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.     

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent -?2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.     

Locally Resolving Measurements of PSD,Particle Concentration and Particle Velocity by Means of TFS with Dual Beams

Transmission fluctuation spectrometry with spatial correlation (TFS‐SC) is based on transmitting two beams of radiation through a flowing suspension, whereby the distance of the beam centers is varied. Thus, the spatial correlation of the transmission fluctuations of the two beams is determined as a function of the beam distance. By numerical modeling, the transition functions of the correlation are found as a function of beam distance, beam diameters, particle diameter and beam intersection angle. Experimentally determined spatial correlation spectra can be inverted to obtain the particle concentration and particle size distribution by using the theoretical transition functions for mono‐sized particles. In addition, time correlations can be used to extract information on particle velocity. Some experimental results obtained by TFS‐SC are presented and discussed. This method appears promising for application in the local resolving of measurements of PSD, particle concentration and particle velocity in two‐phase flows, both in the laboratory and in process control.     

Long-range strain correlations in sheared colloidal glasses

Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external stress, we force structural rearrangements, and we identify long-range correlations in the fluctuations of microscopic strain and elucidate their scaling and spatial symmetry. The applied shear induces a transition from homogeneous to inhomogeneous flow at a critical shear rate, and we investigate the role of strain correlations in this transition.     

Acceleration correlations and pressure structure functions in high-reynolds number turbulence

We present measurements of fluid particle accelerations in turbulent water flow between counterrotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, nonintrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our measurements are in good agreement with the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high-Reynolds number turbulence by Obukhov and Yaglom in 1951 [Prikl. Mat. Mekh. 15, 3 (1951)]. The measured pressure structure functions display K41 scaling in the inertial range.     

Hydrodynamic screening and axisymmetric turbulence in the transient sedimentation of a dilute suspension at small Reynolds number

A theory of settling of a dilute suspension of identical spherical particles in a viscous incompressible fluid is developed on the basis of the equations of transient Stokesian dynamics. The equations describe hydrodynamic interactions between particles moving under the influence of a constant force, starting to act at a particular instant of time. For a dilute suspension, a monopole approximation can be used. It is argued that the growth of velocity fluctuations is bounded by a combination of two effects, destructive interference of the flow patterns of individual particles, and a rearrangement of particle positions leading to a time-dependent microstructure of the suspension. After a long time, the microstructure tends to a steady state. The corresponding structure factor is described phenomenologically. The corresponding pair correlation function and the velocity correlation functions describing axisymmetric turbulence on the length scale of the mean distance between particles are evaluated.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Non-identical particle correlations in STAR

The correlation function of non-identical particles is sensitive to the relative space-time asymmetries in particle emission. Analysing pion-kaon, pion-proton and kaon-proton correlation functions, measured in the Au+Au collisions by the STAR experiment at RHIC, we show that pions, kaons and protons are not emitted at the same average space-time coordinates. The shifts between pion, kaon and proton sources are consistent with the picture of a transverse collective flow. Results of the first measurement of proton-lambda correlations at STAR are in agreement with recent CERN and AGS data.     

Charge distribution and correlation functions near the boundary of a weakly nonideal plasma

We consider the electric double layer formed near the boundary of a weakly nonideal multicomponent classical plasma as a result of interparticle correlations. On the basis of the generalized plasma uncoupling of the equilibrium chain of BBGKY equations, which correctly takes into account correlations of particles at small distances, we find the two-particle and one-particle correlation functions near the surface of the plasma. The asymptotic form of the two-particle correlation function along the boundary of the plasma falls off as the power law 1/r³. The solution obtained here is qualitatively consistent with earlier results, but it takes into account particle correlations at small distances and hence does not have a singularity at the boundary of the plasma. Therefore in a charge-asymmetric plasma there are two correlation radii, the Debye radius D and the radius /tr2D. The thermodynamic functions of the surface layer are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 72–77, March, 1989.     

Cross-correlation properties of multiply-scattered dichromatic light from flowing colloidal particles

The cross-correlation properties of dichromatic light multiply-scattered by colloidal particles in a uniform flow are studied experimentally. It is shown that the correlation peak value of intensity fluctuations depends on the optical thickness of the sample and the number density of particles, whereas the decay time of cross-correlation functions is almost independent of the characteristics of particle suspensions. This result indicates that the number fluctuations as well as the speckle fluctuations contribute to the temporal variations in the intensity, and that the velocity of the uniform flow is measurable without being affected by the diffusive motion of the scatterers. The effect of wavelength difference is also examined.     

Influences of magnetic particle–particle interactions on orientational distributions and rheological properties for a colloidal dispersion composed of rod-like particle with a magnetic moment normal to the particle axis

We have investigated mainly the influences of magnetic particle–particle interactions on the orientational distribution and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane since the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the increase in the viscosity because the mean-field vector has only a component along the magnetic field direction.     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

Velocity fluctuations in fluidized suspensions probed by ultrasonic correlation spectroscopy

Velocity fluctuations in a fluidized suspension of particles are investigated using two new ultrasonic correlation spectroscopies: diffusing acoustic wave spectroscopy and dynamic sound scattering. These techniques probe both the local strain rate and rms velocity of the particles, providing important information about the spatial extent of velocity correlations. Our results demonstrate the power of these techniques to probe particle dynamics of fluidized suspensions, and suggest that the velocity correlations are essentially independent of Reynolds numbers for Re(p)<1.     

Sorting on periodic surfaces

Particles moving on crystalline surfaces and driven by external forces or flow fields can acquire velocities along directions that deviate from that of the external force. This effect depends upon the characteristics of the particles, most notably particle size or particle index of refraction, and can therefore be (and has been) used to sort different particles. We introduce a simple model for particles subject to thermal fluctuations and moving in appropriate potential landscapes. Numerical results are compared to recent experiments on landscapes produced with holographic optical tweezers and microfabricated technology. Our approach clarifies the relevance of different parameters, the direction and magnitude of the external force, particle size, and temperature.     

The quantum mechanics of particle-correlation measurements in high-energy heavy-ion collisions

The Hanbury Brown–Twiss (HBT) effect in two-particle correlations is a fundamental wave phenomenon that occurs at the sensitive elements of detectors; it is one of the few processes in elementary particle detection that depends on the wave mechanics of the produced particles. We analyze here, within a quantum mechanical framework for computing correlations among high-energy particles, how particle detectors produce the HBT effect. We focus on the role played by the wave functions of particles created in collisions and the sensitivity of the HBT effect to the arrival times of pairs at the detectors, and show that the two detector elements give an enhanced signal when the single-particle wave functions of the detected particles overlap at both elements within the characteristic atomic transition time of the elements. The measured pair correlation function is reduced when the delay in arrival times between pairs at the detectors is of order of or larger than the transition time.     

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. Due to these anisotropic responses and fluctuations, the violation of the fluctuation-dissipation theorem (FDT) is distinct for different components. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an effective temperature.     

Statistical transport theory of reacting two-component fluid: Light scattering from an A⇄B liquid

A theory of light scattering from a simple A?B reacting fluid in which molecular anisotropy has been neglected is presented. The theory is a molecular-statistical one based on Mori's linear response formalism. The time-dependent correlation functions are associated with transport coefficients and the zero time correlation functions are associated with thermodynamic derivatives. The effects of the reaction are observed from both density and concentration fluctuations as well as from cross correlations between density and concentration fluctuations.     

Negative viscosity due to magnetic properties of a non-dilute suspension composed of ferromagnetic rod-like particles with magnetic moment normal to the particle axis

The negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis, have been investigated. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rod-like particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.     

Three-dimensional particle cluster tracking algorithm using affine transformation

In Particle Image Velocimetry (PIV), the cross correlation tracking technique is widely used to analyze the particle images. The technique assumes that the fluid motion, within small regions of the flow field, is given by parallel movements over short time intervals. However, actual flow fields may have some distorted motion, such as rotation and shear. Therefore, if the distortion of the flow field is not negligible, the fluid motion can not be tracked well using the cross correlation technique. The author proposed a new particle tracking technique, based on the particle cluster matching using linear Affine Transformation. The algorithm can be applied to flow fields which exhibit characteristics such as rotation and shear. The deformation of the cluster pattern is expressed by the linear Affine Transformation. The parameter of the transformation can be determined using the least square technique from the particle positions. The effectiveness of the tracking techniques, including 3D cross correlation, Spring Model and Affine Transformation, were evaluated with synthetic data of three-dimensional flow field. The cross correlation technique could be applicable to the small deformation cases. When the deformation of particle pattern between two images are very large, the pattern deformation could not be expressed by the Affine Transformation, i.e., linear transformation, resulting in mis-tracking. However, the Spring Model technique was found to be more effective even in the larger deformation condition, because the Spring Model does not assume the linear transformation.