Cyclic motion of a grafted polymer under shear flow

The long-time dynamics of a single end-tethered chain under shear flow are studied using molecular and Brownian dynamics simulations of a flexible polymer. As observed in previous experiments with tethered DNA [Phys. Rev. Lett. 84, 4769 (2000)], under a flow sheared at constant rate the chain performs a cyclic motion. But, contrary to what has been previously suggested, a well-defined characteristic period exists and it is clearly revealed in the cross spectra of the chain extension along flow and gradient directions. The main cycling time scales like the time needed to stretch the polymer by convection, being about 10 times the relaxation time of the chain in flow. This coherent recursive motion introduces long memory in the fluid and suggests resonance effects under periodic external forcing.     

Oscillating viscosity in a lyotropic lamellar phase under shear flow

We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.     

Observation of droplet size oscillations in a two-phase fluid under shear flow

Experimental observations of droplet size sustained oscillations are reported in a two-phase flow between a lamellar and a sponge phase. Under shear flow, this system presents two different steady states made of monodisperse multilamellar droplets, separated by a shear-thinning transition. At low and high shear rates, the droplet size results from a balance between surface tension and viscous stress, whereas for intermediate shear rates it becomes a periodic function of time. A possible mechanism for such kinds of oscillations is discussed.     

Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow

Experimental results on the tank-treading-tumbling transition in the dynamics of a vesicle subjected to a shear flow as a function of a vesicle excess area, viscosity contrast, and the normalized shear rate are presented. Good agreement on the transition curve and scaling behavior with theory and numerical simulations was found. A new type of unsteady motion at a large degree of vesicle deformability was discovered and described as follows: a vesicle trembles around the flow direction, while the vesicle shape strongly oscillates.     

Probability analysis of contact forces in quasi-solid-liquid phase transition of granular shear flow

The quasi-solid-liquid phase transition exists widely in different fields,and attracts more attention due to its instinctive mechanism.The structure of force chains is an important factor to describe the phase transition properties.In this study,the discrete element model(DEM) is adopted to simulate a simple granular shear flow with period boundary condition on micro scale.The quasi-solid-liquid phase transition is obtained under various volume fractions and shear rates.Based on the DEM results,the probability distribution functions of the inter-particle contact force are obtained in different shear flow phases.The normal,tangential and total contact forces have the same distributions.The distribution can be fitted as the exponential function for the liquid-like phase,and as the Weibull function for the solid-like phase.To describe the progressive evolution of the force distribution in phase transition,we use the Weibull function and Corwin-Ngan function,respectively.Both of them can determine the probability distributions in different phases and the Weibull function shows more reasonable results.Finally,the force distributions are discussed to explain the characteristics of the force chain in the phase transition of granular shear flow.The distribution of the contact force is an indicator to determine the flow phase of granular materials.With the discussions on the statistical properties of the force chain,the phase transition of granular matter can be well understood.     

Brownian motion in a fluid in elongational flow

Brownian motion of a spherical particle in stationary elongational flow is studied. We derive the Langevin equation together with the fluctuation-dissipation theorem for the particle from nonequilibrium fluctuating hydrodynamics to linear order in the elongation-rate-dependent inverse penetration depths. We then analyze how the velocity autocorrelation function as well as the mean square displacement are modified by the elongational flow. We find that for times small compared to the inverse elongation rate the behavior is similar to that found in the absence of the elongational flow. Upon approaching times comparable to the inverse elongation rate the behavior changes and one passes into a time domain where it becomes fundamentally different. In particular, we discuss the modification of thet ^–3/2 long-time tail of the velocity autocorrelation function and comment on the resulting contribution to the mean square displacement. The possibility of defining a diffusion coefficient in both time domains is discussed.     

Nonlinear interaction between two components of motion upon precipitation of a heavy particle in a shear flow

When heavy particles move in a shear flow, the drag depends on the Reynolds number and, hence, on the magnitude of the particle velocity relatively to the medium. This leads to a nonlinear interaction between various components of motion. For example, when a particle precipitates in a horizontal air flow with vertical shear, it also acquires horizontal motion relative to air in addition to vertical motion. These two components of motion contribute to the hydrodynamic drag coefficient by affecting the Reynolds number and thereby influence each other. Steady motion of a particle in a flow with constant vertical shear is analyzed. Dimensionless criterion of significance of the nonlinear effect under consideration is determined. It is demonstrated that this effect can be significant in the near-surface atmospheric layer in the case of storm wind.     

Instability of a lamellar phase under shear flow: formation of multilamellar vesicles

The formation of closed-compact multilamellar vesicles (referred to in the literature as the "onion texture") obtained upon shearing lamellar phases is studied using small-angle light scattering and cross-polarized microscopy. By varying the shear rate gamma;, the gap cell D, and the smectic distance d, we show that: (i) the formation of this structure occurs homogeneously in the cell at a well-defined wave vector q(i), via a strain-controlled process, and (ii) the value of q(i) varies as (dgamma;/D)(1/3). These results strongly suggest that formation of multilamellar vesicles may be monitored by an undulation (buckling) instability of the membranes, as expected from theory.     

Correlated motion of two particles in a fluid

Conditional velocity cross correlation functions of the form <v_i (0)v_j (t); r_ij (0)> in the Lennard-Jones fluid are investigated by molecular dynamics simulation. As shown in previous work, these cross correlation functions may be related to memory functions in a similar manner as the usual velocity auto-correlation function. To compute the memory functions, a modified version of Detyna and Singer's algorithm has been used.     

Orientation and dynamics of a vesicle in tank-treading motion in shear flow

Experimental results on mean inclination angle and its fluctuation due to thermal noise in tank-treading motion of a vesicle in shear flow as a function of vesicle excess area, normalized shear rate, viscosity, and viscosity contrast between inner and outer fluids, , are presented. Good quantitative agreement with theory made for was found. At the dependence is altered significantly. Dependence of the vesicle shape on shear rate is consistent with theory. A tank-treading velocity of the vesicle membrane is found to be a periodic function close to that predicted by theory.     

Characteristic periodic motion of polymers in shear flow

The motion of both free and tethered polymer molecules as well as rigid Brownian rods in unbound shear flow is found to be characterized by a clear periodicity or tumbling frequency. Periodicity is shown using a combination of single molecule DNA experiments and computer simulations. In all cases, we develop scaling laws for this behavior and demonstrate that the frequency of characteristic periodic motion scales sublinearly with flow rate.     

Swinging and tumbling of fluid vesicles in shear flow

The dynamics of fluid vesicles in simple shear flow is studied using mesoscale simulations of dynamically triangulated surfaces, as well as a theoretical approach based on two variables: a shape parameter and the inclination angle, which has no adjustable parameters. We show that, between the well-known tank-treading and tumbling states, a new "swinging" state can appear. We predict the dynamic phase diagram as a function of the shear rate, the viscosities of the membrane and the internal fluid, and the reduced vesicle volume. Our results agree well with recent experiments.     

Interface motion in a planar spin-flip model derived from exclusion on the line

We consider a two-dimensional spin-flip model, which can be interpreted as the limit of the Ising model at low temperature and a small nonzero external field. In the hydrodynamic limit and for a special class of initial conditions, the motion of the interface is governed by a nonlinear partial differential equation with a lattice-distorted curvature term. In our proofs we use results about the hydrodynamic behavior of the weakly asymmetric exclusion process on the integers and also on the nonnegative integers with a trap at the boundary.     

Scalings of elliptic flow for a fluid at finite shear viscosity

Within a parton cascade approach we investigate the scaling of the differential elliptic flow v₂(p_T) with eccentricity _x and system size and its sensitivity to finite shear viscosity. We present calculations for shear viscosity to entropy density ratio η/s in the range from 1/4π up to 1/π, finding that the v₂ saturation value varies by about a factor 2. Scaling of v₂(p_T)/_x is seen also for finite η/s which indicates that it does not prove a perfect hydrodynamical behavior, but is compatible with a plasma at finite η/s. Introducing a suitable freeze-out condition, we see a significant reduction of v₂(p_T) especially at intermediate p_T and for more peripheral collisions. This causes a breaking of the scaling for both v₂(p_T) and the p_T-averaged v₂, while keeping the scaling of v₂(p_T)/v₂. This is in better agreement with the experimental observations and shows as a first indication that the η/s should be significantly lower than the pQCD estimates. We finally point out the necessity to include the hadronization via coalescence for a definite evaluation of η/s from intermediate p_T data.     

Simulation of front motion in a reacting condensed two phase mixture

The computational technique is developed in order to provide the scale capturing for numerical simulation of the thermal processes. The thermal front motion and gas flow dynamics as well as the rate of particle growth during the Carbon Combustion Synthesis of Oxides (CCSO) were predicted using the numerical simulation. In CCSO the exothermic oxidation of carbon nanoparticles generates a self-sustained thermal reaction front that propagates through the solid reactant mixture converting it to the desired complex oxides. The combusted carbon is emitted from the sample as carbon dioxide and its high rate of release increases the product porosity and friability. It was shown that the complicated finger front instability can be developed during the carbon combustion synthesis. This phenomenon results from a vortex gas flow in the reaction zone fed by the carbon dioxide co-flow and oxygen counter-flow filtration.     

Internal motion of a small element of fluid in an inviscid flow

We look at the internal motion of a small element of fluid in inviscid and incompressible flows by neglecting the actions of the other elements which constitutes the whole fluid. This free motion of the elements leads, in a finite time, to the divergence of the velocity field in the element and to its flattening in a plane.     

Roughness and dynamics of a contact line of a viscous fluid on a disordered substrate

We have studied the roughness and the dynamics of the contact line of a viscous liquid on a disordered substrate. We have used photolithographic techniques to obtain a controlled disorder with a correlation length ξ = 10μm. Liquids with different viscosity were used: water and aqueous glycerol solution. We have found that the roughness W of the contact line depends neither on the viscosity nor on the velocity v of the contact line for v in the range 0.2-20μm/s. W is found to scale with the length L of the line as L ^ζ with a roughness exponent ζ = 0.51±0.03. This value is similar to the one obtained with superfluid helium. In the present experiment, we have checked that the motion of the contact line is actually overdamped, so that the phenomenological equation first proposed by Ertas and Kardar should be relevant. However, our measurement of ζ is in disagreement with the predicted value ζ = 0.39. We have also analyzed the avalanche-like motion of the contact line. We find that the size distribution does not follow a power law dependence. Received 18 April 2002