| Summary: | 博士 === 國立臺灣大學 === 化學工程學研究所 === 91 === When a charged solid surface comes into contact with an electrolyte solution, the solid surface is covered by a layer of ions that bears net charges of opposite sign but equal magnitude. This structure is the so-called electric double layer. When a driving force field is applied, the ionic concentration distributions inside the double layer are changed and a relative movement at the solid-liquid interface will be developed. This relative motion is termed the electrokinetic phenomenon and has received quite an amount of attention, due to its wide application in the areas of biological, medical and engineering sciences. On the other hand, the surface charge for biological colloids, polymer latices, and particles of metal oxides in electrolyte solutions is usually determined by the dissociation of ionizable surface groups and/or adsorption (or site-binding) of specific ions. The degree of these dissociation and adsorption reactions will be a function of the local concentrations of these ions at the particle surface. Since the ionic concentration distributions in the electric double layer surrounding the particle are changed during the particle's movement, the extent of the surface reactions and the magnitudes of the surface charge density and surface potential will be changed accordingly. This is the so-called charge regulation phenomenon. In this thesis, we analyze how the charge-regulation phenomenon affects the electrokinetic properties.
In chapter 2, we are concerned with the electrokinetic flow in a long capillary pore bearing permanently adsorbed or covalently bound polyelectrolytes in its inside wall. The density of the ionogenic functional groups is assumed to be uniform throughout the surface polymer layer, but the charge regulation phenomenon in the adsorbed layer is taken into account. Both the cases of a capillary tube and a capillary slit are investigated. The linearized Poisson-Boltzmann equation for the electric potential is employed; however, no assumptions are made as to the thickness of the electric double layer relative to the radius of the capillary tube (or half thickness of the capillary slit) or the thickness of the surface polymer layer. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. The bulk electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential for the electrokinetic flow in the capillaries are analytically calculated. Our results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density within the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution. The charge-regulation effect tends to shorten the Debye screening length within the surface polymer layer. The intensity of this effect also depends on the regulation characteristics. The magnitudes of the electric potential (or space charge density) and the electric current density for the cases of a capillary slit and a capillary tube are quite different and the differences vary with the thickness of the charge-regulating surface polymer layer.
Next, in chapter 3, the electrophoresis and electric conduction in a dilute suspension of charged composite particles, each composed of a solid core and a surrounding porous shell, with an arbitrary thickness of the electric double layers are analytically studied. The porous shell of a particle is treated as a solvent-permeable, ion-penetrable, and charge-regulating surface polymer layer of finite thickness with uniformly distributed ionogenic functional groups and frictional segments. The electrokinetic equations that govern the electrostatic potential profile, electrochemical potential distributions of ionic species, and the fluid flow field are linearized and solved by the use of a regular perturbation method. Analytical expressions for the electrophoretic mobility of the charge-regulating composite sphere and for the electric conductivity of the suspension are derived as linear functions of these charge densities. The results demonstrate that the charge regulation phenomenon tends to shorten the Debye screening length within the surface polymer layer again and to reduce the magnitudes of the electrophoretic mobility and electric conductivity compared to the case that the fixed charge density in the surface polymer layer is a constant. The intensity of this effect depends on the regulation characteristics. The charge-regulation characteristics determine the value of charge density within the surface polymer layer.
Analytical expressions for the electrophoretic mobility and electric conductivity of a concentrated suspension of identical, charge-regulating, colloidal spheres are obtained in chapter 4. The effects of particle interactions are taken into account by employing a combination of the hydrodynamic cell models and the electrokinetic cell models. The charge regulation due to association/dissociation reactions of functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. No assumption is made about the thickness of the double layers relative to the radius of the particles. The overlap of adjacent double layers is allowed and, for the derivation of the electric conductivity, the relaxation effect in the diffuse layer surrounding each particle is included. The electrokinetic equations are linearized and solved by the use of a regular perturbation method. Closed-form formulas for the electrophoretic mobility and electric conductivity of the suspension of charge-regulating spheres are derived. Our results indicate that the charge regulation effects on the electrophoretic mobility and the effective conductivity appear starting from the leading order of the equilibrium surface potential which depends on the regulation characteristics, and the volume fraction of the suspension. Note that the electrophoretic mobility and effective conductivity are not necessarily affected by the charge-regulation coefficient. It depends on which electrokinetic cell model is used. The numerical results of the effective conductivity also reveal that the analysis with non-overlapping double layers underestimates the conductivity, and the error increases with the volume fraction of the particles and can be meaningful.
Finally, in chapter 5, the body-force-driven migration in a concentrated suspension of spherical charge-regulating particles with an arbitrary thickness of the electric double layers is analyzed. The effects of particle interactions are taken into account by employing a hydrodynamic cell model. The linearized form of the charge regulation boundary condition is employed. The overlap of the double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations are linearized and solved by a regular perturbation method to derive the closed-form formulas for the settling velocity of the charge-regulating spheres and for the sedimentation potential in the suspension. The results show that the charge regulation effects on the sedimentation in a suspension appear starting from the leading order of the equilibrium surface potential which is determined by the regulation characteristics and the volume fraction of the suspension. The influence of the effects of overlapping double layers of adjacent particles on the sedimentation velocity and sedimentation potential in suspensions can be quite significant under typical conditions (even when the double layers are thin relative to the radius of particles).
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