Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime. Received 22 February 1999 and Received in final form 14 June 1999     

On the influence of the hydrodynamic interactions on the aggregation rate of magnetic spheres in a dilute suspension

Magnetostatic attraction may lead to formation of aggregates in stable colloidal magnetic suspensions and magneto-rheological suspensions. The aggregation problem of magnetic composites under differential sedimentation is a key problem in the control of the instability of non-Brownian suspensions. Against these attractive forces are the electrostatic repulsion and the hydrodynamic interactions acting as stabilizing effects to the suspension. This work concerns an investigation of the pairwise interaction of magnetic particles in a dilute sedimenting suspension. We focus attention on suspensions where the Péclet number is large (negligible Brownian motion) and where the Reynolds number (negligible inertia) is small. The suspension is composed of magnetic micro-spheres of different radius and density immersed in a Newtonian fluid moving under the action of gravity. The theoretical calculations are based on direct computations of the hydrodynamic and the magnetic interactions among the rigid spheres in the regime of low particle Reynolds number. From the limiting trajectory in which aggregation occurs, we calculate the collision efficiency, representing the dimensionless rate at which aggregates are formed. The numerical results show clear evidence that the hydrodynamic interactions are of fundamental relevance in the process of magnetic particle aggregation. We compare the stabilizing effects between electrostatic repulsion and hydrodynamic interactions.     

Magnetic permeability of a diphasic flow, made of liquid gallium and iron beads

Magnetohydrodynamics studies in laboratory experiments have long been restricted to low magnetic Reynolds number flows, mainly as a result of the very high magnetic diffusivity λ = 1/μσ of common conducting fluids (μ is the fluid's magnetic permeability and σ its electrical conductivity). The best conductivities are found in liquid metals which have a unit magnetic permeability, relative to vacuum. We show experimentally that a suspension of solid particles with a high magnetic permeability in a liquid metal yields an effective medium that has a high electrical conductivity and an enhanced magnetic permeability. The dispersion of the beads results from the turbulent fluid motion. The range of accessible magnetic Reynolds number can be increased by a factor of as much as 4 in our experimental setup. Received 6 March 2000 and Received in final form 13 July 2000     

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.     

Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically. The channel asymmetry is generated by propagation of waves on the channel walls travelling with different amplitudes, phases but with the same speed. The long wavelength and low Reynolds number assumptions are considered in obtaining solution for the flow. The flow is investigated in a wave frame of reference moving with velocity of the wave. Closed form expressions have been obtained for the stream function and the axial velocity component in fixed frame. The effects of phase difference, Knudsen number and magnetic field on the pumping characteristics and velocity field are discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.     

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.     

Sound Attenuation in a Circular Duct of a Viscous Medium in the Absence of Mean Flow

Abstract

An analytical method to study the effect of viscosity of a medium and the wave number on sound propagation and sound attenuation numbers in circular ducts has been presented. The method is based on the variation of parameters of the solution corresponding to the case of inviscid acoustic waves in circular ducts and axisymmetric modes. A mathematical model is constructed to describe the physical problem in general. Three basic assumptions have been considered, namely, each flow quantity has been written as the sum of a steady mean flow and an unsteady acoustic flow quantity. The effect of thermal conductivity of the gas has been neglected as well as no mean flow. The results for a wide range of wave numbers and Reynolds numbers show that for a viscous medium, the propagation number is a weak function of the Reynolds number, and as the Reynolds number increases, the propagation number approaches its inviscid value. Also the propagation number is independent of the wave number. For the attenuation number, it decreases monotonically with the increase of the Reynolds number and it vanishes when Reynolds number exceeds 10⁴.     

Ponderomotive effects in intense pumping wave action on electron and plasma bunches

Ponderomotive effects that arise when an intense plane pumping wave acts on low-concentration electron and plasma bunches are theoretically studied within the framework of a one-dimensional model. Using the Lagrange variables, an electron (plasma) bunch under the action of a pumping field can be represented as a gas comprising macroparticles with ponderomotive and Coulomb interactions. The ponderomotive force at small interparticle distances is attractive, that is, directed oppositely to the Coulomb force; it cannot, however, completely balance the latter. The constructed model is used to study superradiance, which arises when an intense pumping wave acts on an extended electron bunch. Radiation is then scattered in the form of narrow pulses whose amplitude is proportional to the total number of particles in the bunch. In addition, we describe acceleration of a neutral plasma layer, narrow on the wavelength scale, in the field of an intense wave and radiation field-induced partial contraction of an electron bunch with an incompletely compensated charge.     

Linear response theory of sedimentation and diffusion in a suspension of spherical particles

We discuss the problem of sedimentation and diffusion in a suspension of interacting spherical particles. We consider external forces acting on the particles and study the linear response of density and current on the basis of the generalized Smoluchowski equation. The theory leads to a natural distinction between a hydrodynamic and a diffusion current. Each of these is defined as an observable in terms of the generalized mobility matrix. We derive general relations for the response functions.     

Dispersion of a three-level quantum system in a bichromatic field

We consider aspects of the interaction between a V-type three-level quantum system and the bichromatic field of two waves, one of which is assumed to be weak. We trace the dynamics of splitting into individual components for the spectral contours of the absorption coefficient (gain) for the signal wave. We discuss the effect of amplification of the signal wave for its frequency-degenerate two-wave interaction with pumping, when the field frequency is tuned to the “zero dispersion” point. We determine the conditions with respect to the concentration of resonant atoms and the spectral regions of the frequencies of the interacting waves for which, in order to correctly describe the effects under consideration, we need to take into account the effect of pumping and the signal in both dipole-allowed transitions of an ensemble of V type three-level quantum systems. We present the results of numerical calculations of the imaginary and real parts of the susceptibility of the resonant medium at the frequency of the signal wave, as a function of the parameters for the high-power radiation and resonant transitions of the quantum V system. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 5, pp. 631–636, September–October, 2007.     

Possible localized transport induced by a wave propagating along a vacuum–matter interface

Macroscopic derivation of the entrainment of matter induced by a surface elastic wave propagating along the flexible vacuum–matter interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. The critical reflux values associated with the product of the second-order (unit) body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the matter-freezed or zero-volume-flow-rate states for specific Reynolds numbers and wave numbers which might be linked to the evolution of the Universe.     

Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

We construct the hydrodynamic equations for suspensions of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions: (i) Nematic SPP suspensions are always absolutely unstable at long wavelengths. (ii) SPP suspensions support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wave number regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspensions are invariably convectively unstable. (iv) The variance in the number N of particles, divided by the mean , diverges as (2/3 ) in polar-ordered SPP suspensions.     

Possible Dark States Induced by?a?Surface Wave Along?a?Vacuum-Matter Boundary

Possible dark states could be induced after derivations of the entrainment of matter induced by a surface wave propagating along the flexible vacuum-matter boundary by considering the nonlinear coupling between the interface and the rarefaction effect. The nonrelativistic limit of the relativistic Navier-Stokes equations was considered and analytically solved by a perturbation approach. The critical reflux values associated with the product of the second-order body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the critical bounds for possible dark states corresponding to specific Reynolds numbers (ratio of wave inertia and viscous dissipation effects) and wave numbers which might be linked to the dissipative evolution of certain large-scale structure during the relativistic heavy-ion collisions.     

Capture into resonance: a method for efficient control

To achieve large changes in adiabatic invariants using small control input, a conservative dynamical system must possess an internal resonance. Capture into resonance is an inherently probabilistic process. We propose a control method to make it more structured. We study the motion of charged particles in an electromagnetic field as an example of such a system. When the nominal dynamics brings particles close to a resonance surface, a short control pulse forces the capture of a particle into the resonance with the wave. A captured particle is transported by the wave across the energy levels. The second pulse releases a particle from the resonance when the desired energy level is achieved. We discuss the distribution of energy achieved by the method.     

Wave coagulation of a polydisperse gas suspension in the technology of gasification and Cryostatting of liquefied natural gas

We analyze the flow of a polydisperse suspension of methane droplets in a plane channel with simultaneous coagulation of disperse fraction particles under the action of the wave field generated in the carrier medium—gaseous methane—by oscillating parts of the channel walls. The frequency of in-phase oscillations of the walls is equal to the fundamental frequency for the transverse cross section of the channel filled with gaseous methane. In the vicinity of the radiator, a standing wave of the velocity field forms in the direction transverse to the flow and the intensity of coagulation of particles from different fractions upon their collisions increases due to mutual displacement. We describe the evolution of the dispersiveness of a vapor-droplet flow under the action of the wave field of a standing wave whose front moves transversely to the flow.     

Controlled cell aggregation in a pulsed acoustic field

Cell aggregation in ultrasonic resonators can be obtained in a few seconds. Hundreds even thousands of cells can be levitated in suspension and generate 2D or 3D aggregates. Nevertheless, the aggregation rate and the 2D or 3D configurations of the resultant aggregates are very difficult to control. This work reports on a novel way of generating and controlling particle and cell aggregates using pulsed ultrasound. This technique specifically explores (in addition to the ultrasound wave, frequency and amplitude) the time of ultrasound application, i.e. the number of pulses as well as the pulse repetition frequency. We demonstrate that with pulsed ultrasound, particles and/or cells levitate in suspension, as with continuous ultrasound, and the aggregation rate can be modified in a controlled manner. By carefully tuning the number of pulses and the repetition frequency, the 3-D and 2-D configurations of the aggregates can be selectively generated. In addition, pulsed ultrasound limits transducer heating, thus allowing for higher acoustic energies than those currently employed with continuous ultrasound.     

DC conductivity of a suspension of insulating particles with internal rotation

We analyse the consequences of Quincke rotation on the conductivity of a suspension. Quincke rotation refers to the spontaneous rotation of insulating particles dispersed in a slightly conducting liquid and subject to a high DC electric field: above a critical field, each particle rotates continuously around itself with an axis pointing in any direction perpendicular to the DC field. When the suspension is subject to an electric field lower than the threshold one, the presence of insulating particles in the host liquid decreases the bulk conductivity since the particles form obstacles to ion migration. But for electric fields higher than the critical one, the particles rotate and facilitate ion migration: the effective conductivity of the suspension is increased. We provide a theoretical analysis of the impact of Quincke rotation on the apparent conductivity of a suspension and we present experimental results obtained with a suspension of PMMA particles dispersed in weakly conducting liquids.     

Roll waves on flowing cornstarch suspensions

We report a traveling wave instability in low Reynolds number flows of aqueous concentrated suspensions of corn starch. The experimental observations are difficult to reconcile with theoretical predictions based on simple rheological models which indicate that flows are stable at low Reynolds number.     

高超声速条件下7°直圆锥边界层转捩实验研究

在Ma=6低噪声风洞中开展了半锥角7?的直圆锥边界层转捩相关实验研究.利用响应频率达到MHz量级的高频压力传感器对圆锥壁面脉动压力进行了测量,研究了高超声速圆锥边界层中扰动波的发展过程.结果表明:高超声速圆锥边界层中第二模态扰动波产生的位置以及扰动波特征频率和波长等参数受雷诺数影响较大,当单位雷诺数从2×106m~(-1)增加到8×106m~(-1)时,第二模态波的特征频率从55 k Hz增加到226 k Hz;随着单位雷诺数增加,边界层中扰动增长速度加快,第二模态波出现在圆锥表面更靠近上游的位置;相同单位雷诺数条件下,随着第二模态波的向下游传播,其特征频率逐渐减小.通过对比发现自由来流湍流度对边界层中扰动波的发展同样有较大影响,自由来流湍流度降低,边界层中的第二模态波的特征频率明显减小.利用互相关分析得出第二模态扰动波在边界层中的传播速度大约为当地主流速度的0.8—0.9倍.在1?小攻角条件下,圆锥迎风面和背风面边界层发展呈现出明显的差异,背风面边界层中扰动发展提前,第二模态波出现在更靠近上游的位置,而迎风面中扰动发展受到抑制,第二模态波特征频率更大.     

Hydrodynamic regimes of active rotators at fluid interfaces

We analyze the collective motion of suspensions of active rotators at low Reynolds numbers which interact hydrodynamically. We introduce a simple model for a rotator which allows us to classify the relevant dynamical regimes of the suspension. We characterize the collective velocity at which rotators displace and analyze its implications at long times, when these rotator suspensions diffuse. We analyze the differences with respect to diffusion in suspensions of passive particles, and assess the relevance of the Stokes-Einstein relation on rotators' diffusivity.