Charged Particle in an Electrolyte

A double layer is established near the charged surface. The thickness of the double layer, Aq, is roughly 10 nm. Two cases are possible. The size of the charged particle may be larger than Xj) in the case of cells or beads. The particle size may be much smaller than in the case of smaller ions. 

For small particles, the situation can be considered to be analogous to the particle immersed in an insulating medium. This situation corresponds to ions (Na, Ca ,. ..), small ionized proteins, and small strands of DNA in solution. The ionic mobility for this case is similar to 

The particles in this case are enclosed in the Debye-Hiickel double layer, which is much thinner than the particle itself. This case is analogous to the EO situation of the previous section with a change in the frame of reference, that is, the frame of reference is the resulting fluid. Thus, the migration velocity of the particle using equation (6.171b) is 

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Smoluchowsky [161] and Booth [162] both accounted for the increase in viscosity as due to the electrical double layer round a charged particle in an electrolyte and gave expressions for e which included the specific conductivity of the electrolyte, the dielectric constant of the suspending medium, the electrokinetic potential of the particles with respect to the electrol)de and tt e radius of tiie particle (which was to be large in comparison with the thickness of the double layer for the validity of ttie expression). Experimental verification by Chan and Goring [163] of tiie expressions for e, provided by Smoluchowsky [161] and Booth [162] gives confidence for their use. 

When two similarly charged colloid particles, under the influence of the EDL, come close to each other, they will begin to interact. The potentials will detect one another, and this will lead to various consequences. The charged molecules or particles will be under both van der Waals and electrostatic interaction forces. The van der Waals forces, which operate at a short distance between particles, will give rise to strong attraction forces. The potential of the mean force between colloid particle in an electrolyte solution plays a central role in the phase behavior and the kinetics of agglomeration in colloidal dispersions. This kind of investigation is important in these various industries ... 

The first phenomenon, to be discussed in 2.2, concerns the saturation of the force of repulsion between two symmetrically charged bodies (particles) in an electrolyte solution as their charge increases. This effect is a direct consequence of the saturation of the electric field at a finite distance from the surfaces of the bodies and of the field properties at infinity. In the one-dimensional case (for parallel plates) the relevant features follow from a direct computation (see, e.g., [9]). In 2.2 the corresponding effect will be discussed for parallel cylinders and spheres [10]. 

The exact solution for interaction of a system of small spherical particles in an electrolyte is obtained. On the basis of the exact solutions, closed formulae for calculating ion-electrostatic energy of two spheres are derived. Our zero approximation corresponds to results of other authors in simple cases, and generalizes ones in the range of small values where the parameter kH < 2. In this paper we consider the case when surface charges are given, but the problem of spherical particles interaction with given surface potentials can be solved similarly. 

H. Ohshima, Diffuse double layer interaction between two spherical particles with constant surface charge density in an electrolyte solution, Colloid Polymer Sci. 263, 158-163 (1975). 

The surface potential of a uniformly charged soft particle in an electrolyte solution increase in magnitude with decreasing electrolyte concentration. This is not the case for a nonuniformly charged soft particle. The surface charge layer consists of a... 

Charged particles in weak electrolytes have associated with them an electrical double layer. When these particles settle under gravity the double layer is distorted with the result that an electrical field is set up that opposes motion. This effect was first noted by Dorn [74] and was studied extensively by Elton et. al. [75-78] and later by Booth [79,80]. 

The amount of charge at the interface depends on the field strength and the dielectric properties (conductivity and permittivity) of the particle and the electrolyte. However, there is a slight asymmetry in the charge density on the particle which gives rise to an effective or induced dipole across the particle. Note that if the field is removed the dipole disappears, it is induced . The magnitude of the dipole moment depends on the amount of charge and the size of the particle. For a spherical particle in an electrolyte subject to a uniform applied electric field, three cases can be considered ... 

Colloidal particles of the same charge immersed in an electrolyte solution attract each other by van der Waals forces and repel each other by Debye screened interactions (see Eq. 16.70). Why does the ease of coagulation increase rapidly with increasing solution ionic strength ... 

Micro-PIV technique is used to measure the steady velocity of tracer particles in an electrolyte in both open- and closed-end microchannels. Under an applied DC electric field, the observed particle velocity, Wp, evaluated from the micro-PIV measurement is the superposition of the electrophoresis velocity of the charged particle, u. , and the electroosmotic velocity of the electrolyte,... 

Ohshima, H., On the limiting electrophoretic mobility of a highly charged colloidal particle in an electrolyte solution, J. Colloid Interface Set, 263, 337, 2003. 

In general, because of the differences between the permittivities and conductivities of the dispersed phase and the medium, the induced dipole moment of the particle in an electrolyte solution consists of two contributions. One is due to the polarization (orientation) of the molecular dipoles of both phases, and the other is due to the process of accumulation of charges of different signs on opposite poles of the particle. Thus, at very high frequencies (in practice, several MHz) ionic motions in the electrolyte solution and in the double layer toward and around the particle are too rapid for charge accumulation to proceed. Hence, only orientation of dipoles in both the particle and the liquid medium can participate in the dipole. 

Ohshima, H. 2006. Chapter 1. Electrical double layer around a charged colloidal particle in an electrolyte solution. In H. Ohshima Theory of Colloid and Interfacial Electric Phenomena, 12 1-38. Interface Science and Technology. San Diego Academic Press. 

Problem 11.3 Charged colloids in an electrolyte In DLVO theory the interaction energy between two colloidal particles is estimated by the summation of repulsive and attractive contributions to the interaction. In Figure 11.2a the potential curve is illustrated for different values of the double layer thickness (inverted Debye-Huckel parameter), which are related to different concentrations of a monovalent salt, e.g. NaCl. 

H. Ohshima, J. Colloid Interface Sci., 200, 291 (1998). Surface Charge Density/Surface Potential Relationship for a Cylindrical Particle in an Electrolyte Solution. 

We conclude this section by discussing an expression for the excess chemical potential in temrs of the pair correlation fimction and a parameter X, which couples the interactions of one particle with the rest. The idea of a coupling parameter was mtrodiiced by Onsager [20] and Kirkwood [Hj. The choice of X depends on the system considered. In an electrolyte solution it could be the charge, but in general it is some variable that characterizes the pair potential. The potential energy of the system... 

Acids and bases are almost always found as aqueous solutions— that is, dissolved in water. Solutions of both acids and bases are called electrolytes. Electrolytes conduct electricity, which is the movement of electrons or other charged particles. When an acid or a base is dissolved in water, they break down into their ions, which... 

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