安田 修悟

We propose a multiscale computational method for thin-layer flows of complex fluids, termed the synchronized molecular dynamics (SMD) method, which directly couples local molecular dynamics (MD) simulations with a macroscopic lubrication description. In thin layers, the flow can be decomposed into cross-sectional dynamics that are strongly influenced by interfacial effects, and streamwise transport along the channel. The SMD method exploits this separation of scales by sparsely distributing local MD cells along the channel and synchronizing them through macroscopic conservation laws. In this framework, the macroscopic continuity equation is enforced by iteratively updating the external forces applied to each MD cell, thereby allowing the cross-sectional velocity profiles and the streamwise pressure distribution to be obtained without prescribing constitutive relations or boundary conditions. The method is validated for pressure-driven and wall-driven flows of Lennard--Jones fluids in a wedge-shaped channel, demonstrating excellent agreement with a modified Reynolds equation that accounts for boundary slip. The SMD method is further applied to polymeric lubrication flows modeled by the Kremer--Grest chain model. At large pressure differences, the present approach naturally captures pronounced shear-thinning behavior coupled with microscopic polymer conformation dynamics. The results demonstrate that the SMD method provides an efficient and physically consistent framework for the multiscale simulation of complex fluid thin-layer flows.

A kinetic transport equation for chemotactic bacteria, i.e., a kinetic chemotaxis equation, coupled with reaction-diffusion equations for chemoattractants is considered. The Keller-Segel type equation for the population density of bacteria is derived by the asymptotic analysis of the kinetic chemotaxis equation in the continuum limit, where the ratio of the mean run length of bacteria to the characteristic length of the system, i.e., the Knudsen number, vanishes. Monte Carlo (MC) simulations of the kinetic chemotaxis model are performed for the traveling pulse problem with variation in the Knudsen number. The results of MC simulations are numerically compared with the Keller-Segel type equation. It is found that the results of MC simulations approach to that of the Keller-Segel type equation as decreasing the Knudsen number. However, a significant difference still remains for moderately small Knudsen numbers which correspond to the micro scale systems. This result demonstrates an importance of the kinetic chemotaxis model in the micro scale systems.

本稿では，最近，著者らが開発したSynchronized Molecular Dynamics（SMD）法[S.Yasuda and R. Yamamoto, Phys. Rev. X 4, 041011 (2014)] についての解説とそれを用いて2 平板間の高分子液体の潤滑挙動を解析した結果について紹介する．SMD 法では，多数の分子動力学（MD）セルを流体の要素に割り当て，各流体要素おける局所的な物理量をMD 法によって計算する．しかし，ある一定の時間間隔で，システム全体のマクロ物理量（エネルギーや運動量）の輸送方程式が満たされるように，隣接するMD セル間において運動量とエネルギーの交換を行う．これによって，任意の分子モデルを基に，巨視的な移動現象を解析することができるようになる．SMD 法による高分子潤滑の解析では，潤滑中に生じる粘性発熱が高分子液体のレオロジー特性と内部構造にどのように影響するのかを詳細に調べている．せん断流・発熱・内部構造が強く相互作用した結果として，高分子鎖の挙動において，せん断変形が支配的となる領域と温度上昇が支配的となる領域との間に，興味深い転移挙動があることが明らかにされた．

The Synchronized Molecular-Dynamics simulation, which was recently proposed by authors [Phys. Rev. X 4, 041011 (2014)], is applied to the analysis of polymer lubrication between parallel plates. The changes in rheological properties, conformational change of polymer chains, and temperature rise due to the viscous heating are investigated with varying values of thermal conductivity of the polymeric liquid. It is found that with a small applied shear stress on the plate, the temperature of the polymeric liquid only slightly increases in inverse proportion to the thermal conductivity; the apparent viscosity of the polymeric liquid is little affected by changing the thermal conductivity. However, at a large shear stress the transitional behaviors of the polymeric liquid are observed due to the interplay of the shear deformation and viscous heating by changing the thermal conductivity. It is found that this transition is characterized by the Nahme-Griffith number, defined as the ratio of the viscous heating to the thermal conduction.

高速振動平板間にある高分子液体の動的レオロジー特性を古典分子動力学計算と計算流体力学の階層連結計算法を用いて解析した. 高速振動平板上にある流体は慣性の効果によって平板上で振動境界層流れを形成する．高分子液体の局所歪速度は境界層内部で急激に変化し，その結果，その局所的な動的レオロジー特性もまたシアシニング効果や非線形効果によって空間的に大きく変化する．例えば，振動数が大きい場合には，振動板から離れた位置では弾性の方が優位な粘弾性固体的に振舞う高分子液体が，振動板近傍においては弾性の無視できる粘性流体的にその振舞いを大きく変化させる．高分子液体の非線形レオロジー応答については，高分子液体の局所歪は振動板に近づくにつれて単調に急激に増加するにもかかわらず，平板振動数ω₀の高調波成分の非線形応答は振動板のごく近傍において急激に減衰することが分かった．また，振動板近傍の高分子液体の局所応力と局所歪のリサージュ図形において，その一周期の中で弾性率がシアシックニングを示すことも明らかにされた．

The dynamic rheology of a model polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the rapidly oscillating plates, the non-uniform boundary layer flows are generated over the plate, and the local rheological properties of melt are spatially varied according to the local flow fields. At the high oscillation frequencies, the melt forms the three different regimes, i.e., viscous fluid regime (G'<<G"), liquid-like viscoelastic regime (G'<G"), and solid-like viscoelastic regime (G'>G"), over the rapidly oscillating plate. The local strain of the melt at the far distances from the plate decreases as the oscillation frequency increases, so that the local moduli deviate from the linear ones at the low oscillation frequencies while they are close to the linear ones at the high oscillation frequencies. On the contrary, at the near distances, the local strain rate increases as the oscillation frequency, so that the shear thinning is enhanced at the high oscillation frequencies. In the close vicinity of the plate, the dynamic viscosity is mostly independent on the oscillation frequency and the shear thinning which is similar to that occurring in the steady shear flows of the model polymer melt is observed.

ソフトマター流動解析において有効な流体力学計算と分子動力学計算のハイブリット計算法を開発し,高速に振動する平板間における高分子溶液の流動挙動を解析した.高速に振動する平板上での高分子溶液の流れにおいては,振動平板近傍でのシアシニングにより,流れの分布が対応するニュートン流体のものに比べて大きく異なることがわかった.また,高分子溶液の局所的な力学特性を解析した結果,高速に振動する平板上での高分子溶液に対しては,粘性流体,粘弾性液体,粘弾性固体なる3つの異なる力学特性をもつ領域が現れることを明らかにした.

The behavior of supercooled polymer melt composed of short chains with ten beads between rapidly oscillating plates is simulated by using a hybrid simulation of molecular dynamics and computational fluid dynamics. The flow profiles of polymer melt near an oscillating plate are quite different from those of Newtonian fluid. The viscous boundary layer of the melt is much thinner than that of the Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid when ωΤ^R&lsim;1, and the crossover between the liquid-like and solid-like regime takes place around ωΤ^α&sime;1 (where ω is the angular frequency of the plate and Τ^R and Τ^α are Rouse and α relaxation time, respectively).

高速振動平板における過冷却ポリマーメルトの振舞いを分子動力学とCFDのハイブリット法によってシミュレーションした。ポリマーメルトの流れ場はニュートン流体のそれとは全く異なる。例えば、シアシニングのために振動平板上に生じる粘性境界層はニュートン流体のそれに比べてかなり薄くなる。また、振動平板上には、局所デボラ数に従って、三つの異なるレオロジー領域（即ち、粘性流体領域、粘弾性液体領域、粘弾性固体領域）が生じる。w t^R << 1である領域に対してはメルトは粘性流体のように振舞い、液体的な領域と固体的な領域のクロスオーバーはw t^a = 1となる場所で起こる。ここで、w は平板の角振動数、t^Rは局所Rouse緩和時間、t^aは局所アルファ緩和時間である。

We develop a method for multi-scale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In this method, the usual lattice-mesh based simulations are applied for CFD level, but each lattice is associated with a small MD cell that generates a "local stress" according to a "local flow field" given from CFD instead of using any constitutive functions at the CFD level. We carried out hybrid simulations for some elemental flow problems involving simple Lennard-Jones liquids and compared the results with those obtained by usual CFD with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduce the correct flow behavior obtained from usual CFD as long as the mesh size Δx and the time-step Δt of CFD are not too large compared to the system size l_<MD> and the sampling duration t_<MD> of MD simulations performed at each time step of the CFD. Otherwise, the simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail.

せん断流れ場における微粒子凝集体の分散挙動を二相系格子ボルツマン法を応用した新しい微粒子分散系シミュレーション法を用いて調べた.粒子に作用する力としてファン・デル・ワールス粒子間引力とブラウン揺動力を考慮し,粒子に作用する流体抗力と粒子間凝集力の比,I,粒子の直径とデバイ長の比,s,流体抗力とブラウン揺動力の相対的な影響力を表すペクレ数,Pe,についてそれらのパラメータの凝集体の分散挙動への影響を調べた.

Half-space problem of evaporation and condensation of a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. The problem is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] to the case of a gas mixture. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic quantities but also at the level of the velocity distribution function. In addition, accurate formulas of the temperature, pressure, and concentration jumps caused by the evaporation or condensation are constructed for arbitrary values of the concentration of a component gas by the use of the Chebyshev polynomial approximation.