Potential sedimentation

The presence of a charge at the drop surface is of essential importance not only for drop motion, but also for sedimentation in the gravitational field. The problem is formulated in a similar manner, but in the hydrodynamic equations for the external liquid, it is necessary to take into account the Archimedian force 

Introducing pressure n= p — p )gz, where the z-axis is directed we arrive at the following expression 

At 2p + 3p qj/(jj, the expression (9.58) transforms into the Hadamar-Rybczynski formula. If 2p + ip then the drop velocity coincides with 

The distribution of the electric field potential over the drop surface is 

In the previous section, it was shown that in the process of sedimentation of a charged drop in an electrolyte solution, a potential difference is formed at the drop ends, which is determined from the formula (9.60). If the solution contains a series of drops arranged in a line, one after another, then along the column of the mixture, a potential drop is established. This potential drop is known as sedimentation potential [52]. The purpose of this section is to determine the sedimentation potential. 

The electric field induced by sedimentation of colloidal particles under gravity is termed the sedimentation potential. The potential difference is sensed by two identical electrodes placed at different heights. No commercial or home-made apparatus for measurements of potential and IEP based on sedimentation potential have been reported in the recent literature. 

Eor the following commercial instruments referred to in the literature, the principle of operation (probably one of classical electrokinetic phenomena) has not been reported ZP-10 B from Shimadzu, Japan Zeta Reader Mark 21, Mitamura Riken and Sugiura 2 VD. 

When charged particles settle in an aqueous solution, an electric field is induced by the movement of the charged particles relative to the ionic medium, as discussed in Chapter 9. A formula relating the electric field, E (= volts/cm), to the zeta potential, of the particles 

The electric field (E) is different from the applied field E and these two fields are related to each other by continuity of electric current, namely, 

The sedimentation field Esed be obtained by setting (i) equal to be zero in Eq. (24.34), namely, 

For low potentials, it can be shown that sed is related to the electrophoretic mobility p of concentrated soft particles (22.10) by 

In the limit a 0, we have that 0 and soft particles become spherical polyelectrolytes. In this limit, Eq. (24.37) tends to 

Interestingly, the prefactor (24.41) disappears in Eq. (24.42), implying that Eq. (24.42) can be applied for both dilute and concentrated cases. This is again because the polyelectrolyte layer does not contribute to the electrical conductivity K for low potentials, that is, in this case K = K°°. 

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The final and less commonly dealt-with member of the family of electrokinetic phenomena is the sedimentation potential. If charged particles are caused to move relative to the medium as a result, say, of a gravitational or centrifugal field, there again will be an induced potential E. The formula relating to f and other parameters is [72, 77]... 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

There are four related electrokinetic phenomena which are generally defined as follows electrophoresis—the movement of a charged surface (i.e., suspended particle) relative to astationaiy hquid induced by an applied ectrical field, sedimentation potential— the electric field which is crested when charged particles move relative to a stationary hquid, electroosmosis—the movement of a liquid relative to a stationaiy charged surface (i.e., capiUaty wall), and streaming potential—the electric field which is created when liquid is made to flow relative to a stationary charged surface. The effects summarized by Eq. (22-26) form the basis of these electrokinetic phenomena. 

FIGURE 31.2 Schematic design of cells for studying electrophoresis (a) and sedimentation potentials (b). 

The electrokinetic processes can actually be observed only when one of the phases is highly disperse (i.e., with electrolyte in the fine capillaries of a porous solid in the cases of electroosmosis and streaming potentials), with finely divided particles in the cases of electrophoresis and sedimentation potentials (we are concerned here with degrees of dispersion where the particles retain the properties of an individual phase, not of particles molecularly dispersed, such as individual molecules or ions). These processes are of great importance in particular for colloidal systems. 

The movement of a charged particle with respect to an adjacent liquid phase is the basic principle underlying four electrokinetic phenomena electrophoresis, electroosmosis, sedimentation potential, and streaming potential. 

Of the four electrokinetic phenomena, two (electroosmotic flow and the streaming potential) fall into the region of membrane phenomena and will thus be considered in Chapter 6. This section will deal with the electrophoresis and sedimentation potentials. 

A further electrokinetic phenomenon is the inverse of the former according to the Le Chatelier-Brown principle if motion occurs under the influence of an electric field, then an electric field must be formed by motion (in the presence of an electrokinetic potential). During the motion of particles bearing an electrical double layer in an electrolyte solution (e.g. as a result of a gravitational or centrifugal field), a potential difference is formed between the top and the bottom of the solution, called the sedimentation potential. 

The streaming potential (Dorn effect) relates to a movement of liquid that generates electric potential, and electroosmosis occurs when a direct electric potential causes movement of the liquid. The sedimentation potential relates to sedimentation (directed movement) of charged particles that generates electric potential, and electrophoresis occurs when a direct electric potential causes a movement of charged particles. 

Sedimentation potential A potential is created when charged particles settle out of a suspension. This gives rise to sedimentation potential,... 

Sedimentation potential This is due to the electric field created by charged particles sedimenting in a liquid. This situation is the opposite of electrophoresis. 

If a liquid moves tangential to a charged surface, then so-called electrokinetic phenomena arise [101]. Electrokinetic phenomena can be divided into four categories Electrophoresis, electro-osmosis, streaming potential, and sedimentation potential [102], In all these phenomena the zeta potential plays a crucial role. The classic theory of electrokinetic effects was proposed by Smoluchowski2 [103],... 

The opposite effect to electrophoresis is the generation of a sedimentation potential. If a charged particle moves in the gravitational field or in a centrifuge, an electric potential arises — the sedimentation potential. While the particle moves, the ions in the electric double layer lag somewhat behind due to the liquid flow. A dipole moment is generated. The sum of all dipoles causes the sedimentation potential. 

Sedimentation potential - the electric field which is created when charged particles move relative to stationary liquid (i.e. the opposite of electrophoresis). 

Electrophoresis has the greatest practical applicability of these electrokinetic phenomena and has been studied extensively in its various forms, whereas electro-osmosis and streaming potential have been studied to a moderate extent and sedimentation potential rarely, owing to experimental difficulties. 

Areas impacted by wastewaters with sediments potentially contaminated by (in)organic pollution ... 

Sedimentation potential, in which charged species are made to move relative to stationary liquid creating an electric field (Figure 4.7). 

Good descriptions of practical experimental techniques in conventional electrophoresis can be found in Refs. [81,253,259]. For the most part, these techniques are applied to suspensions and emulsions, rather than foams. Even for foams, an indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis. In bubble microelectrophoresis the dispersed bubbles are viewed under a microscope and their electrophoretic velocity is measured taking the horizontal component of motion, since bubbles rapidly float upwards in the electrophoresis cells [260,261]. A variation on this technique is the spinning cylinder method, in which a bubble is held in a cylindrical cell that is spinning about its long axis (see [262] and p.163 in Ref. [44]). Other electrokinetic techniques, such as the measurement of sedimentation potential [263] have also been used. 

Solid Liquid Sedimentation potential" Force of gravity Potential difference... 

Zeta potential was the first, experimentally available value characterizing edl. The potential of the solid particles in the electrolyte solutions may be determined on the basis of one of the four following phenomena microelectrophoresis, streaming potential, sedimentation potential and electroosmosis. The most popular of them and the best described theoretically and methodically is the electrophoresis. Other papers, concerning the electrophoretic mobility, stationary level determination and the theory of the charged particles transportation in the electric field are still published. 

Dorn effect Dorn potential, and - sedimentation potential... 

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