Particles In Fluid Flow Research Articles

The acoustic generation of internal flow and rotation of levitated fluid particles

The detailed motions of levitated fluid particles in response to acoustic fields have become a topic of renewed interest because of the potential application of containerless processing techniques to a number of fundamental studies in heat or mass transfer and crystal growth. In these situations, acoustic fields are generally used to generate internal circulation to boost the transport rates, or to control the rotational motion of a levitated solution droplet. Two instances where such effects have been discovered and are being exploited will be discussed. The first case involves millimeter-size gas or vapor bubbles ultrasonically trapped in a resonant liquid cell and displaying vigorous internal circulation due to the excitation of high-frequency capillary waves at their interface. The second example deals with the drive of rotational motion of levitated droplets in ambient air and the effects of viscosity on this coupling. The results indicate that acoustic streaming flows are responsible for the generation of this controlled torque. [Work sponsored by NASA.]

An Experimental Investigation of Convergent Flow To Horizontal Wells

Abstract If the problem of fluid flow in a reservoir toward a well cannot beapproximated as a two-dimensional one, the analytical treatment becomes verydifficult. This is especially true when horizontal wells are involved and theend-effect cannot be neglected. There are, in the literature, mathematical expressions to calculateproductivity of horizontal wells for various geometric configurations and manyof these include the effect of flow convergence. Some of them appear to besignificantly in error. The paper describes experiments with an electrolytic model. This approachuses the analogy between the flow of fluid particles, driven by fluidpotential, in a porous medium and movement of ions, driven by electricalpotential, in an electrolyte. A simple and low-cost experimental setup permitsthe testing of various theoretical equations and the results are presented. Introduction In many cases the flow of fluids in a homogeneous reservoir toward a well, vertical or horizontal, can be analyzed simply when the problem istwo-dimensional. In some situations this approach may be sufficient; but when, because of more complicated geometry, the effect of convergence toward the tipof a well (as, for example, in the case of a vertical well partiallypenetrating a liquid- bearing porous matrix layer) has to be taken intoaccount, the difficulties of establishing the flow pattern and, consequently, calculations of the well productivity, may be significant. A common simplification is the assumption of the uniform flux along theactive well length. But this approach, as pointed out by Muskat(l), does notgive the correct results, even for the relatively simple case of a partiallypenetrating vertical well and steady-state flow. The situation becomes more difficult for horizontal wells of finite lengthdraining bounded volumes. There is usually a problem of convergent flow towarda well in a plane perpendicular to the well's axis, but on top of this there isa three-dimensional convergence toward the tips of the well. Probably in somesituations when, for example, the well is very long and draining a thin layerand narrow pattern, this additional convergence can be neglected.

On the theory of advective effects on biological dynamics in the sea

A general theoretical approach to the study of advective effects on biological oceanographic dynamics is formulated and some simple examples are presented. The theory of characteristics provides a model which rigorously combines aspects of local biological dynamics with consideration of fluid particle flow along Lagrangian trajectories. A local kinematical analysis is carried out for gradients both of velocity and of biological state variables. This is followed by a study of the effects of a stretching deformation, which contains a frontogenetic effect, on one‐ to three‐component biological systems. Problems include the approach to local biological equilibria and the stabilities of the equilibrium states; the competition between biological and advective equilibria; and nonlinear grazing processes and nutrient utilization.

Particle fracture, retention, and fluid flow in metal matrix composite friction joints

Friction joining of metal matrix composite (MMC)/MMC and MMC/AISI 304 stainless steel base materials is examined using a combination of experimental testing and numerical modeling. In particular, the fracture of reinforcing particles during the friction-joining operation is investigated. The particle diameter and interparticle spacing decrease and the area fraction of particles markedly increases in material immediately adjacent to the bondline. Smaller particles are observed in frictionwelded joints produced using high friction pressures. The principal effect of the forging operation is in decreasing the interparticle spacing. There was excellent correspondence between predicted fluid flow in A1/A1 joints and experimental test results examining the transfer of Al2O3 particles during the alloy 6061/alloy 6061 friction-joining operation. It is suggested that small-diameter particles formed due to fracture early in the friction-joining operation are retained at the bondline of MMC/MMC joints as a direct consequence of the flow of plasticized material and reinforcing particles in the contact zone. A combination of numerical modeling of fluid flow and direct experimental testing have confirmed that Al2O3 particles transfer from the stationary to the rotating boundary in MMC/MMC friction joints. Also, limit cycles embedded within the flow favor the retention of smalldiameter fractured particles at the bondline of MMC/MMC joints. A quite different situation exists in dissimilar MMC/AISI 304 stainless steel joining. In dissimilar joints, a dynamically quiescent region is formed immediately adjacent to the stainless steel boundary. It is suggested that the absence of flow of plasticized material promotes retention of fractured alumina particles in dissimilar joints.

Computer simulation of concentrated fluid-particle suspension flows in axisymmetric geometries

To investigate the particle migration effects and fluid-particle interaction occurring in the flow of highly concentrated fluid-particle suspensions, a numerical method has been developed for effective computer simulation in arbitrary axisymmetric geometries. In the mathematical flow model the suspension is treated as a generalized Newtonian fluid where the effective flow properties of the suspension (density and viscosity) are determined by the local volume fraction of the particles. The description of the particle motion is governed by a modified transport equation with diffusion coefficients accounting for the effects of shear-induced particle migrations. The strongly coupled system of flow and transport equations is solved by applying the Galerkin finite element method and a velocity-pressure projection scheme. The numerical results in tube flow demonstrate strong particle migration towards the center of the tube and an increasing blunting of the velocity profiles which is in good agreement with an available analytical solution. In the case of flow through a stenosed tube model, particle concentration is lowest at the site of maximum constriction whereas a strong accumulation of particles can be seen in the recirculation zone downstream of the stenosis.

Transient non-Newtonian flow of a suspension with a compressible particle phase

Equations governing transient two-phase fluid-particle laminar flow over an infinite porous flat plate are developed. Both phases are assumed to behave as non-Newtonian power-law fluids. The mathematical model accounts for particle-phase viscous and diffusive effects. The particles are assumed spherical in shape and having a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate initial and boundary conditions using an iterative, implicit, tri-diagonal finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to illustrate special trends of the solutions.

Compressible two-phase boundary-layer flow with finite particulate volume fraction

A continuum mathematical model governing compressible boundary-layer fluid-particle flow and heat transfer over a semi-infinite flat plate is developed. This model is based on separate balance laws of mass, linear momentum, and energy for both phases and allows for finite particle-phase volume fraction and viscous stresses. It is found that the volume fraction of suspended particles and, therefore, the particle-phase density is uniform in the boundary layer. Using this fact, the governing nonlinear partial differential equations are simplified and solved numerically by an iterative finite-difference method. Graphical results for flow and heat transfer properties are presented for various values of the particle-fluid viscosity ratio and the power index parameter for the viscosity-temperature relation.

Solutions for fluid-particle flow and heat transfer in a porous channel

Equations governing transient flow and heat transfer aspects of a particulate suspension with a constant finite volume fraction in a porous channel are developed. The steady-state problem is solved analytically and the transient problem is solved numerically by an iterative implicit finite difference scheme. The variations of the velocity and temperature profiles, volume flow rates, skin-friction coefficient, and the wall heat transfer coefficient with time and other physical parameters are illustrated graphically and discussed.

Numerical Models for Two-Phase Turbulent Flows

Numerical models for turbulent fluid-particle flows are reviewed. The two approaches typically used for modelling the dispersed (particle) phase are the trajectory and two-fluid formulations, while volume- averaged models are most common for the continuous (fluid) phase. The review is structured according to the turbulence models used for the continuous phase: turbulence energy-dissipation models, large- eddy simulations, direct numerical simulations, and discrete vortex models. The applications of these models to simulate particle dispersion due to fluid turbulence and the adjustments to the models to account for the modulation of the carrier phase turbulence by the particles are addressed.

Flow of non-newtonian particulate suspension with a compressible particle phase

Continuum equations for a two-phase fluid-particle flow are developed and applied to the problem of steady, laminar flow over an infinite porous flat plate. Both phases are assumed to behave as non-Newtonian power-law fluids. The effects of particle-particle interaction and diffusion of particles are taken into account in the mathematical model. In addition, the particle phase is assumed to have a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate boundary conditions using an iterative, implicit finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to elucidate interesting features of the solutions.

Remobilizing Surfactant Retarded Fluid Particle Interfaces: II. Controlling the Surface Mobility at Interfaces of Solutions Containing Surface Active Components

Convection of adsorbed surfactant along a fluid particle surface can accumulate surfactant at the trailing end of the particle. The nonuniform surface tensions that result cause Marangoni stresses which retard the surface mobility. This is the second part of a two-part study on controlling the mobility of surfactant laden interfaces. In Part 1 ( Phys. Fluids A 3, 3 (1991)), we established that a surfactant that is kinetically quickly exchanging at concentrations above its CMC can be used to control the surface mobility. Micelles of the surfactant, acting as monomer sources, keep the sublayer concentration uniform at the CMC. The surface concentration, in equilibrium with the sublayer, is made uniform and the Marangoni stresses along the interface are removed. A range of stress conditions from significantly retarded to stress-free interfacial motion can be achieved by varying the surfactant concentration about the CMC. In this study, it is demonstrated that this regulation mechanism is effective even when one of the fluid phases contains surface active components that by themselves would retard the surface flow. For this case, the concentration of remobilizing surfactant can be made large compared to the concentration of the other surface active components. The remobilizer therefore dominates adsorption along the interface and prevents the significant adsorption of the retarding surface active components. Surface mobility control is demonstrated experimentally using a three-phase periodic fluid particle flow that is very sensitive to Marangoni stresses.

Generalized diffusion theory of micromorphicly deformable particle-fluid continuum and bubble-liquid two-phase flows

In the paper [1] the basic concepts and equations were derived for the micromorphicly deformable particle-fluid two-phase flows, the constitutive equations have been constructed. The flow us fluid with deformable spherical particles, when the particle only expands radially, rotates and translates, is considered in this paper. For this case one can obtain the full motion's equations system. These equation together with the constitutive equations are sufficient to determine all of unknowns, and they can be used to study the bubble- liquid two-phase flow. The problems of kinematic wave and acoustic wave propagation in the bubble-liquid two-phase flow is studied.

Modelling of solid-liquid adsorption: effects of adsorbent heterogeneity

Effects of adsorbent heterogeneity on the adsorption of cobalt phthalocyanine dye on activated carbon have been studied. Adsorption experiments were carried out by varying the temperature and adsorbent mass in batch adsorbers and, in addition, the adsorbent particle size and fluid flow rate in a continuous stirred tank reactor (CSTR)-type adsorber in order to investigate the equilibrium and the kinetics of adsorption. The Brunauer-Emmett-Teller (BET), Langmuir with uniform distribution (LUD) and Langmuir-Freundlich equations are able to represent the equilibrium data with similar accuracy within the range of measurements. Reasonably large values of the heterogeneity parameter (2.69–2.86) show that the carbon surface is energetically heterogeneous. A mathematical model that describes the adsorption dynamics, including film-, pore- and concentration-dependent surface diffusion on an energetically and structurally heterogeneous adsorbent, is presented here and fitted to the experimental concentration vs. time curves obtained in the continuously stirred tank adsorber. Structural heterogeneity of the carbon, if not accounted for in the kinetic model, can be responsible for the very strong concentration dependence of the surface diffusion coefficient and for the variation in the parameter D o with particle size and adsorber porosity as shown in this work.

Transient heat and mass transfer of interacting vaporizing droplets in a linear array

A validated computer simulation model, based on an extended finite element software package, has been developed for the detailed analysis of colinear interacting vaporizing droplets in a heated air stream. The complete transport equations describing transient laminar axisymmetric fluid-particle flow with phase change have been solved for three closely-spaced n-octane fuel droplets and a free-stream ambient with Re 0 = 100, T ∞ = 1000 K and p ∞ = 10 atm. Of interest are the gas-phase temperatures jmd vapor concentrations with time, the transient interfacial phenomena and integral properties, such as Nu g , Sh g and c D , for each droplet. Comparisons with approximate analyses of three colinear monodisperse droplets and empirical studies for a solitary blowing sphere are included.

Dynamics of particles floating on liquid flowing in a semicircular open channel

The dynamic characteristics of surface-floating particles in liquids flowing in a two-dimensional, semicircular open channel is studied experimentally. For high visibility in the experiments, relatively large particles are employed whose particle-liquid density ratio is either equal to or less than unity. Particles of different size and geometry are tested in a water-glycerin mixture. A video camera traces the pathline of each particle from which the velocity and direction of particle motion are evaluated. Liquid velocity distribution is determined by hot-film anemometry. A modified dynamics (Basset-Boussinesq-Oseen) equation is derived and numerically solved by means of a finite-difference technique to determine fluid velocity. A new dimensionless parameter is disclosed which is pertinent to both particle geometry and fluid flow conditions. It correlates particle trajectory and velocity, trajectory dispersion and fluid-particle velocity ratio.

Effect of particle velocity fluctuations in particle-fluid flows

For many purposes, the flow of a particle-fluid mixture can be described by equations of balance of mass and momentum for each material, i.e., for the particles and the fluid. These equations must be supplemented by constitutive equations for the stresses and the momentum interaction. The stress in the particle component due to the random motions of the particles can be significant in some flows. In addition, the velocity fluctuations of the particles induce velocity fluctuations in the fluid, resulting in a stress there. Moreover, the momentum interaction term is also affected, resulting in a stress-like term. In this paper, the terms resulting from the particle velocity fluctuations are calculated by averaging the flow around a single sphere. The stresses and momentum interaction terms are given in terms of the average velocity and volume fraction fields, and the fluctuation stress for the particles. The particle stress must be given by a separate constitutive assumption. A framework for the particle velocity fluctuations that accounts for the evolution of the particle temperature is given. Constitutive equations for the stresses in the components, the Reynolds stress in the fluid, the momentum interaction and the interaction work term are calculated by averaging the appropriate quantity using the inviscid flow around a single sphere whose velocity is the mean particle velocity plus a velocity perturbation. The averaging process used is a version of ensemble averaging wherein the particle position is assumed to be distributed over the interior of a spherical “cell”, and the particle velocities are distributed so that the average of the fluctuation is zero, and the average of the negative of the fluctuation dyad is the particle Reynolds stress.

The fluid—particle flow phase diagram and the ideal sealing state for a vertical moving bed

A fluid—particle flow phase diagram, which correlates thirteen modes of moving-bed operations, has been established using the following basic dimensionless equation for pressure drop: ( d p d L )′ 1/ m = u′ s- u′ f This relation was deduced by modifying the Kwauk equation for moving beds. The ideal sealing state where no fluid passes through the moving bed is discussed in detail. This state defines a limiting condition for the operation of industrial diplegs and downcomers.

Remobilizing surfactant retarded fluid particle interfaces. I. Stress-free conditions at the interfaces of micellar solutions of surfactants with fast sorption kinetics

Surfactant molecules adsorb onto the interfaces of moving fluid particles and are convected to regions in which the surface flow converges. Accumulation of surfactant in these regions creates interfacial tension gradients that retard the surface flow. In this study it is argued theoretically and demonstrated experimentally that fluid movement on the surface of a drop or bubble can remain unhindered in the presence of a single adsorbed surfactant if, relative to the convective rate of transport of adsorbed surfactant along the surface, desorption is fast, and the bulk concentration is high enough so that diffusion away from the particle is fast. For this circumstance, a uniform surface concentration of surfactant is maintained, and no gradients in surface tension arise to retard the surface velocity. The fluid particle flow behaves as it would in the absence of surfactant save that it has a reduced, uniform surface tension. The remobilization of surfactant-laden interfaces of fluid particles is demonstrated experimentally in a three-phase periodic slug flow in a capillary tube in which a train of alternating air and aqueous slugs ride on an annular wetting film of fluorocarbon oil. Surfactant, dissolved in the aqueous slug phase, adsorbs onto and retards the aqueous–oil interface. The hydrodynamics of this flow is such that small changes in the mobility of this interface create large shear rates in the oil layer. This significantly increases the pressure drop required to drive the slug train at constant velocity. Three surface adsorbers are used to demonstrate surface remobilization: The polyethoxy, nonionic surfactants Triton X-100 and Brij-35, which have fast desorption kinetics and do not retard the surface flow at high concentrations and, as a counter example, the desorption hindered protein bovine serum albumin, which is shown to be unable to remobilize an interface even at high concentration.

MATHEMATICAL MODELING OF PARTICLEFLUID TWO-PHASE FLOW

Two-phase flow is modeled by considering interactions between partocles and their surrounding fluid at three scales: micro-scale of particle size, meso-scale of cluster size, and macro-scale for the overall particulate system consisting of clusters carried by the surrounding dilute phase. A further constraint has been found necessary to describe the stability of the twophase flow: the total energy always seeks a minimum for the dynamics of such particulate systems. The modeling can be used to explain numerous phenomena in particle-fluid flow, such as flow regime transitions and the heterogeneity of the two-phase system. It not only reflects the physical nature of the particle-fluid flow, but also makes possible quantitative description for both gas-solid (G/S) and liquid-solid (L/S) systems.

Temperature distribution and heat transfer in a particle-fluid flow past a heated horizontal plate

The temperature distribution in a laminar two-phase flow of a particle-fluid mixture over a heated horizontal plate is considered. Analytical expressions for the temperature fields and heat fluxes in each phase are obtained. It is found that the temperature distribution in a two-phase mixture flow differs from the corresponding single-phase case. Temperature profiles of the phases are independent of the distance along the plate and controlled by such mixture parameters as the particle size and concentration, the density ratio between the phases and the value of the Prandtl number. Moreover, the temperature fields of the phases in the mixture flow are independent of the horizontal velocity components and have a structure similar to that of a velocity profile of a single-phase flow over a flat plate at zero incidence with uniform suction.