Yoji Nakajima

Calculation of electrostatic force between two charged dielectric spheres by the re-expansion method

Abstract In the calculation of the electrostatic force between two charged dielectric spheres, it is not easy to include the contribution of higher-order polarization which becomes very important when the spheres are closely located. We found that the re-expansion technique proposed by Washizu for the precise calculation of the dielectrophoretic force on a single sphere in an arbitrary external electrostatic field can be applied directly to a two-particle system. In this paper, the mathematical procedure for the application and some examples of the numerical calculation are presented. Comparison with existing methods, i.e., the method of successive images for conducting spheres and the bispherical coordinate method, shows the validity of the present approach. Convergence of the re-expansion method is poor if the ratio of the radii of the spheres is large and if the particles are closely spaced. Therefore, calculation of the force between a sphere and a dielectric plane wall is the hardest problem for the re-expansion method. Hence the electrostatic force on a small sphere resting on a large sphere is calculated to show that we can use the re-expansion method even for this case by substituting a large sphere for a plane wall in the force calculation.

Electrostatic collection of submicron particles with the aid of electrostatic agglomeration promoted by particle vibration

Abstract Submicron particles suspended in flue gas receive an attraction due to electrostatic polarization to the charged core particles. In order to make efficient use of the polarization forces, we have considered the use of strong vibration of core particles or the application of intense acoustic wave. The electrostatic polarization force has been evaluated precisely by the re-expansion method. Since the streaming around the core particle was also important for the analysis, we have used the method of matched asymptotic expansions to find a perturbation solution to Navier–Stokes equations. These results have been combined to simulate the motion of a small dust particle around the charged core particle to calculate the agglomeration kernel. For obtaining the agglomeration kernel experimentally, we have contrived a novel apparatus to measure the changes in size and electrostatic charge of a single core particle, on which monodisperse submicron particles agglomerated. An improved LDV technique for accurate measurement of core size and charge are also given in the appendix. Although the observed values for the agglomeration kernel scattered, the agreement between the observed and the calculated kernel was reasonable to show the theoretical consideration is acceptable.

Electrostatic field and force calculation for a chain of identical dielectric spheres aligned parallel to uniformly applied electric field

Abstract We apply the re-expansion method proposed by Washizu to a linear particle chain aligned in the direction of a uniform electric field. The calculated results show that the potential distribution around the particles becomes very complicated and the electric field is highly concentrated near the contact points of particles. The pearl-chain forming force rapidly increases with increasing number of particles and reaches a saturation value for chains consisting of some tens of particles. The force at a contact point in a particle chain is reduced near both the ends of the chain but is still much stronger than the interaction force of the two particles. The present method can be extended to cases of coated particles. One example of the application is a new model for the surface roughness of electro-rheological (ER) particles. A layered particle model, in which the surface roughness is replaced with an equivalent surface layer, provides a more reasonable method for the force calculation, because the existing gap model is too sensitive to the fictitious interstice representing the roughness. Another example is the effect of surface coating to reduce the electric field at the contact points. Such a coating will be preferable for ER particles to prevent electrical breakdown in the fluid.

Experimental discussion on maximum surface charge density of fine particles sustainable in normal atmosphere

Abstract The maximum surface charge density for large spherical particles in normal atmosphere is thought to be 27 μC/m2, assuming that the electric breakdown field strength of air is 3 MV/m. For a given surface charge density, however, the layer of a very high electric field strength for electron avalanche in air around the particle becomes thin, when the particle size is small. As a result, a higher limit in the surface charge density is expected for small particles. In the present experiment, droplets with high surface charge density in the size range between 1 and 6 μm in diameter are prepared by evaporating negatively charged liquid particles of 45 μm. For a few kinds of liquids, the size and the charge of individual droplets are measured simultaneously by using an LDV system to obtain frequency histograms for the charges of droplets with several narrow size ranges. The results indicate that the maximum surface charge density sustainable in atmosphere for negatively charged particles depends mainly on the particle size and is inversely proportional to the square root of particle size to give very high surface charge density in micrometer order size range.

Scavenging of submicron particles by coarse particles under the effects of electrostatic field and particle vibration

Abstract The technique of electrostatic coagulation aided by the hydrodynamic effect of a vibrating particle is proposed for the scavenging of submicron particles: a highly charged particle of a few micrometers in diameter is vibrated to induce a secondary steady flow around the particle. The flow blows the submicron particles into a region close to the charged particle, where the electrostatic gradient force becomes strong enough to adsorb the submicron partilces on to the charged particle. the experimental results show that the scavenging rate is greatly enhanced by the complementary use of the electrostatic and hydrodynamic effects.

Vertical distributions of stable isotopic compositions and bacteriochlorophyll homologues in suspended particulate matter in saline meromictic Lake Abashiri

We determined chloropigment composition as well as stable carbon and nitrogen isotopic compositions of dissolved and particulate species in saline meromictic Lake Abashiri. We observed a sharp peak of bacteriochlorophyll e in a narrow redox boundary zone and the upper monimolimnion, indicating a dense population of brown-colored strains of green sulfur bacteria around the chemocline. Nitrogen isotopic records of particulate nitrogen and dissolved ammonium suggested that the green sulfur bacteria in the redox boundary zone assimilated either ammonium or dinitrogen through the nitrogen fixation pathway. In the anoxic monimolimnion, several lines of evidence suggest that a major portion of particulate organic matter originated from the overlying mixolimnion and redox boundary zone.

Electrostatic scavenging of submicron particles aided by the hydrodynamic effect of particle vibration

A particle of a few micrometers in diameter with a high electrostatic charge is strongly vibrated to induce a secondary flow around the particle. The flow blows the submicron particles into a region close to the charged particle, where the electrostatic gradient force becomes strong enough to adsorb the submicron particles on to the charged particle. The experimental results show that the agglomeration rate is greatly enhanced by the complementary use of the electrostatic and the hydrodynamic effects. In this paper, a fundamental consideration on the electrostatic agglomeration is also presented in combination with the concept of agglomeration volume in the acoustic agglomeration.

Theoretical discussion on two types of critical state for ignition of an autoxidative powder bed

A model calculation of spontaneous ignition in an autoxidative powder bed has shown that the critical state can be classified into Frank-Kamenetskii and oxygen-deficient types. The first type includes an irreversible transient process to ignition at the critical point and its thermal stability is rather frail against the changes in ambient conditions. In the second type, the oxygen diffusion suffocatingly controls the rate of heat generation in the bed and the thermal stability is comparatively robust. The types can be largely discriminated by the material and the porosity of the bed.

Efficacy and risk of aeration to prevent self-heating powder bed from spontaneous ignition

The effect of aeration on the thermal stability of a self-heating powder bed is mathematically discussed. Judging from the thermal characteristics in the steady state, aeration greatly improves the thermal stability. It is also shown, however, that a steady state solution for the temperature distribution in the bed always accompanies an unstable equilibrium solution. It follows that once the steady state temperature distribution is forced through the unstable one by some external disturbances, the powder bed starts to run away towards an ignition and loses stability even after the disturbances are removed. An aerated powder bed is rather susceptible to this kind of ignition. To avoid possible risk of such an ignition, a restorable limit of the temperature distribution for a given aerated powder bed is proposed. Aeration should be controlled so that the temperature at any position in the powder bed is kept well below the restorable limit distribution.

The determination of effective densities in the permeability technique

Abstract The permeability technique is useful for the measurement of the specific surface of fine powders, using the Kozeny-Carman equation. When the sample to be tested is a mixture of two materials the results obtained do not always fit this equation. It is proposed here that this is due to the difficulty of estimating the effective densities of the components. A method is derived for obtaining values for the effective density of non-spherical or porous materials which allows the surface area to be determined.