Suspension Of Small Particles Research Articles

Size dependent growth behaviour related to the mosaic spread in ammonium sulphate crystals

The growth rate of small (1–120 μm) ammonium sulphate crystals, which were removed from a 970 L crystallizer via a fines classification line, were measured in a 2 L growth cell. An exponential size dependent growth (SDG) curve was used to model the data, revealing a size dependent growth rate up to a size of 220 μm. The same crystals were dried and sieved and the level of internal strain (“mosaic spread”) measured using the high intensity synchrotron radiation source. The results showed that the average mosaic spread and also the spread in mosaic spreads reduced with increasing crystal length. These results are consistent with the SDG rate measured for the small particles in suspension and points to internal lattice strain as being the cause of the SDG.

Parallel computational microhydrodynamics: scalable load-balancing strategies

The hydrodynamic interactions in a suspension of small particles in a viscous fluid is computed by a boundary integral velocity representation featuring a completed double-layer potential (completed double-layer boundary integral equation method or CDL = BIEM). A multiple expansion is used to represent interactions between distance particles, leading to a considerable improvement in computational speed. The resulting large linear system of equations provides an ideal setting for asynchronous iterative solvers (block Gauss-Seidel) on a message-passing MIMD parallel computer (Intel iPSC/860 Hypercube) using a supervisor-workers load-balancing strategy. Our benchmark results as a function of problem size and number of processors suggest that our algorithm will scale successfully to the massively parallel computers of the future.

Microhydrodynamics of particulate: Suspensions

Recent advances in the study of suspensions of small particles are reviewed. The advances considered fall within the categories of suspension rheology, sedimentation, dynamic simulation, and experimental techniques. One subtopic emphasized throughout this review is hydrodynamic diffusion, which arises due to the fluctuating motion of particles as they experience interactions with neighboring particles in a sheared or sedimenting suspension. The net effect of these interactions is that particles will migrate from regions of high concentration to low concentration, and from regions of high shear to low shear.

Further results for convection driven by the differential sedimentation of particles

When a well-mixed suspension of small particles is emplaced below a clear fluid whose density is greater than that of the interstitial fluid, but less than that of the bulk suspension, the subsequent settling of the dense particles releases buoyant interstitial fluid and drives convection in the overlying layer. Mixing of interstitial fluid and some entrained particles into the overlying fluid causes the density of the overlying fluid to evolve with time and changes the rate of descent of the interface between the sedimenting and convecting regions. These effects are investigated experimentally in a simple rectangular geometry using suspensions of spherical glass particles. It is found that the convecting region is well mixed in both composition and particle concentration and that the interfacial velocity may be predicted from the instantaneous (uniform) bulk density of the upper layer and the distribution of the particle settling velocities. In the case of an overlying density gradient, the convection does not extend through the depth of the overlying fluid but erodes the base of the gradient to form a well-mixed layer between the gradient and the sedimenting fluid. On completion of the first cycle of sedimentation-driven convection, sedimentation from this well-mixed layer produces further cycles of sedimentation-driven convection, which are of successively decreasing intensity and increasing duration. Whether the overlying fluid is uniform or stratified, both theory and experiment show that the particles that are lifted into the convection are smaller on average than those which settle at the base of the lower layer. Thus, when the lifted particles are eventually allowed to settle there is a discontinuity generated in the variation of the size distribution of particles with height in the final sedimented pile. This phenomenon may be an important mechanism for secondary layering in the deposits from turbidity currents and pyroclastic flows.

Interrelationships of Particle Structure and Flow in Concentrated Suspensions

Numerous commercial products either exist as concentrated suspensions of small particles or involve the processing of concentrated suspensions during some stage of their manufacture. Examples include foods, adhesives and glues, ceramic dispersions, paints, and polymer dispersions such as polyvinyl chloride plastisols. As a result, it is important for engineers to understand the flow behavior of these systems and how the flow behavior affects the way these materials can be processed.For mahy years, progress in understanding the flow behavior of concentrated suspensions was slow compared to progress on dilute systems, partly because of how the study of suspensions evolved. Building on Einstein's classical work for dilute suspensions of rigid spheres, many authors attempted to modify his equations to predict the flow behavior of more concentrated suspensions, but the extension of Einstein's work met with limited success, because nonhydrodynamic interactions cari be just as important as the hydrodynamic interactions considered by Einstein, and multiple particle interactions quickly complicate the problem as the particle concentration increases.

Convection and particle entrainment driven by differential sedimentation

When a suspension of small particles is overlain by a clear fluid whose density is greater than that of the interstitial fluid, but less than that of the bulk suspension, the settling of the dense suspended particles can lead to vigorous convection in the overlying fluid. This novel situation is investigated experimentally and theoretically. A sharp interface is observed between the convecting upper region and a stagnant lower region in which there is unimpeded sedimentation at low Reynolds number. There is no transport of fluid from the upper region into the lower, though there is mixing of both buoyant fluid and entrained particles from the lower region into the upper. The interface between the two regions is found to descend at a constant velocity. Systematic laboratory measurements have determined how this velocity depends on the densities of the layers and the distributions of settling velocities of the particles. A theoretical description is developed which calculates the evolution of the density of the lower region due to differential sedimentation of polydisperse particles. Buoyancy arguments based on the calculated density profile are used to place upper and lower bounds on the amount of particle entrainment into the upper layer and on the rate of fall of the interface between the convecting and sedimenting regions. The theoretical predictions are in good agreement with the experimental observations. The analysis of the interaction between convection and sedimentation in the system considered here may be particularly relevant to the description of evolving crystal-rich layers in magma chambers and of silt-laden outflow from rivers, and has a wide range of other industrial, environmental and geological applications.

The rate of coagulation of particles in a sedimenting dispersion at large Péclet number

The coagulation rate of a dilute polydisperse suspension of small particles is considered for large Péclet number, P ij , which provides a measure of the ratio of the relative gravity-induced motion to Brownian motion between two rigid spheres. In particular, a two-term expansion for the dimensionless coagulation rate (capture efficiency) as function of inverse Péclet number has been developed by using a regular perturbation method. It is found that Brownian diffusion can act to decrease the coagulation rate. Therefore, the additivity assumption is not valid in this regime.

Settling suspensions of colloidal silica: observations and X-ray measurements

Suspensions of colloidal particles execute Brownian motion and thus exhibit thermodynamic properties analogous to those of molecular systems. Hard-sphere colloidal silica suspensions undergo a disorder–order transition, i.e. freezing or crystallization, at high volume fractions. In suspensions of small particles the slow sedimentation permits the transition to occur at the bottom where the bulk of the crystalline sediment is formed by one-dimensional crystallization, as illustrated with photographs and scanning electron microscopy. X-Ray tomography measurements reveal a volume fraction discontinuity coincident with the observed crystal boundary occurring between the sediment and hindered setting region of the Kynch theory. Larger particles, however, form amorphous sediments because their rate of accumulation at the bottom exceeds the maximum crystal growth rate, in accord with classical kinetic theory. This theory is paired with Kynch's kinematic theory using an experimental sedimentation coefficient to interpret observations of settling suspensions.

Aerodynamik des Atemstroms im Nasenrachen*

The authors present a new technique for studying airflow patterns and particle deposition in the nasopharynx. The nasal cavities and the nasopharynx from the head of a human cadaver were filled with siliconrubber and a "positive" model was then produced by moulding with plastic. An apparatus was constructed to provide calibrated flow of propandiol in both directions. Flow characteristics were visualized by introducing small particles in suspension or by injecting methylene blue with a needle. In addition, test aerosol was drawn in through the model to demonstrate dust deposition sites in the nasopharynx. In the future, this method will enable us to examine the nasopharyngeal airflow patterns and deposition sites of inhaled particles.

EFFECTIVE CONDUCTIVITY OF A DILUTE SUSPENSION AT MODERATE PARTICLE PECLET NUMBERS

The contribution of a shear field to the effective conductivity of a dilute suspension of small particles freely suspended in a viscous fluid is examined. The case of long cylindrical inclusion aligned parallel to the vorticity of a simple shear flow is calculated for particle Peclet numbers of O(1). The solution involves a combination of a domain perturbation and a numerical calculation for the far and the near fields, respectively. The resulting convective contribution to the bulk heat flux is compared with previous asymptotic analysis for Pe → ∞.

Elementary theory of pseudo-turbulence in finely-dispersed suspensions

Relations are obtained to characterize the standard deviations of fluctuation velocity and the self-diffusion coefficients of the phase in flows of suspensions of small particles.

A small particle (iron oxide) suspension for detection of latent fingerprints on smooth surfaces

A small particle suspension of iron oxide black (Fe 3O 4) powder has been formulated for developing latent fingerprints on smooth surfaces. This new reagent was compared with the reported reagents known as small particle reagent (SPR) or molybdenum disulfide in suspension, and was found to be superior with regard to sensitivity, clarity and contrast. Excellent results were obtained on dry, wet or frost-covered smooth surfaces irrespective of whether the latent fingerprints were new or old. The developed black fingerprints are cleared very easily by washing with soap and water. The method was tested on specimen fingerprints taken from thirty donors. Scanning electron microscopic studies were performed on several powders to determine the particle size and to correlate it with the behaviour of small particle suspensions prepared from these powders.

Spreading of the interface at the top of a slightly polydisperse sedimenting suspension

The interface at the top of a dilute sedimenting suspension of small particles which are not identical does not remain sharp but instead becomes increasingly diffuse as the sedimentation proceeds. For more concentrated suspensions, the self-sharpening effect of hindered settling leads to a considerable reduction in the observed spreading of the sedimenting interface. In order to quantify this spreading, a light extinction technique was used to measure the concentration profile in the interface of a suspension of particles with a small spread of sizes as it fell past a thin sheet of light. A particle volume-fraction range of 0.002 ≤ Φ0 ≤ 0.15 was examined, and each fluid-particle system had a particle Reynolds number less than 10−3 and a Péclet number greater than 107 so that inertia and colloidal effects were negligible. Calculations of the spreading arising from the small degree of polydispersity in particle sizes and the self-sharpening effect are presented. Surprisingly, the measured vertical thickness of the interface was found to be several times that predicted from this theory.It is proposed that the observed spreading may be attributed to hydrodynamic interactions between particles that lead to fluctuations in particle settling velocities about the mean. An analysis of the data shows that the measured interface thickness, after subtracting off that predicted from polydispersity and self-sharpening, increases approximately with the square root of the settling distance and may therefore be described as a diffusion process, termed ‘self-induced hydrodynamic diffusion’. By sealing the hydrodynamic diffusivity as $D = au_{\frac{1}{2}}\hat{D}(\Phi_0)$, where u½ is the median hindered settling velocity, a is the median particle radius, and Φ0 is the volume fraction of particles well below the interface, an approximate analysis of the data was used to infer that the dimensionless scaled diffusion coefficient, $\hat{D}$, is between 1 and 2 for the smaller particle volume fractions examined, increases very rapidly with increasing concentration to a value between 10 and 15 for particle concentrations of a few percent by volume, and then levels off or declines slightly as the particle concentration is increased further.

Theory of Faraday rotation by dilute suspensions of small particles

We consider Faraday rotation by a dilute suspension of small particles embedded in a host. Using the Maxwell-Garnett approximation, we obtain an expression for the complex effective dielectric tensor of the composite in the low concentration limit. The Faraday coefficient becomes anomalously large near the surface plasmon frequency of the small particles. Numerical examples are given for the frequency-dependent off-diagonal part of the dielectric tensor and for the angle of rotation.

Scanning Electron Microscopy of Damage by Dust Deposits to Leaves and Petals

Dried droplets of prepared aqueous suspensions of small particles of silica gel, glass, clay, and silicon carbide on surfaces of leaves and petals were examined by scanning electron microscopy. Epidermal cells collapsed only in areas treated with suspensions known from previous studies to increase water loss from leaves and petals, while cells in the surrounding untreated areas remained turgid. The boundary between areas of turgid and collapsed cells corresponded almost exactly to the boundary of the area covered with dried deposits of the aqueous suspension. The deposits causing epidermal cell collapse also visibly altered the cuticular surface of leaves of Phaseolus coccineus L.

Hydromagnetic Stokes flow in a rotating fluid with suspended small particles

An initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about an axis normal to the plate. The flow is generated in the fluid-particle system due to non-torsional oscillations of a given frequency superimposed on the plate in the presence of a transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities, and the wall shear stress. The small and the large time behaviour of the solutions is discussed in some detail. The ultimate steady-state solutions and the structure of the associated boundary layers are determined with physical implications. It is shown that rotation and magnetic field affect the motion of the fluid relatively earlier than that of the particles when the time is small. The motion for large times is set up through inertial oscillations of frequency equal to twice the angular velocity of rotation. The ultimate boundary layers are established through inertial oscillations. The shear stress at the plate is calculated for all values of the frequency parameter. The small and large-time behaviour of the shear stress is discussed. The exact solutions for the velocity of fluid and the wall shear stress are evaluated numerically for the case of an impulsively moved plate. It is found that the drag and the lateral stress on the plate fluctuate during the non-equilibrium process of relaxation if the rotation is large. The present analysis is very general in the sense that many known results in various configurations are found to follow as special cases.

Ca2+ buffer sites in intact bovine rod outer segments: Introduction to a novel optical probe to measure ionic permeabilities in suspensions of small particles

The nature of the Ca2+ buffer sites in intact rod outer segments isolated from bovine retinas (ROS) was investigated. The predominant Ca2+ buffer in intact ROS was found to be negatively charged groups confined to the surface of the disk membranes. Accordingly, Ca2+ buffering in ROS was strongly influenced by the electrostatic surface potential. The concentration of Ca2+ buffer sites was about 30 mM, 80% of which were located at the membrane surface in the intradiskal space. A comparison with observations in model systems suggests that phosphatidylserine is the major Ca2+ buffer site in ROS. Protons and alkali cations could replace Ca2+ as mobile counterions for the fixed negatively charged groups. At physiological ionic strength, the total number of these diffusible, but osmotically inactive, counterions was as large as the number of osmotically active cations in ROS. The surface potential is dependent on the concentration of cations in ROS and can be measured with the optical dye neutral red. Addition of cations to the external solution led to the release of the internally bound dye as the cations crossed the outer membrane. The chemical and spectral properties of the dye enable its use as a real-time indicator of cation transport across the outer envelope of small particles in suspension. In this study, the dye method is illustrated by the use of well-defined ionophores in intact ROS and in liposomes. In the companion paper this method is used to describe the cation permeabilities native to ROS.

Microwave probing of electronic processes in small particle suspensions

The electronic properties of small particles of semiconducting materials have attracted considerable attention because they can mediate the photolytic decomposition of water1–6; a property which may prove useful in solar energy storage devices. Information about the initial electron–hole state formed on photolysis and the subsequent conduction and electron transfer processes occurring at the particle–solvent interface has previously been gained indirectly through steady-state and flash-photolysis studies of colloidal solutions that also contain well known electron donor and/or acceptor molecules. A more direct, ‘electrical’ method of probing such systems might be expected to lead to a more detailed understanding of the primary photoionization event and the ensuing bulk and surface electronic processes. We demonstrate here the feasibility of such direct probing of microscopic particles of semiconductor materials (TiO2, CdS and Se) suspended in a nonpolar liquid medium.

Gated Raman spectroscopy (GRAS): A new experimental approach for the measurement of Raman signals of particles in suspension

A new technique for the measurement of Raman spectra of small particles in suspension, such as biological cells, is described. The particles flow through a rectangular glass capillary mounted at the sample position of a laser Raman microspectrometer. The measuring volume inside the glass capillary is comparable to the volume of the particles. The elastic forward light scattering of the laser beam by the particles is used to monitor the presence of a particle in the measuring volume. Photon pulses from the Raman detector are counted only when a particle is inside the measuring volume. In this way the background signal caused by the suspending medium is suppressed, thus allowing measurement at very low particle concentrations. The technique, which is called gated Raman spectroscopy (GRAS) combines features such as: efficient light collection, suppression of background, and the possibility to use high laser powers. A great advantage is that this technique can be used for the study of (living) biological cells under physiological conditions. The GRAS technique is demonstrated with polystyrene particles and with unicellular algae chlorella vulgaris.

A theory of thixotropic plastic viscoelastic fluids with a time-dependent yield surface and its comparison to transient and steady state experiments on small particle filled polymer melts

Suspensions of small particles in polymer melts exhibit a time-dependent thixotropic responses. Previous theories of the behavior of such systems while including the capability of predicting non-Newtonian viscosities, normal stresses and yield values (indicating stresses below which there is no flow), have not treated thixotropy. Such a theory is presented here. A time and deformation rate dependent von Mises form yield function is proposed to represent the thixotropic and plastic characterisitcs. This is combined with a non-linear viscoelastic constitutive equation. The theory is compared with experimental data for carbon black and calcium carbonate filled polystyrene melts. Reasonably good agreement is obtained with both transient and steady-state experiments.