Slender Particles Research Articles

Precipitation mechanism of calcium carbonate fine particles in a three-phase reactor

Calcium carbonate (CaCO 3) particles are produced from precipitate in an aqueous suspension of calcium hydroxide (Ca(OH) 2) by injecting CO 2 gas. Three types of calcite particles, i.e. rhombohedral, rounded and slender particles, were finally obtained by changing the operating conditions, though in the early stage of the reaction amorphous calcium carbonate is always formed. The relationship between the particle shape or size and the operating conditions is investigated, and the mechanism of formation of these types of particles is discussed.

Separation of screw-sensed particles in a homogeneous shear field

The Stokes motions of three-dimensional screw-sensed slender particles in a homogeneous shear field are investigated, including the effects of buoyancy. Conclusions are drawn about the possibility of achieving a separation of mixtures of right- and left-handed particles. The linearity of the Stokes equations allows complex flows to be solved by adding the effects of the several terms which describe the flow in which the particle is immersed. The homogeneous shear flow considered here consists of three such terms; solutions for a series of 12 unit motions are sufficient to determine the hydrodynamic resistance tensors. The forces and torques experienced by screw-sensed particles are calculated from these 51 resistance tensors, using slender-filament theory. The results allow an estimate of the range of buoyancy parameters for which gravitational sedimentation can be neglected. The fundamental component of the particle motion is a rotation, at approximately the same angular velocity as that of the fluid. Superimposed on this are variations, of large period, in the particle orientation. A phase plane analysis is used to find the terminal orientations. Very long calculation times are required for the phase portrait. An approximate method based on azimuthally-averaged equations is developed to avoid the requirements for long time integration.

ENHANCEMENT OF THE SEDIMENTATION RATES OF FIBROUS SUSPENSIONS

The settling of suspensions of slender rod-like particles with large aspect ratios was studied. The novel technique of enhancement of sedimentation rates by the addition of buoyant particle promoters was applied to such suspensions. The settling rates could be increased by many times by this simple technique. Sedimentation velocity increases of between 5 to 7 times have been observed for fibrous suspensions of concentrations of about 0.5%. A statistical analysis of the experimental data was performed to establish a correlation for the enhancement in settling velocities. The sediment volume was unaffected by the presence of buoyant particles. The buoyant parjticles were found to adsorb some surfactants onto their surfaces.

Rheology of suspensions of rodlike particles

Suspensions of rigid rodlike particles in Newtonian suspending fluids are considered. We discuss the dependence of the relative viscosityμr upon the volume fraction of particlesϕ, their aspect ratioar, and the particle orientation distribution when the particles are sufficiently large that hydrodynamic forces are dominant. Theoretical results are reviewed for a variety of long slender particles. Experimental results obtained using classical rheometrical techniques are discussed. It is shown that whenar⩽25, data from several laboratories agree and they indicate thatμr depends more strongly uponϕ thanar. Previous experimental results using falling ball rheometry are discussed as well as some more recent findings. These are shown to provide insights heretofore unavailable into the macroscopic rheology of suspensions of randomly oriented and oriented rods.

Some asymptotic results for planar extension

Approximations to planar and uniaxial extensional viscosities are obtained in the limiting case of large extension rate. Model fluids for which results are obtained are the Phan-Thien-Tanner model, the Acierno-Marrucci model, the Giesekus model, and a FENE-dumbbell model. Detailed microstructural models for a dilute solution of rigid rodlike molecules, following Doi and Edwards, and a dilute suspension of slender axisymmetric particles, following Brenner, are also discussed. The effect of using the decoupling approximation (and avoiding solving the equation for the orientational distribution function) is examined, and the relation between results of Brenner and of Doi and Edwards for extensional flows of solutions and suspensions is exhibited. In all these cases, apart from any solvent contribution to the viscosity, it is shown that the elongational viscosity and the planar extensional viscosity are equal at high rates of extension. Under the same conditions the cross-viscosity in planar extension becomes vanishingly small in comparison with the planar extensional viscosity.

Drying Rate of Wood Particles With Longitudinal Mass Transfer

The drying of small wood particles of shape L:W:t = 3 to 5:2:1 is examined by three numerical models, and results are compared to measurements. (i) A one-dimensional rectangular model has liquid water concentrated in the center of a particle, and this is removed as an evaporation front propagates into the liquid. (ii) The one-dimensional model is also treated by the volume-averaged, or “smeared” approach, for which the moisture at any point is a distribution of liquid and vapor. For the simple rectangular geometry, the frontal and smeared models give similar results. (iii) Equivalent spherical particles are analyzed by a smeared model which includes capillarity. Reasonable agreement is obtained between the spherical results and the measurements, though an overprediction in drying rate occurs for slender particles.

Purification of a high molecular weight actin filament gelation protein from Acanthamoeba that shares antigenic determinants with vertebrate spectrins.

I have purified a high molecular weight actin filament gelation protein (GP-260) from Acanthamoeba castellanii, and found by immunological cross-reactivity that it is related to vertebrate spectrins, but not to two other high molecular weight actin-binding proteins, filamin or the microtubule-associated protein, MAP-2. GP-260 was purified by chromatography on DEAE-cellulose, selective precipitation with actin and myosin-II, chromatography on hydroxylapatite in 0.6 M Kl, and selective precipitation at low ionic strength. The yield was 1-2 micrograms/g cells. GP-260 had the same electrophoretic mobility in SDS as the 260,000-mol-wt alpha-chain of spectrin from pig erythrocytes and brain. Electron micrographs of GP-260 shadowed on mica showed slender rod-shaped particles 80-110 nm long. GP-260 raised the low shear apparent viscosity of solutions of Acanthamoeba actin filaments and, at 100 micrograms/ml, formed a gel with a 8 microM actin. Purified antibodies to GP-260 reacted with both 260,000- and 240,000-mol-wt polypeptides in samples of whole ameba proteins separated by gel electrophoresis in SDS, but only the 260,000-mol-wt polypeptide was extracted from the cell with 0.34 M sucrose and purified in this study. These antibodies to GP-260 also reacted with purified spectrin from pig brain and erythrocytes, and antibodies to human erythrocyte spectrin bound to GP-260 and the 240,000-mol-wt polypeptide present in the whole ameba. The antibodies to GP-260 did not bind to chicken gizzard filamin or pig brain MAP-2, but they did react with high molecular weight polypeptides from man, a marsupial, a fish, a clam, a myxomycete, and two other amebas. Fluorescent antibody staining with purified antibodies to GP-260 showed that it is concentrated near the plasma membrane in the ameba.

The Motion of Slender Particles in Shear Flow

A model was developed for calculating the motion of dilute suspensions of rigid, slender particles in a uniformly sheared viscous liquid, taking into ac count interactions between particles. The model was applied to the plane Couette flow problem in which particles are suspended in a liquid moving parallel to a plane with a uniform, shearing motion. The results of the model were compared to existing data, and good agreement was found between the calculated and experimental results. Using the model, results were also ob tained which illustrate the major effects of particle-particle interactions on the angular motion of the particles.

On the orderly nature of the motion of nonspherical aerosol particles. III. The effect of the particle—wall fluid-dynamic interaction

The motion of slender small bodies in a viscous medium near solid obstacles was studied theoretically and checked experimentally for physically similar situations in a liquid or a gas. The study was directed toward the understanding of the fluid-dynamic effect of a wall on the force, torque, and trajectories of slender aerosol particles, which was not considered until now in aerosol transport mechanics. The fluid-dynamic forces and torques operating on the particles were calculated, for very small Reynolds number and continuous-fluid conditions, by matching the inner and outer expansions of the solution to the Stokes equations, all in a region where both expansions were supposed to hold. Out of this matching, we obtained the distribution of Stokeslets on the body's axis, which led to the evaluation of the above forces and torques. The calculations were performed for a motion in a liquid, which made possible a comparison with experiments; the results, however, are indicative also for a gas. The trajectories of cylindrical particles subjected to the action of fluid-dynamic, inertial, and gravitational forces were numerically computed. The situations investigated were a (two-dimensional) motion in a still medium near an (infinite) wall with various inclinations to the horizontal, and (two-dimensional) motion within a Couette and a Poiseuille horizontal flow. It has been found that the wall exerts on the motion of our particles a noticeable influence which is manifested in their vertical, horizontal, and rotational velocities. The experiments, for a motion near a vertical plane, were carried out by continuous photographing of a macroscopic cylinder moving in a viscous liquid under conditions similar to those existing in aerosol systems. A satisfactory correlation between the experimental and the computational results was achieved, which established confidence in our theoretical calculational method.

The stress field of slender particles oriented by a non-Newtonian extensional flow

An analysis is presented of the creeping motion around a flow-oriented slender particle in a material medium subject to a uniaxial extension in the far field. A general quasi-steady rheological model is adopted, of a kind representing isotropic (Noll) fluids subject to time-independent velocity gradients, or isotropic solids subject to time-independent strain fields. The analysis is based on the premise of a shear-dominated motion in the near field, which is joined asymptotically to the extension-dominated motion in the far field. For axisymmetric particles, and to the order of terms in slenderness considered here, the far-field perturbation due to the particle can be represented as a distributed coaxial line force in a transversely isotropic medium whose strength is governed by the structure of the near-field rheology.On the basis of the results for a single particle, a formula is derived for the stress contribution due to the presence of oriented slender fibres in dilute suspension in a non-Newtonian fluid. For certain simple rheological models exhibiting a strong shear-thinning behaviour, the particle contribution to tensile stress is greatly diminished relative to the Newtonian case, as was predicted by an earlier rudimentary treatment (Goddard 1975). The present analysis is thought to be highly promising for applications to general composite materials.

Tensile stress contribution of flow-oriented slender particles in non-newtonian fluids

A formula is derived for the intrinsic stress contribution from closely-spaced, rod-like rigid particles suspended in a non-Newtonian liquid subject to a simple extensional flow. The present results indicate that, compared to the Newtonian-fluid result given previously by Batchelor [1], a much smaller particle-stress effect may occur in non-Newtonian fluid, owing to shear thinning and possible tensile stiffening in the fluid itself. While unsubstantiated by any critical experimental test, this prediction appears to agree qualitatively with some recent experimental observations of Charrier and Rieger [29] on glass fibers in polymer melts. Further work is suggested for the relevant slender-body theory, particularly the far-field body influence in non-linear fluids.

The slow motion of slender rod-like particles in a second-order fluid

The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.

Heat conduction in metal‐filled polymers: The role of particle size, shape, and orientation

AbstractElongated metal or other conductive particles can be added to a polymer or other poor conductor to produce a composite of enhanced conductivity. Elongated particles are generally more effective than spherical or irregular particles but very slender particles can be dramatically more effective. For example, cylindrical copper particles with length/diameter (L/D) = 20, randomly dispersed in epoxy resin at a loading of 5 percent copper by volume yield a composite with a thermal conductivity about 1.5 times that of the base resin. However, the same volume of copper particles with L/D = 50 can increase the conductivity by a factor of 5 or more.This paper presents a new type of analysis for predicting the thermal conductivity of disperse composites from the properties of the component phases and elementary characterizations of particle shapes and orientation. This analysis successfully predicted the sensitivity to particle shape which was confirmed by experiments also reported in this paper. These results suggest that highly elongated particles may be used to achieve dramatic modifications of thermal conductivity and the analysis presented here may be a useful tool in the design or development of disperse composites of specific thermal conductivity. The analysis may also apply to other properties such as electrical conductivity or magnetic permeability.

Equivalent ellipsoidal axis ratios of slender rod-like particles

Equivalent ellipsoidal axis ratios of slender rod-like particles

The force distribution on a slender twisted particle in a Stokes flow

The theory of Stokes flows about slender particles is considered for the case in which the particle cross-section is arbitrary and non-uniform along the axis of the particle, subject to certain smoothness assumptions. As distinct from previous works on slender particles in which the particle is represented approximately by a line distribution of Stokeslets, the representation adopted here is the exact one of a surface distribution of Stokeslets. This representation may then be used to recover the familiar one-dimensional integral equation for the equivalent line density of Stokeslets, together with estimates for the range of particle shapes for which the equation is valid. Within this range it is found that there is a class of particles for which the established perturbation scheme, which is used to obtain a solution to the integral equation, is singular. This class of particle shapes is illustrated by the example of a uniformly twisted particle whose pitch of twist is large enough compared with the cross-sectional dimension to ensure the validity of the equation, but small enough to make the usual method of solution singular. It is shown how the equation may be transformed so that an approximate solution can be found by means of a regular perturbation scheme. The results indicate that, for each of the axial and transverse components of motion, there is an equivalent particle of circular cross-section for which the total force and couple are the same as for the original particle. However, the radii of the equivalent cylinders are different for each component, the transverse component being affected by the twist while the axial component is not.

On the smoothing of stochastic couples in the theory of Brownian rotations of slender particles

On the smoothing of stochastic couples in the theory of Brownian rotations of slender particles

Three-Dimensional Presentation of Electrostatic Fields by Trajectories

The three-dimensional presentation of electrostatic fields by trajectories of charged slender particles in viscous medium is considered. Some Laplacian fields are presented with charged cotton fibers in air.

Separation and structure of components of nuclear polyhedrosis virus of the silkworm.

Morphology of structural components of nuclear polyhedrosis virus (NPV) particles of the silkworm (Bombyx mori Linné) was studied by electron microscope using negative staining. NPV particles isolated from polyhedra could be separated into five structural components by centrifugation in sucrose density gradients. The lowest band (band I) was found to consist of thick rod-shaped particles (330 by 80 nm) with knobby surfaces and with occasional protrusion at one end. The second band from the bottom (band II) was shown to consist mainly of slender rod-shaped particles (360 by 60 nm), in which internal structures were visible as a dense mass. Regular striations were also seen on the surface of these particles. By treatment with mercaptoethanol, these particles were drastically damaged, and in some cases the internal substances were partially released, producing empty inner membranes of various degrees of disintegration. In bands III and IV, both empty spherical and empty rod-shaped membranes were present. Band III was rich in empty spherical membranes which were shown to be the outer membranes of thick rod-shaped particles. The empty rod-shaped membranes, the inner membranes, were mainly located in band IV and have cross striations on the surface. It is remarkable that the uppermost band (band V) consisted purely of small spherical particles, somewhat heterogeneous in size and shape (around 20 to 25 nm in diameter), indicating the particles to be the degradation product of the virus particles. Similar particles could also be observed within the empty inner membranes.