Behavior of Submicron Particles Suspending in a Fluid

Submicron particles or ultrafine particles have been paid increasing attention in various fields, and attention seems to be shifted to smaller and smaller particles with the times. In fact, detection, characterization and control of particles of 0.1 pm or smaller in size have become important in clean rooms for semiconductor production processes, in fine ceramics industries, in combustion processes, and in atmospheric or indoor environmental problems, and so on. Some topics on submicron particles suspending in a gaseous or liquid medium will be briefly introduced in this paper. In the former section of this paper, typical size-dependent properties of a particle are looked through, and topics on coagulation and deposition which may play an important roll in a particle dispersed system in industrial processes are introduced in the following sections.


Introduction
Submicron particles or ultrafine particles have been paid increasing attention in various fields, and attention seems to be shifted to smaller and smaller particles with the times. In fact, detection, characterization and control of particles of 0.1 pm or smaller in size have become important in clean rooms for semiconductor production processes, in fine ceramics industries, in combustion processes, and in atmospheric or indoor environmental problems, and so on.
Some topics on submicron particles suspending in a gaseous or liquid medium will be briefly introduced in this paper. In the former section of this paper, typical size-dependent properties of a particle are looked through, and topics on coagulation and deposition which may play an important roll in a particle dispersed system in industrial processes are introduced in the following sections.

Size-dependent properties of submicron particles
Typical size-dependent properties of particles suspending in air and in water are shown in Fig. 1 fogether with the corresponding equations. The solid lines in the figure are those in air, while the dashed lines in water and the onepoint dashed line are in low-pressure air. The curves appearing in the figure are briefly explained in the following.
Terminal settling velocity in the gravity field, ut, decreases both in air and in water with the decrease in particle size, as is expressed by Eq. (1 ). The distortion in the small size range of the solid line of ut is caused by the slip coefficient Cc which is size-dependent as shown in Eq. (2). The slip coefficient Cc increases with the decrease in size of particles suspending in a gaseous medium, but it is always unity for particles suspending in a liquid medium. It increases with the decrease of gas pressure p as shown in Eq. (3), an example of which is shown in Fig. 1 When a particle is small, Brownian motion which is caused by random variations in the incessant bombardment of molecules against the particle occurs. The average absolute value of Brownian displacement in one second, /, is shown in Fig. 1, which is obtained as t = 1 sec in Eq. (4). The intersections of the curves of l and ut lie in around 0.5 pm in air and 1 pm in water. If one may observe the settling velocity of such a small particle in a -short time, it will be a resultant velocity caused by both gravitational settling and Brownian motion. D in Eq. ( 4) is the particle diffusion coefficient which is given by Eq. (5). The larger values of D indicate that more vigorous Brownian motion and more rapid particle transfer in a particle concentration gradient occur. As is seen in Fig. 1, the particle diffusion coefficient in water is much smaller than that in air. r g in Fig. 1 is called relaxation time and is given by Eq. (6). It has a unit of time and it characterizes the time required for a particle to relax its velocity to a new condition of forces. When a particle is projected into a stationary fluid with a velocity U 0 , it will travel a finite distance before it stops. Such a distance is called stop-distance and is given by U 0 r g. So r g can be a measure of inertial motion of a particle in a fluid.
Be in Fig. 1 is the electrical mobility which expresses the velocity of a charged particle in an electric field of unit strength. The steady particle velocity in an electric field E is given by EBe. Since Be depends upon the number of elementary charge which a particle carries, ,. .s:: Part1cle diameter dp [,um]  7), nP should be made clear to determine Be· nP is predictable with aerosol particles in most cases, where particles are charged by diffusion of ionsl). An example where particles are charged in a large number of bipolar ions by diffusion is shown in Fig. 2.
In a liquid, on the other hand, it is difficult to predict nP in general because of the complex interaction between a particle and surronding ions. Figure 3 shows the particle trajectories in air in a vertical parallel plate electrodes. The zigzag movement in the figure is caused by Brownian motion and the trajectories in the vertical direction indicate that the particles are electrically neutral, say, uncharged. PdiP~ in Fig. 1 is the ratio of the vapor pressure on a droplet surface to that on a flat surface of the same liquid. Vapor pressure on a droplet surface increases with the decrease of droplet diameter. This phenomenon is called Kelvin effect and is given by Eq. (8). If the supersaturation of water vapor S surrounding a single isolated water droplet is larger than pd/p~, the droplet grows by condensation of surrounding water vapor. If S < pd/p~, that is, the surrounding supersaturation lies in below the curve Pd /p ~ in Fig. 1, the water droplet disappears by evaporation. Thus the curve pd /p ~ in Fig. 1 indicates the critical relationship between droplet diameter and the surrounding vapor pressure that the droplet can be stable. In the liquid phase, however, it is not clear that Eq. (8) can be applicable.
When a temperature gradient is established in a gas, the aerosol particles in that gas are driven from high to low temperature regions. This effect is called thermophoresis. The curve uth in Fig. 1 is an example (NaCI particle in air) of thermophoretic velocity at a unit temperature gradient, that is, I °C/cm. If the temperature gradient is 10°C/cm, uth becomes ten times higher than that shown in the figure.
The curve denoted as pulse height illustrates a typical photomultiplier response of scattered light from a particle. The intensity of scattered light is proportional to six power of the particle diameter when particle size is smaller than the wave length of incident light. The curve demonstrates the steep decrease in intensity of scattered light from a particle. Figure 4 illustrates the change in the number concentration of cigarette smoke particles with time by Brownian and turbulent coagulation. Initial p~rticles (at t = 0 sec) have about 0.9 ,urn in geometric mean diameter, 1.4 in geometric standard deviation and I 0 7 particles per cubic centimeter in concentration. Figure 4-(a) shows the number change due to Brownian coagulation in a closed chamber (vertical cylinder: 19 em in diam. and 20 em in height). Figures  4-(b) and (c) show the number change due to turbulent coagulation in the chamber with buffle plates stirred by six flat-bladed turbine (diameter is 9 cm) 2 ). The intensity of turbulence of Fig. 4-( c) is higher (average energy dissipation rate e 0 =c 4 x 10 7 cm 2 /s 3 ) than that of Fig. 4-(b) (e 0 =c 7 x I 0 6 cm 2 /s 3 ). It is seen    where K is coagulation rate constant. The values of K for Brownian and turbulent coagulation in a gaseous and a liquid-phase is shown in Fig. 5. The time to reach half of the initial particle number concentration are illustrated in Table 1. The value of K for turbulent coagulation, on the other hand, is proportional to d~ v'€; : this means that turbulent coagulation plays an important roll when particle size becomes large, which is illustrated in Fig. 5 for monodisperse particles and the given intensities of turbulence.

--T-----------
Coagulation in a liquid, mainly -in water, is somewhat different from that in a gas because particles are highly charged in water in most cases. When particles are charged in the same polarity in water, the electrostatic repulsion  between two particles, which is shown as the energy barrier in Fig. 6-(b), prevents coagulation. The energy barrier as high as 20K T (K : Boltzmann constant, T: absolute temperature) is enough to prevent coagulation, which can be easily attained by adding appropriate dispersion agents in water. Submicron particles in a gaseous medium, on the other hand, can not be highly charged since ion concentration in a gaseous medium is generally low compared with that in water, and then electrical repulsion may hardly be expected, which is shown in Fig. 6-(a). This means that submicron particles in a gas can not be held stable in a state of high concentration, which is one of the disadvantages of industrial particle production processes in a gaseous medium.

Deposition
Deposition of submicron particles suspending in a fluid onto surfaces exposed to that fluid is caused by particle diffusion, inertial motion and additional external forces such as gravitational, thermophoretic and electrostatic forces. Particle deposition caused by diffusion and electrostatic force becomes important in a su bmicron size range, whereas deposition by inertial and gravitational forces is less important in that range, which is obvious in Fig. 1 (seeD, Be, Tg and ut)· Decrease in particle number concentration of an aerosol flowing through a horizontal pipe in a laminar state, for an example, is shown in Fig. 7, where R is the pipe radius, u xav the mean velocity of the flowing aerosol, x the tube length, and n 0 and n are, respectively, the particle number concentration at the pipe inlet Another example which may be important for particle production processes in gaseous media is shown in Fig. 8. The plots are the experimental results obtained in a closed cylindrical vessel similar to the former section: The abscissa ~ in the figure is deposition rate constant which is a measure of particle deposition rate, and is defined as follows, Ns in the figure is the revolution of stirrer and E 0 the corresponding average energy dissipation rate. It is seen in the figure that turbulence clearly enhances particle deposition on walls and that Brownian deposition is predominant in the smaller size range whereas deposition due to gravitational settling is predominant in the larger size range. The plots in the figure are obtained by the present author and his co-workers3>, and the lines are those calculated from the theory proposed by Crump and Seinfeld 4 >.
If there exists a temperature gradient in the vicinity of a wall which has lower temperature than a fluid, thermophoresis shown in Fig. 1 enhances particle deposition on the wall.
Particle deposition is also enhanced if particles are charged in opposite polarity to a wall. If aerosol particles are charged in bipolarity, a wall charged in either polarity can enhance deposition of particles charged in opposite polarity to that wall.
The deposition mechanism of particles suspending in a liquid is essentially the same as that in a gas if the electrical repulsion  shown in Fig. 6-(b) is not strong. However, particle deposition in a liquid medium is thought to be less important than in a gaseous medium, because, in a liquid medium, electric double layer repulsion is not neglected in most cases, particle diffusion coefficient, gravitational settling velocity and inertial effect are small, and because re-entrainment of particles once caught at walls takes place rather easily com pared with that in a gaseous medium.

Conclusion
Size-dependent behavior, mainly dynamic behavior, of submicron particles suspending in a fluid has been summarized. And then the topics on coagulation and particle deposition on walls have been outlined. Another interest-KONA No. 3 (1985) ing topics on submicron particles from an industrial point of view will be gas-or liquid-toparticle conversion, that is, particle production process, but unfortunately it is too complicated and has not well been understood for the time being.