liquid form over a temperature range of 0 to 140 °C. Other techniques covered in this review include microwave-assisted enzymatic extraction, ultrasound-assisted extraction, supercritical fluid technology, high pressure-assisted extraction, and pulse electric field-assisted extraction. These techniques are considered environmentally friendly because they exhibit less hazardous chemical synthesis, use renewable feedstock, and reduce the chemical load and emissions generated by organic solvents. Aqueous enzymatic extraction is a novel technique that uses enzymes as the medium for extraction of oil. Selection of the enzymes solely depends on the structure of the oilseed and the composition of the cell wall. Studies reveal an enzyme to substrate ratio of 1% to 8%, the temperature of 40 to 55 °C, and a pH of 4 to 8 to be typical for enzymatic extraction of oil from different oilseeds. Microwave-assisted extraction has proven to impart significant effects on mass transfer and offers high throughput and extraction efficiency. A microwave power of 275 to 1,000 W and a temperature range of 30 to 60 °C are noticed in the different studies. The review presents a comprehensive account of the modern extraction techniques, the parameters responsible for yield and quality, and their industrial applications. Besides, the review highlights the optimized parameters for oil extraction from different oil-bearing materials.

Novel oil extraction technologies: Process conditions, quality parameters, and optimization.

Advanced electrode processing of lithium ion batteries: A review of powder technology in battery fabrication

Aiming at improving the food quality during microwave process, this article mainly focused on the numerical simulation of shape effect, which was evaluated by microwave power absorption capability and temperature distribution uniformity in a single sample heated in a domestic microwave oven. This article only took the electromagnetic field and heat conduction in solid into consideration. The Maxwell equations were used to calculate the distribution of microwave electromagnetic field distribution in the microwave cavity and samples; then the electromagnetic energy was coupled as the heat source in the heat conduction process in samples. Quantitatively, the power absorption capability and temperature distribution uniformity were, respectively, described by power absorption efficiency (PAE) and the statistical variation of coefficient (COV). In addition, we defined the comprehensive evaluation coefficient (CEC) to describe the usability of a specific sample. In accordance with volume or the wave numbers and penetration numbers in the radial and axial directions of samples, they can be classified into different groups. And according to the PAE, COV, and CEC value and the specific need of microwave process, an optimal sample shape and orientation could be decided.

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Shape Effect on the Temperature Field during Microwave Heating Process

The Knudsen pump (KP) is a kind of micro-pump that can form thermally induced flows induced by temperature fields in rarefied gas environments. It has the advantages of having no moving parts, simple structure, easy construction and extension, a wide range of energy sources, and low energy consumption. With the development of Micro/Nano Electro Mechanical Systems (MEMS/NEMS), extensive studies have been conducted on KPs, and the applications of KPs have widened. In order to obtain efficient flow fields in KPs, it is necessary to adopt modern computational methods for simulation and analysis. In many circumstances, the simulation and experimental results have good agreement. However, there seems to be no comprehensive review on KPs at present. In this paper, KPs are first defined and classified according to the flow mechanisms of the thermally induced flows. Then, the three aspects of configurations, performance, and applications of KPs in the current state of research are reviewed and analyzed. Finally, the current problems of KP are discussed, and some suggestions are provided for future research and applications. Knudsen pumps are micro-sized, non-mechanical gas pumps that can be useful in a range of biomedical and mechanical fields. Zhang and his team from China’s North-eastern University analyzed Knudsen pumps’ configurations, performance, applications, and current problems. In Knudsen pumps, gas flow is induced by temperature gradients along the walls of the device. They benefit from low energy consumption and ease of manufacture. Different configurations, realized through the placement of variably heated walls, offer multiple mechanisms to transport rarefied gases. Knudsen pumps can be used, amongst other applications, to generate a vacuum, deliver fluids, and separate gases. Micro-channels play a key role in Knudsen pump efficiency and gas flow operation; however, there is a lack of research into efficiency which the authors say should be addressed in future research.

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Knudsen pumps: a review

Sensitivity analysis of intermittent microwave convective drying based on multiphase porous media models

Numerical simulation of thermal edge flow in ratchet-like periodically patterned micro-channels

A Knudsen pump operates under the thermal transpiration effect or the thermal edge effect on the micro-scale. Due to the uneven temperature distribution of the walls in the channel axis direction or the constant temperature of the tips on the walls, directional thermally-induced flow is generated. In this paper the Direct Simulation Monte Carlo (DSMC) method is applied for N2–O2 gas mixtures in the ratios of 4:1, 1:1, and 1:4 with different Knudsen numbers in a classic rectangular Knudsen pump to study the flow characteristics of the gas mixtures in the pump. The results show that the changing in the gas physical properties does not affect the distribution of the velocity field, temperature fields, or other fields in the Knudsen pump. The thermal creep effect is related to the molecular mass of the gas. Even in N2 and O2 gas mixtures with similar molecular masses, N2 can be also found to have a stronger thermal creep effect. Moreover, the lighter molecular weight gas (N2) can effectively promote the motion of the heavier gas (O2).

Shiwei Zhang

Papers

Shape Effect on the Temperature Field during Microwave Heating Process

Knudsen pumps: a review

Sensitivity analysis of intermittent microwave convective drying based on multiphase porous media models

Numerical simulation of thermal edge flow in ratchet-like periodically patterned micro-channels

Study of Flow Characteristics of Gas Mixtures in a Rectangular Knudsen Pump.