Synchronized molecular-dynamics simulation for the thermal lubrication of a polymeric liquid between parallel plates

The Synchronized Molecular-Dynamics simulation which was recently proposed by authors [Phys. Rev. X {\bf 4}, 041011 (2014)] is applied to the analysis of polymer lubrication between parallel plates. The rheological properties, conformational change of polymer chains, and temperature rise due to the viscous heating are investigated with changing the values of thermal conductivity of the polymeric liquid. It is found that at a small applied shear stress on the plate, the temperature of polymeric liquid only slightly increases in inverse proportion to the thermal conductivity and the apparent viscosity of polymeric liquid is not much affected by changing the thermal conductivity. However, at a large shear stress, the transitional behaviors of the polymeric liquid occur due to the interplay of the shear deformation and viscous heating by changing the thermal conductivity. This transition is characterized by the Nahme-Griffith number $Na$ which is defined as the ratio of the viscous heating to the thermal conduction at a characteristic temperature. When the Nahme-Griffith number exceeds the unity, the temperature of polymeric liquid increases rapidly and the apparent viscosity also exponentially decreases as the thermal conductivity decreases. The conformation of polymer chains is stretched and aligned by the shear flow for $Na<1$, but the coherent structure becomes disturbed by the thermal motion of molecules for $Na>1$.Comment: 19 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1401.124

Volcano effect in chemotactic aggregation and an extended Keller-Segel mode

Aggregation of chemotactic bacteria under a unimodal distribution of chemical cues was investigated by Monte Carlo simulation and asymptotic analysis based on a kinetic transport equation, which considers an internal adaptation dynamics as well as a finite tumbling duration. It was found that there exist two different regimes of the adaptation time, between which the effect of the adaptation time on the aggregation behavior is reversed; that is, when the adaptation time is as small as the running duration, the aggregation becomes increasingly steeper as the adaptation time increases, while, when the adaptation time is as large as the diffusion time of the population density, the aggregation becomes more diffusive as the adaptation time increases. Moreover, notably, the aggregation profile becomes bimodal (volcano) at the large adaptation-time regime while it is always unimodal at the small adaptation-time regime. The volcano effect occurs in such a way that the population of tumbling cells considerably decreases in a diffusion layer which is created near the peak of the external chemical cues due to the coupling of diffusion and internal adaptation of the bacteria. Two different continuum-limit models are derived by the asymptotic analysis according to the scaling of the adaptation time; that is, at the small adaptation-time regime, the Keller-Segel model while, at the large adaptation-time regime, an extension of KS model, which involves both the internal variable and the tumbling duration. Importantly, either of the models can accurately reproduce the MC results at each adaptation-time regime, involving the volcano effect. Thus, we conclude that the coupling of diffusion, adaptation, and finite tumbling duration is crucial for the volcano effect

Rheology of a supercooled polymer melt near an oscillating plate: an application of multiscale modeling

The behavior of a supercooled polymer melt composed of short chains with ten beads near an oscillating plate are simulated by using a hybrid simulation of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, the macroscopic dynamics are solved by using CFD, but, instead of using any constitutive equations, a local stress is calculated by using a non-equilibrium MD simulation associated at each lattice node in the CFD calculation. It is seen that the local rheology of the melt varies considerably in a thin viscous diffusion layer that arises near an oscillating plate. It is also found that the local rheology of the melt is divided into the three different regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, according to the local Deborah number $De$, which is defined with the Rouse or $\alpha$ relaxation time, $\tau_R$ or $\tau_\alpha$, and the angular frequency of the plate $\omega$ as $De^R$=$\omega\tau_R$ or $De^\alpha$=$\omega\tau_\alpha$. The melt behaves as a viscous fluid when $De^R\lesssim 1$, and the crossover between the liquid-like and solid-like regime takes place around $De^\alpha\simeq 1$

A Model for Hybrid Simulations of Molecular Dynamics and CFD

We propose a method for multi-scale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, usual lattice-mesh based simulations are applied for CFD level, but each lattice is associated with a small MD cell which generates a "local stress" according to a "local flow field" given from CFD instead of using any constitutive functions at CFD level. We carried out the hybrid simulations for some elemental flow problems of simple Lennard-Jones liquids and compared the results with those obtained by usual CFDs with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduced the correct flow behavior obtained from usual CFDs as far as the mesh size $\Delta x$ and the time-step $\Delta t$ of CFD are not too large comparing to the system size $l_{\rm MD}$ and the sampling duration $t_{\rm MD}$ of MD simulations performed at each time step of CFDs. Otherwise, simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail.Comment: 17 pages including 9 figure