Sediments Brownian motion

Electrophoretic migrations are always superimposed on other displacements, which must either be eliminated or corrected to give accurate values for mobility. Examples of these other kinds of movement are Brownian motion, sedimentation, convection, and electroosmotic flow. Brownian motion, being random, is eliminated by averaging a series of individual observations. Sedimentation and convection, on the other hand, are systematic effects. Corrections for the former may be made by observing a particle with and without the electric field, and the latter may be minimized by effective thermostating and working at low current densities. 

In this discussion of colloid stability we will explore the reasons why colloidal dispersions can have different degrees of kinetic stability and how these are influenced, and can therefore be modified, by solution and surface properties. Encounters between species in a dispersion can occur frequently due to any of Brownian motion, sedimentation, or stirring. The stability of the dispersion depends upon how the species interact when this happens. The main cause of repulsive forces is the electrostatic repulsion between like charged objects. The main cause of attractive forces is the van der Waals forces between objects. 

As discussed in Chapters 1-7, diffusion, Brownian motion, sedimentation, electrophoresis, osmosis, rheology, mechanics, interfacial energetics, and optical and electrical properties are among the general physical properties and phenomena that are primarily important in colloidal systems [12,13,26,57,58], Chemical reactivity and adsorption often play important, if not dominant, roles. Any physical chemical feature may ultimately govern a specific industrial process and determine final product characteristics, and any colloidal dispersions involved may be deemed either desirable or undesirable based on their unique physical chemical properties. Chapters 9-16 will provide some examples. 

It is appropriate to consider first the influences of long-range flocculation or collision mechanisms. Depending on the size and movement of dispersed droplets, different mechanisms will play different roles in the collision process. In a compact electrostatic coalescer (CEC), Brownian motion, sedimentation, laminar shear, turbulent shear, or turbulent inertia may play a role in droplet movement owing to hydrodynamic effects. Additionally, electrophoretic and dielectrophoretic forces, arising from the apphed electric field, may act on dispersed droplets. 

Surface Potential and Dispersion Stabilization. Most emulsions, suspensions, and foams are not thermodynamically stable, but may well possess some degree of kinetic stability. Encounters between dispersed species can occur due to Brownian motion, sedimentation, and/or stirring. The stability of the dispersion depends upon how the particles interact when this happens. More details are given in reference [153]. Surfactants are frequently involved in the stabilization of colloidal dispersions of droplets, particles or bubbles by increasing the electrostatic repulsive forces. 

Encounters between colloidal species can occur frequently due to any of Brownian motion, sedimentation, or stirring. If velocity or shear gradients are present and are sufficiently large, the frequency of collisions depends on the volume fraction of solids and the mean velocity gradient. Assuming that sedimentation is slow compared to other collision mechanisms, the overall aggregation rate, —diV/df, is... 

Mhen two particles approach each other, due to Brownian motion, sedimentation or processing forces, they flocculate or repel depending on the character and magnitude of the interparticle forces. The general equation describing these forces consists of attractive and repulsive terms ... 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

The control of sedimentation is required to ensure a sufficient and uniform dosage. Sedimentation behavior of a disperse system depends largely on the motion of the particles which may be thermally or gravitationally induced. If a suspended particle is sufficiently small in size, the thermal forces will dominate the gravitational forces and the particle will follow a random motion owing to molecular bombardment, called Brownian motion. The distance moved or displacement, Dt, is given by ... 

Increasing the radius of the suspended particles, Brownian motion becomes less important and sedimentation becomes more dominant. These larger particles therefore settle gradually under gravitational forces. The basic equation describing the sedimentation of spherical, monodisperse particles in a suspension is Stokes law. It states that the velocity of sedimentation, v, can be calculated as follows ... 

Electrophoresis involves the movement of a charged particle through a liquid under the influence of an applied potential difference. A sample is placed in an electrophoresis cell, usually a horizontal tube of circular cross section, fitted with two electrodes. When a known potential is applied across the electrodes, the particles migrate to the oppositely charged electrode. The direct current voltage applied needs to be adjusted to obtain a particle velocity that is neither too fast nor too slow to allow for errors in measurement and Brownian motion, respectively. It is also important that the measurement is taken reasonably quickly in order to avoid sedimentation in the cell. Prior to each measurement, the apparatus should be calibrated with particles of known zeta potential, such as rabbit erythrocytes. 

Liquid-solid transitions in suspensions are especially complicated to study since they are accompanied by additional phenomena such as order-disorder transition of particulates [98,106,107], anisotropy [108], particle-particle interactions [109], Brownian motion, and sedimentation-particle convection [109], Furthermore, the size, size distribution, and shape of the filler particles strongly influence the rheological properties [108,110]. More comprehensive reviews on the rheology of suspensions and rubber modified polymer melts were presented by Metzner [111] and Masuda et al. [112], respectively. 

Sedimentation analyses must be carried out at concentrations which are sufficiently low for interactive effects between particles to be negligible so that their terminal falling velocities can be taken as equal to those of isolated particles. Careful temperature control (preferably to 0.1 deg K) is necessary to suppress convection currents. The lower limit of particle size is set by the increasing importance of Brownian motion for progressively smaller particles. It is possible however, to replace gravitational forces by centrifugal forces and this reduces the lower size limit to about 0.05 p,m. 

Deposition efficiencies for particles in the respiratory tract are generally presented as a function of their aerodynamic diameter (e.g. [8,12]). Large particles (> 10 pm) are removed from the airstream with nearly 100% efficiency by inertial impaction, mainly in the oropharynx. But as sedimentation becomes more dominant, the deposition efficiency decreases to a minimum of approximately 20% for particles with an aerodynamic diameter of 0.5 pm. When particles are smaller than 0.1 pm, the deposition efficiency increases again as a result of dif-fusional displacement. It is believed that 100% deposition due to Brownian motion might be possible for particles in the nanometer range. 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

Fig. 2 compares collision kernels calculated for a 250 nm particle as function of the collision partner size for Brownian motion, laminar and turbulent shear flows as well as sedimentation at 25 °C in water based on the equations given... 

In this chapter the thermal motion of dissolved macromolecules and dispersed colloidal particles will be considered, as will their motion under the influence of gravitational and centrifugal fields. Thermal motion manifests itself on the microscopic scale in the form of Brownian motion, and on the macroscopic scale in the forms of diffusion and osmosis. Gravity (or a centrifugal field) provides the driving force in sedimentation. Among the techniques for determining molecular or particle size and shape are those which involve the measurement of these simple properties. 

Experiments on transfer of submicrometre radioactive particles to smooth surfaces (Wells Chamberlain, 1967 Chamberlain et al., 1984) have shown that the dependency of vg on D213 holds over many orders of magnitude of D. This means that the transport by Brownian diffusion becomes progressively less effective as the particle size increases. For example a particle of 0.1 pm diameter has a diffusivity of 6.8 x 10 10 m2 s 1, a factor 1.2 x 104 smaller than that of I2 vapour. Since D does not depend on the particle density, it is appropriate to discuss transport by Brownian motion in terms of the particle diameter. The aerodynamic diameter, dA, is equal to dppp2 where pp is the particle density in c.g.s. units (g cm-3) not SI units (kg m-3), and is the appropriate parameter for particles with dp> 1 pm, for which impaction and sedimentation are the mechanisms of deposition. 

In the pulmonary region, air velocities are too low to impact particles small enough to reach that region, and the mechanisms of deposition are sedimentation and Brownian diffusion. The efficiency of both processes depends on the length of the respiratory cycle, which determines the stay time in the lung. If the cycle is 15 breaths/min, the stay time is of the order of a second. Table 7.1 shows the distance fallen in one second and the root mean square distance travelled by Brownian diffusion in one second by unit density particles (Fuchs, 1964). Sedimentation velocity is proportional to particle density, but Brownian motion is independent of density. Table 7.1 shows that sedimentation of unit density particles is more effective in causing deposition than Brownian diffusion when dp exceeds 1 pm, whereas the reverse is true if dp is less than 0.5 pm. For this reason, it is appropriate to use the aerodynamic diameter dA equal to pj dp when this exceeds 1 pm, but the actual diameter for submicrometre particles. 

The lines in Fig. 7.4 are the results of theoretical calculations, using models of the respiratory tract (Yu Diu, 1982). The points are measurements with radioactive aerosols. Numerous other determinations of fractional deposition in the whole tract have been made, using non-radioactive methods to count the number of particles in the inhaled and exhaled air (Heyder et al., 1986 Schiller et al., 1988). Fractional deposition is least for particles of about 0.2 to 0.5 m diameter. Table 7.1 shows that the combined effect of sedimentation and Brownian motion is then at a minimum. 

Filtration is a physical separation whereby particles are removed from the fluid and retained by the filters. Three basic collection mechanisms involving fibers are inertial impaction, interception, and diffusion. In collection by inertial impaction, the particles with large inertia deviate from the gas streamlines around the fiber collector and collide with the fiber collector. In collection by interception, the particles with small inertia nearly follow the streamline around the fiber collector and are partially or completely immersed in the boundary layer region. Subsequently, the particle velocity decreases and the particles graze the barrier and stop on the surface of the collector. Collection by diffusion is very important for fine particles. In this collection mechanism, particles with a zig-zag Brownian motion in the immediate vicinity of the collector are collected on the surface of the collector. The efficiency of collection by diffusion increases with decreasing size of particles and suspension flow rate. There are also several other collection mechanisms such as gravitational sedimentation, induced electrostatic precipitation, and van der Waals deposition their contributions in filtration may also be important in some processes. 

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