Tetsuro Tsuji

Moving boundary problems for a rarefied gas: Spatially one-dimensional case

Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hookes law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method.

Decay of an oscillating plate in a free‐molecular gas

An infinite plate without thickness is placed in a free‐molecular gas, and an external force, obeying Hooke’s law, is acting perpendicularly on the plate. If the plate is displaced perpendicularly from its equilibrium position and released, then it starts an oscillatory motion, which decays as time goes on because of the drag exerted by the gas molecules. This unsteady motion is investigated numerically, under the diffuse reflection condition, with special interest in the manner of its decay. It is shown that the decay of the displacement of the plate is slow and is in proportion to an inverse power of time. The result complements the existing mathematical study of a similar problem [S. Caprino, et al., Math. Models. Meth. Appl. Sci. 17, pp. 1369–1403 (2007)] in the case of non‐oscillatory decay.

Tailoring particle translocation via dielectrophoresis in pore channels

Understanding and controlling electrophoretic motions of nanoscopic objects in fluidic channels are a central challenge in developing nanopore technology for molecular analyses. Although progress has been made in slowing the translocation velocity to meet the requirement for electrical detections of analytes via picoampere current measurements, there exists no method useful for regulating particle flows in the transverse directions. Here, we report the use of dielectrophoresis to manipulate the single-particle passage through a solid-state pore. We created a trap field by applying AC voltage between electrodes embedded in a low-aspect-ratio micropore. We demonstrated a traffic control of particles to go through center or near side surface via the voltage frequency. We also found enhanced capture efficiency along with faster escaping speed of particles by virtue of the AC-mediated electroosmosis. This method is compatible with nanopore sensing and would be widely applied for reducing off-axis effects to achieve single-molecule identification.

Backward clusters, hierarchy and wild sums for a hard sphere system in a low-density regime

We study the statistics of backward clusters in a gas of hard spheres at low density. A backward cluster is defined as the group of particles involved directly or indirectly in the backwards-in-time dynamics of a given tagged sphere. We derive upper and lower bounds on the average size of clusters by using the theory of the homogeneous Boltzmann equation combined with suitable hierarchical expansions. These representations are known in the easier context of Maxwellian molecules (Wild sums). We test our results with a numerical experiment based on molecular dynamics simulations.

Negative thermophoresis of nanoparticles interacting with fluids through a purely-repulsive potential

Thermophoretic forces acting on nanoparticles are investigated using molecular dynamics simulation. We assume the Lennard-Jones (LJ) potential for the interaction between fluid molecules. On the other hand, the interaction between the nanoparticle and the surrounding fluid molecules are assumed to be either LJ or Weeks-Chandler-Andersen (WCA) potential, where the latter is purely-repulsive. The effect of the interaction potential on the thermophoretic force is investigated for various situations. It is found that the thermophoretic force basically acts in the direction from the hotter side to the colder side of the nanoparticle. However, when the surrounding fluid is in the liquid phase, the force acts in the reversed direction for the case of the WCA potential. It is clarified that the sign reversal is caused by the different structures observed in the distribution of repulsive forces acting on the nanoparticle.

Molecular dynamics study of force acting on a model nano particle immersed in fluid with temperature gradient: Effect of interaction potential

Thermophoresis of a nano particle in a fluid is investigated using molecular dynamics simulation. In order to elucidate effective factors on the characteristics of thermophoresis, simple models for both the fluid and the nano particle are considered, namely, the surrounding fluid consists of Lennard-Jones (LJ) particles and the model nano particle is a cluster consisting of several tens of LJ particles. Interaction between the fluid particle and the model nano particle is described by the LJ interaction potential or repulsive interaction potential with the Lorentz-Berthelot mixing rule. As a preliminary result, the effect of mass on thermophoretic force acting on the model nano particle is investigated for both interaction potentials.

Numerical Analysis of Nonlinear Acoustic Wave Propagation in a Rarefied Gas

Unsteady motion of a rarefied gas in a half space, caused by an infinitely wide plate when it starts a longitudinal and harmonic oscillation, is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. A deterministic method capable of describing the singularities in the molecular velocity distribution function produced by the oscillating plate, which was developed recently by the authors, is used as a solution method, and the unsteady behavior of the gas is obtained accurately. The streaming motion and the attenuation of the wave, observed in the existing work using the direct simulation Monte Carlo (DSMC) method (T. Ohwada and M. Kunihisa, in Rarefied Gas Dynamics, AIP, Melville, 2003, pp. 202-209), are also obtained. In addition, some pieces of numerical evidence that clarify the long-time behavior of the gas are provided. For example, one-period averages of the momentum and energy fluxes across the oscillating plate tend to approach their values for a p...

Artificial Cochlear Sensory Epithelium with Functions of Outer Hair Cells Mimicked Using Feedback Electrical Stimuli

We report a novel vibration control technique of an artificial auditory cochlear epithelium that mimics the function of outer hair cells in the organ of Corti. The proposed piezoelectric and trapezoidal membrane not only has the acoustic/electric conversion and frequency selectivity of the previous device developed mainly by one of the authors and colleagues, but also has a function to control local vibration according to sound stimuli. Vibration control is achieved by applying local electrical stimuli to patterned electrodes on an epithelium made using micro-electro-mechanical system technology. By choosing appropriate phase differences between sound and electrical stimuli, it is shown that it is possible to both amplify and dampen membrane vibration, realizing better control of the response of the artificial cochlea. To be more specific, amplification and damping are achieved when the phase difference between the membrane vibration by sound stimuli and electrical stimuli is zero and π, respectively. We also demonstrate that the developed control system responds automatically to a change in sound frequency. The proposed technique can be applied to mimic the nonlinear response of the outer hair cells in a cochlea, and to realize a high-quality human auditory system.

Numerical study on horizontal convection of a rarefied gas over a non-isothermal plane wall

A rarefied gas over an infinite plane wall with non-uniform periodic temperature distribution is considered under the effect of gravity. The Knudsen number and the Froude number are defined as the mean free path of gas molecules and the scale height at a reference state divided by the length of the period, respectively. Based on the kinetic theory of gases, the steady two-dimensional gas flow is investigated numerically for a wide range of parameters. The cases of a free molecular gas are analyzed by a deterministically accurate method, which enables the computation for large Froude numbers, i.e., vanishingly small gravity. The flow pattern is shown to be slightly effected by the Froude number when the Froude number is large, whereas the flow magnitude is proportional to the inverse of the Froude number. As a result, the flow vanishes in the limit of zero gravity. This is not a trivial consequence because the case of an infinite Froude number is different from the same setting without gravity. The cases o...

Steady flow of highly rarefied gas in half space induced by gravity and non-uniform wall temperature

A gas over an infinite plane wall with non-uniform periodic temperature distribution is considered, where the gas is so rarefied that the collisions between gas molecules are neglected. Moreover, the gas is subject to gravity in the direction toward the wall. The steady state established under the above setting is investigated numerically, on the basis of kinetic theory of gases with the diffuse-reflection boundary condition on the wall. It is found that the two-dimensional steady macroscopic flow near the wall is induced from the colder part to the hotter part, and the density near the cold/hot part of the wall increases/decreases. The observed flow is attributed to the presence of gravity, since it has been known that no flow occurs in the present setting without gravity.