Particles hydrodynamic shear plane

The so-called potential can be taken as a first estimate for the surface potential. The potential is the electrostatic potential at the hydrodynamic shear plane close to the particle surface. It can be determined from electrophoretic mobility measurements of the particles in an electric field (see for example Ref. [23]). The potential is zero when the charge within the shear plane is zero. This is the case as the surface charge plus the charge due to adsorbed ions other than hydrogen (for example AIOH2 in the case of alumina suspensions) is zero. This point is the iso-electro-point (i.e.p.) of the material in the dispersion medium. The suspension pH with respect to the i.e.p. is an important criterion for a first judgement of possible electrostatic stability. 

At some distance from the particle surface (usually identified as the beginning of the diffuse layer in Fig. 3), a hydrodynamic shear plane exists that is characterized by the potential. The magnitude of is directly related to dispersion stability [71]. For oxides, hydroxides, and related materials, is strongly influenced by solution pH and electrolyte concentration and may be modified by surface-active species, such as oxyanions and polyelectrolytes. The key parameter characterizing a powder surface is the isoelectric point pHiep. Under pristine conditions (i.e., no surface contamination), pHiep defines the solution pH at which C = 0 and the particles exhibit a net surface charge of zero. 

For Gg (b), a reasonable (although not strictly correct) procedure is to replace the Stern potential in one of the standard equations for Gg by the zeta potential of the polymer-coated particles this assumes that the plane of hydrodynamic shear corresponds to the periphery of the adsorbed layer. 

The measurement of this surface potential (T g or Pq) is impossible due to the hydrodynamic behavior of the system that generates a thin layer of attached liquid around the particles. However, there is a plane where the shear starts (shear plane), and at this plane the surface potential can be measured and the value is known as the zeta potential ( P ). Besides the indifferent counter- and co-ions in solution, there are also so-called potential determining ions (chemists caU them adsorbing ions). For most systems these are and OH ions that can adsorb directly on the particle surface and alter the -potential. There is a pH value for which the potential becomes zero and is called the isoelectric point (lEP), as shown in Figure 11.6. 

Both the surface potential ij/o and the diffuse layer potential ij/ defy a direct experimental determination. What can be measured are the surface charge density (To (via titration) and the electrokinetic potential or zeta-potential f, which corresponds to the concepmal hydrodynamic slip plane (or shear plane, SP in Fig. 3.3) between the Stem layer and the diffuse layer. Any measurement of the zeta-potential is, therefore, based on relative motion between the particle surface and the diffuse layer (cf. Sect. 2.3.7, Delgado et al. 2007). 

The potential at the distance r = L from the particle surface is defined as the zeta potential, and is equivalent to the electrokinetic potential. More specifically, it is the electrical potential at the location of the hydrodynamic shear (shpping) plane against a point in the bulk fluid far removed from the particle s surface (Figure 2.18). Hence, the zeta potential is the potential difference between the dispersion medium and the stationary layer of fluid attached to the dispersed particle (Figure 2.19). Quantitatively, this can be calculated from the equation ... 

Over the past two decades several devices have been developed to measure and characterize the adhesive interaction of cells with biomaterials, particles, and other cells. These devices share the common experimental strategy that nonadherent spherical cells are allowed to establish adhesive contacts to the test material under quiescent conditions and then are subjected to a weU-defined distractive force. From the examination of large numbers of cells over a range of distractive forces, a probability distribution for cell adhesion as a function of distractive force can be constructed (Figure 34.3). From this distribution, an adhesion characteristic (e.g., T50, the shear stress necessary to detach 50% of the cells [47,86-88] maybe determined. The primary differences between the various devices for measuring cell adhesion is the type of distractive force that is applied (e.g., membrane tension, buoyancy, and hydrodynamic shear stress) and the direction of the force relative to the plane of cell/surface contacts. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

By virtue of the no-slip condition on the surface, a sphere freely suspended in a plane shear flow will rotate at a constant angular velocity fl equal to the flow rotation velocity at infinity. The solution of the corresponding three-dimensional hydrodynamic problem on a particle in a Stokes flow is given in [343]. 

The second most common parameter used to characterize the polymer layer is its thickness. The layer thickness is the principal factor in defining the effectiveness of the polymer as a steric stabilizer. The thickness of the adsorbed layer is usually defined as the distance of the plane of shear from the particle surface. This distance is generally referred to as the hydrodynamic thickness, 8, and is obtained from several different techniques such as measurement of the diffusion coefficient, sedimentation coefficient, or electrophoretic mobility of the particles with and without the presence of the adsorbed polymer layer. 

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