Deformation of a tethered polymer in uniform flow

Static properties of a single polymer fixed at one end and subjected to a uniform flow field are investigated for several polymer models: the Gaussian chain, the freely jointed chain, and the FENE (Finitely Extensible Nonlinear Elastic) chain. By taking into account first the excluded-volume interaction and subsequently also the hydrodynamic interaction, the polymer models are gradually completed and the relevance of each effect for the polymer deformation can be identified. Results from computer simulations of these bead spring chains are compared with analytical calculations using either the conformational distribution function or blob models. To this end, in contrast to the blob model with non-draining blobs introduced for a tethered polymer by Brochard-Wyart, we here develop also a model with free-draining blobs. It turns out that a limited extensibility of the polymer – described by nonlinear spring forces in the model – leads to a flow velocity dependence of the end-to-end distance, segment density, etc. which agrees with the power law predictions of the blob model only for very long chains and in a narrow range of flow velocities. This result is important for comparison with recent experiments on DNA molecules which turn out to be still rather short in this respect. The relative importance of finite extensibility, the excluded-volume effect, and hydrodynamic interactions for polymers in flow is not fully understood at present. The simulation of reasonably long chains becomes possible even when fluctuating hydrodynamic interactions are taken into account without employing averaging procedures by introducing efficient numerical approximation schemes. At medium velocity of the uniform flow the polymer is partially uncoiled and simulations show that the effects of excluded-volume and hydrodynamic interactions are position-dependent. Both are stronger near the free end than near the tethered end of the polymer. A crossover from a nearly non-draining polymer at small flow velocities to a free-draining almost uncoiled chain at large velocities is found in the simulations. Accordingly, models assuming the polymer to be composed of either free- or non-draining subunits, like the two blob models, cannot correctly describe the extension and shape of a tethered polymer in flow, and simple power laws for the polymer extension, etc. cannot be expected. Received 21 June 1999     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.     

Tagged particle fluctuations in uniform shear flow

The nonlinear Boltzmann and Boltzmann-Lorentz equations are used to describe the dynamics of a tagged particle in a nonequilibrium gas. For the special case of Maxwell molecules with uniform shear flow, an exact set of equations for the average position and velocity, and their fluctuations, is obtained. The results apply for arbitrary magnitude of the shear rate and include the effects of viscous heating. A generalization of Onsager's assumption of the regression of fluctuations is found to apply for the relationship between the equations for the average dynamics and those for the time correlation functions. The connection between fluctuations and dissipation is described by the equations for the equal-time correlation function. The source term in these equations indicates that the “noise” in this nonequilibrium state is qualitatively different from that in equilibrium, or even local equilibrium. These equations are solved to determine the velocity autocorrelation function as a function of the shear rate.     

Structure of a tethered polymer under flow using molecular dynamics and hybrid molecular-continuum simulations

We analyse the structure of a single polymer tethered to a solid surface undergoing a Couette flow. We study the problem using molecular dynamics (MD) and hybrid MD-continuum simulations, wherein the polymer and the surrounding solvent are treated via standard MD, and the solvent flow farther away from the polymer is solved by continuum fluid dynamics (CFD). The polymer represents a freely jointed chain (FJC) and is modelled by Lennard-Jones (LJ) beads interacting through the FENE potential. The solvent (modelled as a LJ fluid) and a weakly attractive wall are treated at the molecular level. At large shear rates the polymer becomes more elongated than predicted by existing theoretical scaling laws. Also, along the normal-to-wall direction the structure observed for the FJC is, surprisingly, very similar to that predicted for a semiflexible chain. Comparison with previous Brownian dynamics simulations (which exclude both solvent and wall potential) indicates that these effects are due to the polymer–solvent and polymer–wall interactions. The hybrid simulations are in perfect agreement with the MD simulations, showing no trace of finite size effects. Importantly, the extra cost required to couple the MD and CFD domains is negligible.     

Conformational defects in a conducting polymer

Electrically conducting organic polymers represent serious candidates for some of the electronic materials of tomorrow. The role of certain charge-carrying self-localized states, such as solitons, polarons and bipolarons, in determining the nature of the optical and electronic transport properties of these conjugated polymers is well established. These self-localized states are commonly referred to as ‘defects'. Recently, the list of possible ‘defects’ in these conducting polymers has expanded to include real defects which degrade the electrical properties, but lead to other interesting and potentially useful properties, such as colour changes.     

Thermal fluctuations in a Knudsen flow system

Spatial correlations of thermal fluctuations in a model system are examined. The system is a one-dimensional chain of cells containing a dilute gas and connected by Knudsen apertures. A Monte Carlo simulation is described in which the long range correlations observed agree quantitatively with a general master equation formulation.     

Dynamics of density fluctuations in a turbulent flow

Using a light scattering technique, we find that large density fluctuations in an air jet are clustered in time. A phase-space embedding allows us to propose a simple (S-shaped) manifold underlying the phase-space structure. In this context the temporal complexity naturally arises as stochastic fluctuations are added to the deterministic part of the model.     

Room-temperature fluctuations in the fluorescence of a single polymer molecule

A theoretical model of light absorption and emission by a polymer molecule has been developed using recent experimental data on the room-temperature fluctuations in the fluorescence intensity of single molecules of a PPV-PPyV copolymer containing several tens of chromophores. An analysis of the experimental data based on the proposed model shows evidence of a change in the conformation of a polymer molecule in the triplet state. By applying the theory to the PPV-PPyV copolymer, it is possible to determine the rate constants of the conformation variation, the rates of the transition from the singlet to the triplet state, and the lifetime of the triplet state of the molecule. The theory also predicts some new effects which can be verified by experiment.     

Power fluctuations in a closed turbulent shear flow

We study experimentally the power consumption P of a confined turbulent flow at constant Reynolds number Re. We analyze in details its temporal dynamics and statistical properties, in a setup that covers two decades in Reynolds numbers. We show that nontrivial power fluctuations occur over a wide range of amplitudes and that they involve coherent fluid motions over the entire system size. As a result, the power fluctuations do not result from averaging of independent subsystems and its probability density function Pi(P) is strongly non-Gaussian. The shape of Pi(P) is Reynolds number independant and we show that the relative intensity of fluctuations decreases very slowly as Re increases. These results are discussed in terms of an analogy with critical phenomena.     

Molecular dynamics study of tethered polymers in shear flow

Single macromolecules can now be isolated and characterized experimentally using techniques such as optical tweezers and videomicroscopy. An interesting and important single-molecule problem is that of the dynamics of a polymer chain tethered to a solid surface and subjected to a shear flow. An experimental study of such a system was reported by Doyle et al. (Phys. Rev. Lett. 84, 4769 (2000)), and their results showed a surprising recirculating motion of the DNA chain. We explore this problem using molecular dynamics computer simulations with explicit hydrodynamic interactions. The dynamical properties of a Freely Jointed Chain (FJC) with Finitely Extensible Nonlinear Elastic (FENE) links are examined in similar conditions (i.e., confined between two surfaces and in the presence of a Poiseuille flow). We see the remarkable cyclic polymer motion observed experimentally, and we show that a simple cross-correlation function can be used to measure the corresponding period of motion. We also propose a new empirical equation relating the magnitude of the shear flow to the amount of chain deformation, an equation that appears to apply for both weak and strong flows. Finally, we report on packing effects near the molecularly flat wall, an associated chain-sticking phenomenon, and the impact of the chain hydrodynamic drag on the local fluid flow.     

Numerical study of flow and heat transfer from a torus placed in a uniform flow

Forced convection heat transfer characteristics of a torus (maintained at a constant temperature) immersed in a streaming fluid normal to the plane of the torus are studied numerically. The governing equations, namely, continuity, momentum and thermal energy in toroidal coordinate system, are solved using a finite difference method over ranges of parameters (aspect ratio of torus, 1.4 ≤ Ar ≤ 20; Reynolds number, 20 ≤ Re ≤ 40; Prandtl number, 0.7 ≤ Pr ≤ 10). Over the ranges of parameters considered herein, the nature of flow is assumed to be steady. In particular, numerical results elucidating the influence of Reynolds number, Prandtl number and aspect ratio on the isotherm patterns, local and average Nusselt numbers for the constant temperature (on the surface of the torus) boundary condition. As expected, at large aspect ratio the flow pattern and heat transfer are similar to the case of flow and heat transfer over a single circular cylinder.     

Intensity fluctuations of ultrasonic scattering in a highly turbulent flow

Aspects of ultrasound intensity fluctuations backscattered from additive microstructures in a turbulent flow have been investigated theoretically and experimentally for the conditions of a small insonified volume, a high sound frequency and strong turbulence. These conditions are typically found in high resolution Doppler sonar applications. An easily applicable expression for the auto-correlation of scattering intensity fluctuations is obtained by introducing open-channel turbulence theory, a semi-empirical scalar spectrum (including a Batchelor spectrum) and a Gaussian window function. Experiments carried out in a laboratory-clear water, open-channel flow for different turbulence levels verify the underlying assumptions. A good agreement is found with the predictions made with the above-derived expression. The feasibility of extracting flow information from the backscattered intensity fluctuations is discussed.     

Bulk flow in ferrofluids in a uniform rotating magnetic field

Direct measurements of the bulk flow of a ferrofluid in a uniform rotating magnetic field were obtained using the ultrasonic velocity profile method. The fluid was observed to corotate with the field in a rigid-body-like fashion throughout the bulk of the container, except near the air-fluid interface, where it was observed to counterrotate. The results were found in qualitative agreement with the spin diffusion theory of Zaitsev and Shliomis [J. Appl. Mech. Tech. Phys. 10, 696 (1969)]10.1007/BF00907424.     

Eccentricity fluctuations are not the only source of elliptic flow fluctuations in a multiphase transport model

Sources of event-by-event elliptic flow fluctuations in relativistic heavy-ion collisions are investigated in a multiphase parton transport model(AMPT).Besides the well-known initial eccentricity fluctuations,several other sources of elliptic flow dynamical fluctuations are identified.One is fluctuations in initial parton configurations at a given eccentricity.Configuration fluctuations are found to be as important as eccentricity fluctuations in elliptic flow development.A second is quantum fluctuations in parton-parton interactions during system evolution.A third is fluctuations caused by hadronization and final-state hadronic scatterings.The magnitudes of these fluctuations are investigated relative to the eccentricity fluctuations and the average elliptic flow magnitude.The fluctuations from the latter two sources are found to be negative.The results may have important implications for the interpretation of elliptic flow data.     

How flow changes polymer depletion in a slit

A theoretical model is developed for predicting dynamic polymer depletion under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform fluid flow across a slit containing a solution with polymer chains. The two parallel and infinitely long walls are permeable to solvent only and the polymers do not adsorb to these walls. For a weak flow and a narrow slit, an analytic expression is derived to describe the steady-state polymer concentration profiles in a $ \Theta$ -solvent. In both $ \Theta$ - and good-solvents, we compute the time evolution of the concentration profiles for various flow rates characterized by the Peclet number. The model reveals the interplay of depletion, solvent condition, slit width, and the relative strength of the fluid flow.      

Fractal analysis of river flow fluctuations

We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at s_1×∼12 and s_2×∼130 months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second one is approximately equal to the well-known cycle of sun activity. Using Fourier Detrended Fluctuation Analysis, the sinusoidal trend is eliminated. The values of Hurst exponents of the runoff water of rivers without the sinusoidal trend show a long-range correlation behavior. For the Daugava river, the value of Hurst exponent is 0.52±0.01 and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.