The Couette flow and a thermal problem of a rarefied nitrogen gas between two platinum walls are considered to investigate the characteristics of the reflected gas molecule at a solid surface. The analysis is based on the molecular dynamics (MD) method for the gas-wall interaction together with the direct simulation Monte-Carlo (DSMC) method for the motion of gas molecules. The accommodation coefficients of momentum, translational, and rotational energies of the molecule are obtained. The velocity and rotational energy distributions of the molecule at the wall surface are also obtained. It is found that the Maxwell-type distribution function consisting of specular and diffuse reflections well describes the distribution function of the reflected molecules if the accommodation coefficient involved is chosen properly. It is also found that the flow and temperature fields subject to the Maxwell-type reflection conditions decomposed into each direction of the space coordinates result in good agreements with those of the DSMC combined with the MD calculation.

Flows through a curved duct of square cross-section are numerically studied by using the spectral method, and covering a wide range of curvature of the duct (0 < 0.5) and the Dean number Dn (0 < Dn 8000), where is non-dimensionalized by the half width of the square cross-section. The main concern is the relationship between the unsteady solutions, such as periodic, multi-periodic and chaotic solutions, and the bifurcation diagram of the steady solutions. It is found that the bifurcation diagram topologically changes if the curvature is increased and exceeds the critical value c ≈ 0.279645, while it remains almost unchanged for < c or > c . A periodic solution is found to appear if the Dean number exceeds the bifurcation point, whether it is pitchfork or Hopf bifurcation, where no steady solution is stable. It is found that the bifurcation diagram and its topological change crucially affect the realizability of the steady and periodic solutions. Time evolution calculations as well as their spectral analysis show that the periodic solution turns to a chaotic solution if the Dn is further increased no matter what the curvature is. It is interesting that the chaotic solution is weak for smaller Dn, where the solution drifts among the steady solution branches, for larger Dn, on the other hand, the chaotic solution becomes strong, where the solution tends to get away from the steady solution branches.

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The scattering behaviors of nitrogen molecules reflected at a platinum surface are studied by the molecular dynamics method for the gas-surface interaction. The platinum surface is assumed to physically adsorb xenon molecules. Distributions of molecular velocities after reflection are obtained for the impinging molecules with specified velocities within a small range. The scattering distribution shows a bimodal behavior consisting of diffuse reflection and a distribution shifting to the velocity distribution of the impinging molecules. Comparison between the present scattering distribution and the Cercignani-Lampis-Lord scattering kernel shows large differences. A simple scattering kernel using a bimodal distribution is proposed assuming mutual independence of distributions in each velocity component and is compared favorably to the present scattering distribution. In addition, the scattering kernel of the rotational energy of the molecule is discussed.

The microfluidic sperm-sorting (MFSS) device is a promising advancement for assisted reproductive technology. Previously, poly(dimethylsiloxiane) and quartz MFSS devices were developed and used for intracytoplasmic sperm injection. However, these disposable devices were not clinically suitable for assisted reproduction, so a cyclo-olefin polymer MFSS (COP-MFSS) device was developed. By micromachining, two microfluidic channels with different heights and widths (chip A: 0.3 × 0.5 mm; chip B: 0.1 × 0.6 mm) were prepared. Sorted sperm concentrations were similar in both microfluidic channels. Linear-velocity distribution using the microfluidic channel of chip B was higher than that of chip A. Using confocal fluorescence microscopy, it was found that the highest number of motile spermatozoa swam across the laminar flow at the bottom of the microfluidic channel. The time required to swim across the laminar flow was longer at the bottom and top of the microfluidic channels than in the middle because of the low fluid velocity. These results experimentally demonstrated that the width of microfluidic channels should be increased in the region of laminar flow from the semen inlet to the outlet for unsorted spermatozoa to selectively recover spermatozoa with high linear velocity.

Non-isothermal flows with convective heat transfer through a curved duct of square cross section are numerically studied by using a spectral method, and covering a wide range of curvature, δ, 0<δ≤0.5 and the Dean number, Dn, 0≤Dn≤6000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr=100, where the outer wall is heated and the inner one cooled. Steady solutions are obtained by the Newton-Raphson iteration method and their linear stability is investigated. It is found that the stability characteristics drastically change due to an increase of curvature from δ = 0.23 to 0.24. When there is no stable steady solution, time evolution calculations as well as their spectral analyses show that the steady flow turns into chaos through periodic or multi-periodic flows if Dn is increased no matter what δ is. The transition to a periodic or chaotic state is retarded with an increase of δ. Nusselt numbers are calculated as an index of horizontal heat transfer and it is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid. If the flow becomes periodic and then chaotic, as Dn increases, the rate of heat transfer increases remarkably.

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