Double electrical layer thickness

An illustration of the effect of micelle/nanoparticle volume fraction on contact line motion is found in [57]. They used 0.1 M NaCl solution to reduce the electrical double layer thickness surrounding the NaDS micelle. At a given number concentration of micelles, decreasing the size of each micelle decreases the volume fraction greatly, since the volume of each spherical micelle varies as the third power of the radius. Thus, the addition of electrolyte effectively reduced the micellar volume fraction in the aqueous medium. The authors found that the oil droplet that would otherwise become completely detached from the solid surface, came back to reattach itself to the solid when electrolyte was present. They rationalized this finding as being caused by the inability of the weakened structural disjoining forces to counteract the attraction of the oil drop to the solid surface. 

Two additional stabilizing influences will be summarized next that of viscoelastic films and that of solid-particle films. In general, where electrical surface charge is an important determinant of stability, it is easier to formulate a very stable O/W emulsion than a W/O emulsion because the electric double layer thickness is much greater in water than in oil. (This is sometimes incorrectly stated in terms of greater charge being present on droplets in an O/W emulsion.) However, there are ways to effectively stabilize W/O emulsions. 

Application of MGC theory to Eq. (11) shows that dex is proportional to 7c—1, often termed the electrical double layer thickness [23]... 

FIG. 6 Comparison between MGC theory (open symbols) and the disk model (filled symbols) for the dependence of Vcx on the electrical double layer thickness [Eq. (14)]. The number of unit layers in a quasicrystal is a fixed parameter for each set of curves [34],... 

A linear relationship exists between the ESA or CVP amplitude and the volume fraction of the suspended particles. At relatively high-volume fractions, hydrodynamic and electric double-layer interactions lead to a non-linear dependence of these two effects on volume fraction. Generally, non-linear behavior can be expected when the electric double-layer thickness is comparable to the interparticle spacing. In most aqueous systems, where the electric double layer is thin relative to the particle radius, the electro-acoustic signal will remain linear with respect to volume fraction up to 10% by volume. At volume-fractions that are even higher, particle-particle interactions lead to a reduction in the dynamic mobility. 

Debye Length A parameter in the Debye—Hiickel theory of electrolyte solutions, k-1. For aqueous solutions at 25 °C, k = 3.288y7 in reciprocal nanometers, where I is the ionic strength of the solution. The Debye length is also used in the DLVO theory, where it is referred to as the electric double-layer thickness. See also Electric Double-Layer Thickness. 

Electric Double-Layer Thickness A measure of the decrease of potential with distance in an electric double layer. It is the distance over which the potential falls to 1/e, about one-third, of the value of the surface potential. Also termed the Debye length. 

Thickness of the Electric Double Layer See Electric Double-Layer Thickness. 

The electric double layer thickness is a function of the fluid ionic strength. For aqueous solutions having a symmetric electrolyte (e.g., NaCl), the electric double layer thickness, 1/k, at 25 °C is (54)... 

On a final note, keep in mind that the expression (7.61) for the thickness Ap of the Debye layer is valid for an infinite diluted symmetric electrolyte. Paper [25] derives an expression for the electric double layer thickness for the case of an infinite diluted asymmetric electrolyte, and [26, 27] derive the following expression for Ao for the case of a slightly diluted electrolyte ... 

It is never possible to obtain an exact analytical solution of the electrodiffusion equation, and the standard practice is to seek approximate solutions under some sort of assumptions. In macroscopic membranes whose thickness is many times greater than the electric double layer thickness Planck s approximation, assuming that the system obeys the local electric neutrality... 

If the electric parameters such as the surface electric charge of the nanochannel, the nanoparticle, the external applied electric field, and the bulk ionic concentrations keep constant, the same size nanoparticles move faster in the bigger nanochannels. It can be explained as follows In the nanochannels, the electric double layer thickness is comparable with the channel s dimensions, and the electroosmotic velocity is not independent of the size of the nanochannels. By increasing the size of the nanochannel, the electric potential of EDL at the center of the nanochannel reduces, and thus the nanoparticle moves easier in the nanochannel. This is similar to the electrokinetic motion of the particles in the nucrochannel with thick EDL where increasing the size of the microchannel intensifies the velocity of the particle [6]. 

Reciprocal electrical double layer thickness, m Compressibility index Viscosity of filtrate or liquid in a feed. Pa s Dimensionless time... 

Figure 7 shows the dimensionless bubble translation speed Ca as a function of the surfactant (anionic surfactant since the glass capillary used has positive surface charge) ionic concentration for various electric field strengths [17]. At low concentrations, given that the Debye screening length scales as the inverse of the square root of the concentration, the electric double layer thickness becomes compa-... 

Steric stabilization of a colloidal dispersion is achieved by attaching long-chain molecules to colloidal particles (Fig. 3.6). Then when colloidal particles approach one another (for example due to Brownian motion), the limited interpenetration of the polymer chains leads to an effective repnlsion which stabilizes the dispersion against flocculation. Steric stabilization has several advantages compared to charge stabilization. First, the interparticle repulsion does not depend on electrolyte concentration, in contrast to charge-stabilized colloids where the electric double-layer thickness is very sensitive to ionic strength. Second, steric stabilization is effective in both... 

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