Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.     

The rates of bimolecular thermal reactions taking into account local medium fluctuations

The contribution of local medium fluctuations to the rates of thermal chemical reactions was calculated for the first time. It was shown for the “ideal gas” model that the fluctuation contribution to a rate constant was proportional to the specific volume of particles and amounted to 1–10% already at densities of about 20 atmosphere densities. For this reason, chemical kinetics calculations of reaction rates should be performed taking into account local medium fluctuations before taking into account specific volume in the equation of state.     

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.     

The influence of random fluctuations on the behaviour of an aerosol

The purpose of the paper is to assess in a general manner the influence of random fluctuations in the local velocity, deposition rate, growth rate and coagulation constant on the behaviour of an aerosol. Using stochastic methods of probability theory we have shown that fluctuations in the local velocity lead to a broadening of the volume distribution which increases with time. The fluctuation in the deposition rate has a destabilizing effect and reduces the deterministically calculated rate of decay. Fluctuations in growth rate lead to the broadening of an initially monodisperse distribution and allow for evaporation and condensation. The rate of increase of suspended mass arising from this condensation-evaporation process is greater than the corresponding deterministic value.The effect of fluctuations in the coagulation constant leads to a decrease in the usual rate of removal of particles, although this is a small effect.The fluctuations are assumed to be stationary, random functions of time or position and in most cases are taken to be Gaussian variables. However, it is found that the infinite range of the Gaussian can lead to certain unphysical results and other distributions are examined.     

Electromagnetic fluctuations during fast reconnection in a laboratory plasma

Experimental evidence for a positive correlation is established between the magnitude of electromagnetic fluctuations up to the lower-hybrid frequency range and enhancement of reconnection rates in a well-controlled laboratory plasma. The fluctuations belong to the right-hand polarized whistler wave branch, propagating obliquely to the reconnecting magnetic field, with a phase velocity comparable to the relative drift velocity between electrons and ions. The measured short coherence lengths indicate their strongly nonlinear nature.     

Giant stress fluctuations at the jamming transition

We study the stress response to a steady imposed shear rate in a concentrated suspension of colloidal particles. We show that, in a small range of concentrations and shear rates, stress exhibits giant fluctuations. The amplitude of these fluctuations obeys a power-law behavior, up to the apparition of a new branch of flow, leading to an excess of high amplitude fluctuations which exhibit a well-defined periodicity.     

Experimental Study of Sheared Poloidal Flows in a Linear Plasma Machine

The radial profiles of fluctuations have been investigated in the Santander Linear Plasma Machine (SLPM). Experimental evidence of significant poloidal and E×B sheared flow has been observed in the plasma periphery. The resulting shearing rate of poloidal flow is comparable to the inverse of the correlation time of fluctuations, and the radial correlation is significantly reduced in the shear layer location. The possible role of flows driven by fluctuations and electron temperature gradients to explain these results is at present under investigation.     

Plastic Strain Localization and Its Stages in Al-Mg Alloys

The paper describes an experimental technique based on the use of a Vic-3D contactless digital optical system and digital image correlation for research in the mechanical behavior of a solid and its plastic deformation with space-time inhomogeneities. Using this technique, we analyze the evolution of inhomogeneous strain and local strain rate fields in AMg2m alloy at constant uniaxial tension rates. The analysis reveals quasi-periodic strain field homogenization in jerky flow: alternating phases of active local plastic flow (shear banding) and macroscale strain levelling. Also analyzed are the parameters of localized microscale plastic flow such as the height and width of shear bands, their velocity, and coefficient of plastic strain inhomogeneity. From a series of mechanical tests, the influence of the specimen geometry and loading rate on these parameters is estimated.     

Vorticity alignment and negative normal stresses in sheared attractive emulsions

Attractive emulsions near the colloidal glass transition are investigated by rheometry and optical microscopy under shear. We find that (i) the apparent viscosity eta drops with increasing shear rate, then remains approximately constant in a range of shear rates, then continues to decay; (ii) the first normal stress difference N1 transitions sharply from nearly zero to negative in the region of constant shear viscosity; and (iii) correspondingly, cylindrical flocs form, align along the vorticity, and undergo a log-rolling movement. An analysis of the interplay between steric constraints, attractive forces, and composition explains this behavior, which seems universal to several other complex systems.     

Arterial stenosis murmurs: an analysis of flow and pressure fields

The flow field distal to an arterial stenosis is simulated by a confined turbulent jet with moderate Reynolds numbers. The wall pressure fluctuations are related to the momentum fluctuations of the jet by the Poisson equation. A Green's function was derived to satisfy the boundary conditions on a cylindrical surface. This allows the solution of the Poisson's equation to include only a volume integral of the fluctuating momentum, weighed by the relative distance between the source and the sensor. The velocity fluctuations on the jet centerline and at the middle of the shear layer were measured using a laser Doppler anemometer. The wall pressure fluctuations were detected simultaneously by an array of nine wall-mounted pressure transducers along the axial direction. Cross correlation performed between the velocity and pressure fluctuations reveals that the pressure fluctuations were mostly imposed by the passage of turbulent eddies with a convective velocity that is a function of the jet exit velocity. The Strouhal number, defined by the frequency of the passing large-scale structure, is a function of the initial conditions only very close to the jet exit. Further downstream, where the effect of the initial conditions is lost, the Strouhal number approaches a constant irrespect of the jet Reynolds number. The contribution of a source near the jet exit to wall pressure fluctuation near the reattachment is rather weak due to the rapidly decaying weighting function in the axial direction. However, for sources located within one nozzle diameter from the sensor, the cross-spectral density function has a high magnitude with maximum coherence where the pressure spectral changes its slope.     

绝热搅拌槽内流体平均剪切速率的一种计算方法

基于流体流动的剪切速率与能量耗散率、以及能量散率与流体温升速率的关系,提出了根据搅拌过程中流体温升速率计算绝热搅拌槽内流体平均剪切速率的方法,并会对一个实验室用的小型高速搅拌系统,建立了流体平均剪切速率与流体黏度及搅拌转速关系的经验模型。本方法确定的是全槽流体的平均剪切速率,其应用不受叶轮类型的限制,可用于湍流搅拌,弥补了Metzner-Otto方法的若干不足。对于控温搅拌槽,可先在绝热条件下确定平均剪切速率与搅拌转速、流体流变性参数及体积的关系。     

Generalized nonlinear master equations for local fluctuations: Dimensionality expansions and augmented mean field theory

By application of a projection operator technique we derive a formally exact generalization of the nonlinear mean field master equation introduced recently for the study of local fluctuations in a reacting medium. Our starting point is a phenomenological cell master equation. The results of our theory are applicable to the theory of a fluctuating hydrodynamic reacting system. The mean field equation is placed on a firm theoretical foundation by showing it to be the lowest order approximation in an expansion in the dimensionality of the physical space keeping the product of the number of nearest neighbors (an increasing function of dimensionality) and the typical diffusion coefficient constant. A more accurate nonlinear master equation that allows for the correlation and fluctuations in the environment of a given volume element is derived in the form of an augmented mean field equation.Work supported in part by a grant from the National Science Foundation.     

Infrared spectroscopy and ultrasonic velocimetry as a tool for probing conformational flexibility of proteins

Abstract

Because of the crucial importance of structural fluctuations for function and stability of proteins, there is a strong interest for the relationships between structural fluctuations, the parameters of protein denaturation and the kinetics of H/D-exchange. Structural fluctuations can be described by volume and entropy fluctuations and these quantities are accessible via the isothermal compressibility, the thermal expansion and the isobaric heat capacity.

Our aim is to present the principal problem concerning the experimental procedures to answer those questions using lysozyme and α-lactalbumin. Whereas the transition parameters and the kinetics of the H/D-exchange were obtained using FTIR spectroscopy, the adiabatic compressibility was obtained by a combination of ultrasonic velocimetry and densitometry. It could be shown that the stability of the investigated proteins is correlated with reduced volume fluctuations. The expected direct correlation between H/D exchange rates and structural fluctuations could not be seen and it is assumed that the interactions are more complex than from the intuitive point of view.     

Instabilities in wormlike micelle systems

Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows.      

Observations of the collapse of dilute lyotropic lamellar phases under shear flow

Experimental evidence of the collapse of dilute lamellar phases due to shear flow is presented. Two systems are used: one composed of brine and an ionic surfactant, and another composed of water, a nonionic surfactant, and cosurfactant. We observe this transition for a range of lamellar spacings and brine salinity. The results are in reasonable agreement with recent theory in which the suppression of fluctuations by shear plays an important role.     

Shear-induced ordering of lamellar and gyroid structures observed in a nonionic surfactant/water system

The shear-induced ordering of lamellar and gyroid structures of a nonionic surfactant C₁₆E₇/D₂O system in a Couette shear cell ( 0.001 < < 10 s^-1, : shear rate) has been investigated by using a small angle neutron scattering technique. In the lamellar phase, the steady shear flow having > 0.01 s^-1 suppresses undulation fluctuations of lamellae (Maxwell effect). This suppression of fluctuations brings two effects; 1) shear-induced lamellae ordering toward a parallel orientation and 2) obstruction of a lamellar↦gyroid transition. It is quite interesting to note that there is a characteristic shear rate range ( 0.01 < < 0.3 s^-1), where both effects take place. We have also investigated the shear effects on the gyroid phase. Below the characteristic shear rate range, the gyroid structure keeps three-dimensional network lattice, while above the characteristic shear rate range, the gyroid structure transforms to the parallel orientation lamellae (shear-induced gyroid-lamellar transition). Thus the shear flow having the characteristic shear rate plays very important roles in shear ordering phenomena. Received 26 June 2000 and Received in final form 12 January 2001     

Hydrodynamics and the fluctuation theorem

The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume, and time. We study the fluctuation theorem in computer simulations of planar shear flow. The simulations are performed by employing the method of multiparticle collision dynamics, which captures both thermal fluctuations and hydrodynamic interactions. The main outcome of our analysis is that the fluctuation theorem is verified at any averaging time provided that the measurement volume exhibits a specific dependence on a hydrodynamic time scale.     

Shear banding in mesoscopic dusty plasma liquids

We experimentally demonstrate shear banding and construct a microscopic dynamic picture of a sheared 2D mesoscopic dust Coulomb liquid at the kinetic level. Under the topological constraints from the discreteness and finite boundary, the nonlinear threshold-type response of motion to the local stress induced by thermal and external drives leads to shear thinning and the enhanced avalanche-type local topological transitions with stress relaxation in the form of clusters. It causes the formation of the outer shear bands in which the mean shear rate, the velocity fluctuations, and the structural rearrangement rate are all enhanced, and leaves a weakly perturbed center band. The typical size of the cooperative hopping vortex (about three interparticle distance) sets up a common length scale for the widths of the confinement induced layering and the shear band.     

Particle dynamics in sheared granular matter

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity V(y) declines strongly with distance y from the moving wall, independent of the shear rate and of the shear dynamics. Local rms velocity fluctuations deltaV(y) scale with the local velocity gradient to the power 0.4+/-0.05. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature [deltaV(y)](2) and density dependent viscosity.     

Fluctuations of dielectric constant in a system of hard spheres

The correlation function for fluctuations of a dielectric constant in a latex-like suspension of spherical particles was calculated. An exact analytical expression was derived for the correlation function using the Percus-Yewick approximation for a system of hard spheres. The obtained results made it possible to calculate the indicatrix of single scattering, the extinction coefficient, and the transport mean path. It is shown that, starting with a volume content of about ten percent, the “gas” approximation becomes invalid, and optical parameters begin to depend on concentration in quite a complicated manner. In particular, the extinction length and the mean transport path, which are the basic parameters in describing the coherent effects in multiple scattering, vary nonmonotonically with concentration. It is found that there exists a range of sizes and concentrations of scattering particles in which an effect similar to the emergence of blue phase in liquid crystals can be observed.