Double layer thickness dimensionless

For electrostatically stabiUzed suspensions, this maximum volume fraction will depend primarily on the dimensionless double layer thickness, Ka, and the electrostatic interaction energy through the dimensionless surface potential, T g(= etpelksT). Because the dimensionless double layer thickness can be large (i.e., 10-100) when the salt concentration is low, the effective volume fraction at which the maximum volume fraction is reached can be very small. 

Section VI ends with a general relation in the limit of large double layer thickness that, to the best of our knowledge, is novel. This propert) yields a single reduced representation of the electro-osmotic coefficients for all the studied configurations as functions of a dimensionless double layer thickness. 

FIG. 5 (a) Derivative of the reduced conductivity dGla° )/d(, and (b) coupling coefficient 377 in a cubic array of contacting spheres (solid lines) or oblate ellipsoids (dashed lines) along the horizontal (O) and vertical (+) directions as functions of the inverse dimensionless double layer thickness kR. The dash-dotted line in (a) is the result for spheres of a matched asymptotic expansions technique [13,27],... 

For curved surfaces the shape of the double layer can be described in terms of the dimensionless quantity 1ko which is the ratio of radius of curvature to double-layer thickness. When tea is small, a charged particle may be treated as a point charge when tea is large, the double layer is effectively flat and may be treated as such. 

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-... 

One of the most important quantities to emerge from the Debye-Huckel approximation is the parameter k. This quantity appears throughout double-layer discussions and not merely at this level of approximation. Since the exponent kx in Equation (37) is dimensionless, k must have units of reciprocal length. This means that k has units of length. This last quantity is often (imprecisely) called the thickness of the double layer. All distances within the double layer are judged large or small relative to this length. Note that the exponent kx may be written x/k a form that emphasizes the notion that distances are measured relative to k in the double layer. 

A general mathematical formulation and a detailed analysis of the dynamic behavior of this mass-transport induced N-NDR oscillations were given by Koper and Sluyters [8, 65]. The concentration of the electroactive species at the electrode decreases owing to the electron-transfer reaction and increases due to diffusion. For the mathematical description of diffusion, Koper and Sluyters [65] invoke a linear diffusion layer approximation, that is, it is assumed that there is a diffusion layer of constant thickness, and the concentration profile across the diffusion layer adjusts instantaneously to a linear profile. Thus, they arrive at the following dimensionless set of equations for the double layer potential, [Pg.117]

With increasing time, the concentration at the outer double layer boundary increases while the diffusion layer thickness increases. The Fig. 7.4 plots the non-dimensional surface concentration versus dimensionless time. 

Coalescence frequency J depends on dimensionless parameters k, p, Sa, Sr, t, y, a. The parameter k characterizes relative sizes of interacting drops p is the viscosity ratio of drops and ambient liquid Sa and Sr are the forces of molecular attraction and electrostatic repulsion of drops r is the relative thickness of electric double layer, which depends, in particular, on concentration of electrolyte in ambient liquid y is the electromagnetic retardation of molecular interaction a is relative potential of surfaces of interacting drops. Let us estimate the values of these parameters. For hydrosols, the Hamaker constant is F 10 ° J. For viscosity and density of external liquid take m /s, 10 kg/m. ... 

The Reynolds as well as the Peclet nnmber is zero due to the fact that no external flow field is applied. The distance between the particles related to the thickness of the double layer is similar for all experimental conditions and the dimensionless process time which would be related to the time needed to form the first doublet is not accessible. However, especially the latter would be the target quantity of all stndies. 

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