Takeru Yano

Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase

The evaporation and condensation at an interface of vapor and its condensed phase is considered. The validity of kinetic boundary condition for the Boltzmann equation, which prescribes the velocity distribution function of molecules outgoing from the interface, is investigated by the numerical method of molecular dynamics for argon. From the simulations of evaporation into vacuum, the spontaneous-evaporation flux determined by the temperature of condensed phase is discovered. Condensation coefficient in equilibrium states can then be determined without any ambiguity. It is found that the condensation coefficient is close to unity below the triple-point temperature and decreases gradually as the temperature rises. The velocity distribution of spontaneously evaporating molecules is found to be nearly a half-Maxwellian at a low temperature. This fact supports the kinetic boundary condition widely used so far. At high temperatures, on the other hand, the velocity distribution deviates from the half-Maxwellian.

Turbulent acoustic streaming excited by resonant gas oscillation with periodic shock waves in a closed tube

Resonant gas oscillations with periodic shock waves in a closed tube are studied by executing large-scale computations of the compressible 2-D Navier–Stokes equations with a finite-difference method. In a quasisteady state of oscillation, acoustic streaming (mean mass flow) of large Rs is excited, where Rs is the streaming Reynolds number based on a characteristic streaming velocity, the tube length, and the kinematic viscosity. When Rs=560, relatively strong vortices are localized near the tube wall. The resulting streaming pattern is almost stationary but quite different from that of the Rayleigh streaming. The streaming of Rs=6200 involves unsteady vortices in a region near the center of the tube. Turbulent streaming appears in the result of Rs=56000, where vortices of various scales are irregularly generated throughout the tube.

Molecular dynamics simulation of structural changes of lipid bilayers induced by shock waves : Effects of incident angles

Unsteady and nonequilibrium molecular dynamics simulations of the response of dipalmitoylphosphatidylcholine (DPPC) bilayers to the shock waves of various incident angles are presented. The action of an incident shock wave is modeled by adding a momentum in an oblique direction to water molecules adjacent to a bilayer. We thereby elucidate the effects of incident shock angles on (i) collapse and rebound of the bilayer, (ii) lateral displacement of headgroups, (iii) tilts of lipid molecules, (iv) water penetration into the hydrophobic region of the bilayer, and (v) momentum transfer across the bilayer. The number of water molecules delivered into the hydrophobic region is found to be insensitive to incident shock angles. The most important structural changes are the lateral displacement of headgroups and tilts of lipid molecules, which are observed only in the half of the bilayer directly exposed to a shock wave for all incident shock angles studied here. As a result, only the normal component of the added oblique momentum is substantially transferred across the bilayer. This also suggests that the irradiation by shock waves may induce a jet-like streaming of the cytoplasm toward the nucleus.

Propagation of strongly nonlinear plane wavesa)

The nonlinear propagation of plane waves at high acoustic Reynolds number is studied without the restriction of low amplitude, namely, the weak nonlinearity. The wave is emitted from an infinite plate executing harmonic oscillations into a perfect gas. The method of analysis is based on the simple wave theory up to the shock formation time, and beyond the time on the numerical calculation by means of the upwind finite difference scheme (and partly the weakly nonlinear theory is used jointly with it). The initial sinusoidlike wave profile is progressively distorted as the wave propagates and this leads to the formation of shocks, as well as in the propagation of the weakly nonlinear wave. Then it evolves into a sawtoothlike wave as a whole. The strongly nonlinear wave, however, possesses the following outstanding distinctive features, as contrasted with its counterpart in the weakly nonlinear regime: (i) shock waves that form in a near field propagate with supersonic speed in a quasi‐steady state; (ii) the...

Linear Analysis of Dispersive Waves in Bubbly Flows Based on Averaged Equations

One-dimensional linear dispersive waves in water flows containing a number of small spherical air bubbles are analytically studied on the basis of a set of averaged equations recently derived by the present authors. The set of equations consists of the conservation laws for gas and liquid phases and the equation of motion of bubble wall. In addition to the volume-averaged pressure in each phase, the surface-averaged liquid pressure at the bubble wall is incorporated. The compressibility of water is taken into account as well as that of gas in bubbles, and a model of virtual mass force is included, although the Reynolds stress, viscosity, heat conductivity, and the phase change across the bubble wall are disregarded. The results are summarized as follows: (i) the waves are decomposed into the fast mode, slow mode, and convection mode (void wave). (ii) In the uniform flows, the three modes stably exist for all real wave numbers. (iii) In the limit of infinitesimal void fraction, the explicit representation of the elementary solution is obtained. (iv) The instability does not appear in the range where the present averaged equations are applicable.

Nonlinear analysis of periodic modulation in resonances of cylindrical and spherical acoustic standing waves

The nonlinear resonance of cylindrical acoustic standing waves of an ideal gas contained between two coaxial cylinders is theoretically investigated by the method of multiple scales. The wave motion concerned is excited by a small-amplitude harmonic oscillation of the radius of the outer cylinder, and the formulation of the problem includes the wave phenomenon in a hollow cylinder without the inner one as a limiting case. The spherical standing wave in two concentric spheres is also studied in parallel. The resonance occurs if the driving frequency falls in a narrow band around the linear resonance frequency, and in the weakly nonlinear regime, no shock wave is formed in contrast to the plane wave resonance. A cubic nonlinear equation for complex wave amplitude can then be derived by the method of multiple scales. Using a first integral of the cubic nonlinear equation, we shall demonstrate that the resonant oscillation is accompanied by a periodic modulation of amplitude and phase when the dissipation eff...

Strongly nonlinear waves and streaming in the near field of a circular piston

The propagation of nonlinear waves radiated by a circular piston mounted in an infinite plane rigid wall is numerically studied without the restriction of weak nonlinearity, in the case that the radius of piston is comparable with a typical wavelength of the radiated wave. The piston executes harmonic oscillations and the wave is thereby emitted into an ideal gas of semi‐infinite extent, in which the dissipation effect is supposed to be negligible everywhere except for the discontinuous shock front. The wave phenomenon in the near field caused by the strongly nonlinear effect combined with the diffraction effect is clarified by solving the Euler equations with the upwind finite difference scheme. Owing to the strong nonlinearity, not only the waves emitted directly from the piston face but also the diffraction waves from the edge of the source are distorted and developed into the shock waves. This can lead to a multiple interference of shock waves in the near field. The separation phenomenon at the edge i...

Numerical study of strongly nonlinear acoustic waves, shock waves, and streaming caused by a harmonically pulsating sphere

The nonlinear propagation of spherical waves emitted from a sphere executing harmonic pulsations in an unbounded ideal gas is numerically studied without the restriction of small amplitude, namely, the weak nonlinearity. The energy dissipation due to viscosity and thermal conductivity is supposed to be negligible everywhere except for the discontinuous shock front. By the numerical analysis based on a high‐resolution upwind finite difference scheme, the wave phenomena caused by the strongly nonlinear effect are revealed, which form several striking contrasts to the known results for the weakly nonlinear spherical waves. The profile of the emitted wave is rapidly distorted by the strongly nonlinear effect and shock waves are formed near the sphere. The most remarkable phenomenon is the occurrence of acoustic streaming (mean mass outflow), which gradually reduces the density of the gas near the sphere as time proceeds. In the case that the sphere pulsates with a small amplitude compared with its mean radius...

Linear theory of sound waves with evaporation and condensation

An asymptotic analysis of a boundary-value problem of the Boltzmann equation for small Knudsen number is carried out for the case when an unsteady flow of polyatomic vapour induces reciprocal evaporation and condensation at the interface between the vapour and its liquid phase. The polyatomic version of the Boltzmann equation of the ellipsoidal statistical Bhatnagar–Gross–Krook (ES-BGK) model is used and the asymptotic expansions for small Knudsen numbers are applied on the assumptions that the Mach number is sufficiently small compared with the Knudsen number and the characteristic length scale divided by the characteristic time scale is comparable with the speed of sound in a reference state, as in the case of sound waves. In the leading order of approximation, we derive a set of the linearized Euler equations for the entire flow field and a set of the boundary-layer equations near the boundaries (the vapour–liquid interface and simple solid boundary). The boundary conditions for the Euler and boundary-layer equations are obtained at the same time when the solutions of the Knudsen layers on the boundaries are determined. The slip coefficients in the boundary conditions are evaluated for water vapour. A simple example of the standing sound wave in water vapour bounded by a liquid water film and an oscillating piston is demonstrated and the effect of evaporation and condensation on the sound wave is discussed.

Molecular dynamics study on the evaporation part of the kinetic boundary condition at the interface between water and water vapor

Molecular dynamics simulations of vapor‐liquid equilibrium states and those of evaporation from liquid phase into a virtual vacuum are performed for water. In spite of the formation of molecular clusters in the vapor phase and the presence of the preferential orientation of molecules at the interface due to uneven sharing of the bonding electron pair, essentially the same results as in our previous study for argon are obtained. That is, when the bulk liquid temperature is relatively low, the distribution function of evaporation can be expressed as the product of the equilibrium distribution of saturated vapor at the temperature in the bulk liquid phase and a well‐defined evaporation coefficient, which is determined as a decreasing function of the liquid temperature, and is found to approach unity with the decrease of the temperature.