Particle charge

Overall, it is apparent that, although fat globules are not the predominant milk constituent affecting the rheological properties of milk and cream, they still exhibit a considerable influence. 

Abo-Elnaga, I.G. 1966. Factors affecting creaming of cows and buffaloes milk. Milchwis-senschaft. 21, 429 433. 

Attaie, R., Richter, R.L. 2000. Size distributions of fat globules in goat milk. J. Dairy Sci. 83, 940-944. 

Bakshi, A.S., Smith, D.E. 1984. Effect of fat content and temperature on viscosity in relation to pumping requirements of fluid milk products. J. Dairy Sci. 67, 1157-1160. 

Baumrucker, C.R., Keenan, T.W. 1973. Membranes of mammary gland. VIII. Stability of milkfat globule membrane in secreted milk. J. Dairy Sci. 56, 1092-1094. 

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Particles charged in field migrate to earthed plates... 

More sophisticated approaches to describe double layer interactions have been developed more recently. Using cell models, the full Poisson-Boltzmann equation can be solved for ordered stmctures. The approach by Alexander et al shows how the effective colloidal particle charge saturates when the bare particle charge is increased [4o]. Using integral equation methods, the behaviour of the primitive model has been studied, in which all the interactions between the colloidal macro-ions and the small ions are addressed (see, for instance, [44, 45]). 

We will focus on one experimental study here. Monovoukas and Cast studied polystyrene particles witli a = 61 nm in potassium chloride solutions [86]. They obtained a very good agreement between tlieir observations and tire predicted Yukawa phase diagram (see figure C2.6.9). In order to make tire comparison tliey rescaled the particle charges according to Alexander et al [43] (see also [82]). At high electrolyte concentrations, tire particle interactions tend to hard-sphere behaviour (see section C2.6.4) and tire phase transition shifts to volume fractions around 0.5 [88]. 

D. H. Pontius, L. G. Felix, and W. B. Smith, "Performance Characteristics of a Pilot Scale Particle Charging Device," Preprint 76-42.6, 69th APPCA Annual Meeting Portland, Oregon, June 27—July 1, 1976. 

It can be seen from these two factors, ie, particle charge and van der Waals forces, that the charge must be reduced or the double layer must be compressed to aUow the particles to approach each other closely enough so that the van der Waals forces can hold them together. There are two approaches to the accomplishment of this goal reaction of the charged surface sites with an opposite charge on an insoluble material and neutralization of... 

T pe of particle charging Feed Separation T pe of separator Feed temperature, °C Feed. size, mm Feed rate, metric tons per hour per start d No. of stages of separation... 

Gady found that, depending on the charge of the particle, van der Waals forces dominated over the forces associated with electrostatically charged patches when the particle-to-substrate separation was between 3 and 10 nm, depending on the particle charge. In addition, he found that the distance at which the snap-together occurred required that van der Waals forces dominate over electrostatic. In all his measurements, however, a component of the total attractive force, even at close separations, was observed to be electrostatic in nature. 

Zeta potentials of floe produeed in the plant may also be measured as a means of eontrol. The zeta potential value for optimum eoagulation must be determined for a given wastewater by aetual correlation with jar tests or with plant performance. The control point is generally in the range of 0 to 10 millivolts. If good correlations can be obtained between some zeta potential values and optimum plant performance, then it is possible to make rapid measurements of particle charge to compensate for major variations in wastewater composition due to storm flows or other causes. 

Particle charging and collection can taltc place in different sections, as illustrated in Fig. 13.6. In this two-stage system, the collection of particles takes place in a region without gas ions, i,e the electric field is generated by the high-voltage electrode only. 

Two-stage precipitators consist of separate sections for particle charing and collection. Particle charging is realized with corona wires between grounded metal plates. The collection of particles rakes place in a system of parallel plate electrodes of opposite polarities. Two-stage precipitators are typically used in indoor air cleaning and light industrial applications. 

The properties of gas ions are of great importance for the electrical performance of an electrostatic precipitator. They also are very important for particle-charging processes. The size of gas ions is normally such that they can be regarded as gas molecules carrying a single elementary charge. It can even be assumed that ions form a gas component with a very low- partial pressure. Thus, the thermal motion of gas ions is assumed to be similar to that of gas molecules. The most important parameters describing the properties of gas ions are... 

The concentration of gas ions significantly influences the particle-charging process. The high ion concentration is essential for the effective charging of fine particles. The distribution of ion concentration in a pipe-type electrostatic precipitator can be approximated by using the equations presented in the previous section. 

According to Eq. (13.52), saturation charge is directly proportional to the square of the particle diameter and the external electric field. Particle charging depends also on the composition of the particle, which is taken into account by the relative dielectric constant e,. It is worth noticing that the field charging model should not be applied for small particles (dp < 0.5 pm). 

Particle charging in a electrostatic gas-cleaning system should take place as quickly as possible. Therefore, the time constant f, should be as low as possible. This requires that the ion concentration in the charging region be high. 

The traditional unipolar diffusion charging model is based on the kinetic theory of gases i.e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size dp, particle charge numbers and mean thermal velocity of tons c,. The relationship between particle charge and time according White s... 

White s equation is widely used mainly because it is easy to use and because it gives values which are in reasonable agreement with the experimental ones. However, because this model is based on the kinetic theory of gases, it should be used for small particles only. This model (as many others) assumes that particle charge can be described with a continuous function. Especially in the case of small particles, only the lowest charge numbers (0, 1, 2) are possible, and therefore the model—which does not take into account the discrete charge numbers—is somewhat questionable. 

The most straightforward approach is to assume that the field charging and diffusion charging are independent processes i.e., particle charge can be presented as a sum of charges due to field (s ) and diffusion (sj) charging. Another simple approach to estimating the combined effect is... 

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