Effect of shear flow on the transverse thermal conductivity of polymer melts.

The effect of shear flows on the thermal conductivity of polymer melts is investigated using a reversed nonequilibrium molecular-dynamics (RNEMD) method. We extended the original RNEMD method to simultaneously produce spatial gradients of temperature and flow velocity in a single direction. This method enables accurate measurement of the thermal conductivity in the direction transverse to shear flow. The Weissenberg number defined with the shear rate and the relaxation time of the polymer conformation can uniformly differentiate the occurrence of shear rate dependence of the thermal conductivity across different chain lengths. The stress-thermal rule (STR) (i.e., the linear relationship between anisotropic parts of the stress tensor and the thermal conductivity tensor) holds for entangled polymer melts even under shear flows but not for unentangled polymer melts. Furthermore, once entanglements form in polymer chains, the stress-thermal coefficient in the STR remains independent of the polymer chain length. These observations align with the theoretical foundation of the STR, which focuses on energy transmission along the network structure of entangled polymer chains [B. van den Brule, Rheol. Acta 28, 257 (1989)0035-451110.1007/BF01329335]. However, under driven shear flows, the stress-thermal coefficient is notably smaller than that measured in the literature for a quasiquiescent state without external forces. Although the mechanism of the STR in shear flows has yet to be fully elucidated, our study confirmed the validity of the STR in shear flows. This allows us to use the STR as a constitutive equation for computational thermofluid dynamics of polymer melts, thus having broad engineering applications.

Numerical Study of the Volcano Effect in Chemotactic Aggregation Based on a Kinetic Transport Equation with Non-instantaneous Tumbling.

Aggregation of chemotactic bacteria under a unimodal distribution of chemical cues was investigated by Monte Carlo (MC) simulation 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, the aggregation profile becomes bimodal (volcano) at the large adaptation-time regime when the tumbling duration is sufficiently large while it is always unimodal at the small adaptation-time regime. A remarkable result of this study is the identification of the parameter regime and scaling for the volcano effect. That is, by comparing the results of MC simulations to the continuum-limit models obtained at each of the small and large adaptation-time scalings, it is clarified that the volcano effect arises due to the coupling of diffusion, adaptation, and finite tumbling duration, which occurs at the large adaptation-time scaling.

Effects of internal dynamics on chemotactic aggregation of bacteria.

The effects of internal adaptation dynamics on the self-organized aggregation of chemotactic bacteria are investigated by Monte Carlo (MC) simulations based on a two-stream kinetic transport equation coupled with a reaction-diffusion equation of the chemoattractant that bacteria produce. A remarkable finding is a nonmonotonic behavior of the peak aggregation density with respect to the adaptation time; more specifically, aggregation is the most enhanced when the adaptation time is comparable to or moderately larger than the mean run time of bacteria. Another curious observation is the formation of a trapezoidal aggregation profile occurring at a very large adaptation time, where the biased motion of individual cells is rather hindered at the plateau regimes due to the boundedness of the tumbling frequency modulation. Asymptotic analysis of the kinetic transport system is also carried out, and a novel asymptotic equation is obtained at the large adaptation-time regime while the Keller-Segel type equations are obtained when the adaptation time is moderate. Numerical comparison of the asymptotic equations with MC results clarifies that trapezoidal aggregation is well described by the novel asymptotic equation, and the nonmonotonic behavior of the peak aggregation density is interpreted as the transient of the asymptotic solutions between different adaptation time regimes.

Solidification of the Lennard-Jones fluid near a wall in thermohydrodynamic lubrication.

We investigate the thermohydrodynamic lubrication of the Lennard-Jones (LJ) fluid in plain wall channels by using a molecular-dynamics simulation. It is found that the LJ fluid solidifies near the wall when the viscous heating of the LJ fluid in the bulk regime is sufficiently large. The thickness of the solidified layer increases with the channel width. Thus, a long-range-ordered crystal-like structure forms near the wall in high-speed lubrication when the channel width is large. The mechanism of this counterintuitive solidification is investigated from both macroscopic and microscopic points of view. It is elucidated that the LJ molecules are densely confined in the vicinity of the wall due to the macroscopic mass and heat transport in the bulk regime. In this densely confined regime, the fluid molecules form a crystal-like structure, which is similar to that of the wall molecules, via direct molecular interaction. Band formation is also observed in the solidified region when the channel width is sufficiently large.

Synchronized Molecular-Dynamics Simulation of the Thermal Lubrication of an Entangled Polymeric Liquid.

The thermal lubrication of an entangled polymeric liquid in wall-driven shear flows between parallel plates is investigated by using a multiscale hybrid method, coupling molecular dynamics and hydrodynamics (i.e., the synchronized molecular dynamics method). The temperature of the polymeric liquid rapidly increases due to viscous heating once the drive force exceeds a certain threshold value, and the rheological properties drastically change at around the critical drive force. In the weak viscous-heating regime, the conformation of polymer chains is dominated by the flow field so that the polymers are more elongated as the drive force increases. However, in the large viscous-heating regime, the conformation dynamics is dominated by the thermal agitation of polymer chains so that the conformation of polymers recovers more uniform and random structures as the drive force increases, even though the local shear flows are further enhanced. Remarkably, this counter-intuitive transitional behavior gives an interesting re-entrant transition in the stress⁻optical relation, where the linear stress⁻optical relation approximately holds even though each of the macroscopic quantities behaves nonlinearly. Furthermore, the shear thickening behavior is also observed in the large viscous-heating regime-this was not observed in a series of previous studies on an unentangled polymer fluid. This qualitative difference of the thermo-rheological property between the entangled and unentangled polymer fluids gives completely different velocity profiles in the thermal lubrication system.

Dynamic rheology of a supercooled polymer melt in nonuniform oscillating flows between rapidly oscillating plates.

The dynamic rheology of a 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 quiescent state, the melt is in a supercooled state, and the stress relaxation function G(t) exhibits a stretched exponential relaxation on the time scale of the α relaxation time τ(α) (the structural relaxation of beads) and then follows the Rouse relaxation function characterized by the Rouse relaxation time τ(R) (the conformational relaxation of polymer chains). In the rapidly oscillating plates, nonuniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. The local strain and local strain rate of the melt monotonically decrease with the distance from the plate at each oscillation frequency of the plate, but their dependencies on the oscillation frequency at a fixed distance from the plate vary with the distance. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rheology deviates from the linear moduli at the low oscillation frequencies rather than high oscillation frequencies. On the contrary, near the plate, the local strain rate increases with the oscillation frequency such that the shear thinning is enhanced at high oscillation frequencies. In close vicinity to the plate, the dynamic viscosity is mostly independent of the oscillation frequency, and the shear thinning behavior becomes similar to that observed in steady shear flows. We show the diagram of the loss tangent of the melt for different oscillation frequencies and local strain rates. It is seen that the melt generates three different rheological regimes, i.e., the viscous fluid regime, liquidlike viscoelastic regime, and solidlike viscoelastic regime, according to the oscillation frequency and local strain rate. Nonlinear rheological properties are also investigated by the spectrum analysis and the Lissajous-Bowditch curve. It is found that the fractional amplitude of the higher harmonics to the linear harmonics is suppressed within the boundary layer due to the nonslip boundary on the oscillating plate. We also find that the melt exhibits intercycle shear thinning between different positions but exhibits intracycle shear thickening at a fixed position in the vicinity of the plate.

Multiscale modeling and simulation for polymer melt flows between parallel plates.

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of 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 in a region for omegatauR < approximately 1 , and the crossover between the liquidlike and solidlike regime takes place around omegataualpha approximately equal 1 (where omega is the angular frequency of the plate and tauR and taualpha are Rouse and alpha relaxation time, respectively).