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Electrokinetically Enhanced In Situ Soil Decontamination
Published in Donald L. Wise, Debra J. Trantolo, Remediation of Hazardous Waste Contaminated Soils, 2018
Sibel Pamukcu, J. Kenneth Wittle
where zi = valence of central ion, e0 = electronic charge, κ = Debye-Hückel parameter, θ = dielectric constant of the medium inside the ionic atmosphere sphere, and a = distance of closest approach to the central ion, or sum of the radii of the oppositely charged ions in contact. The first term on the right-hand side is the potential at the surface of the ion, and it is due solely to the charge of the ion itself. The second term is dependent on the ionic concentration, and it is due to the ionic atmosphere surrounding the central ion. The inverse of κ, or l/κ, is taken as the thickness of the spherical ionic atmosphere. Equation (8) is analogous to Eq. (3). Similarly, as the thickness of the ionic atmosphere decreases with increasing ionic concentration (κa increases), the potential of the central ion with respect to its surrounding, or in other words its electrokinetic potential, decreases.
Classical Mechanics and Field Theory
Published in Mattias Blennow, Mathematical Methods for Physics and Engineering, 2018
Problem 10.33. Show that the unbound states of the Kepler problem, i.e., states with E > 0, result in the trajectory of the particle being hyperbolic and compute the deflection angle α, the distance of closest approach ρmin to the center, and the impact parameter d, see Fig. 10.36, in terms of the constants E and L. Hint: Like an ellipse, a hyperbola may be described by the relation ρ=ρ0/(1+ε cos (ϕ)) in polar coordinates, where ε is the eccentricity. Unlike an ellipse, the eccentricity for a hyperbola is ε > 1.
Interrogating the Behavior of Micrometer-Sized Particles on Surfaces with Focused Acoustic Waves
Published in K. L. Mittal, Particles On Surfaces, 2020
Giles J. Brereton, B. A. Bruno
where A and B are Lifshitz-Hamaker constants for the respective materials. The distance of closest approach between the particle and the surface depends on surface roughness, particle shape, and the thickness of any gas film adsorbed at these surfaces and thus presents a problem for realistic estimation. Estimates of typical distances of closest approach vary between h/d ≃ 0.001 for smooth surfaces with minimal adsorption, to h/d ≃ 0.1 for rough surfaces.6 More advanced models for the attractive force between a spherical particle and a surface have also been developed which incorporate effects such as elastic deformation of the particle from its spherical shape when it is in contact with the surface.7
The GMSA for a hard-sphere fluid revisited: evaluation of the Henderson-Blum approximation[*
Published in Molecular Physics, 2019
Alejandra Lozada-Hidalgo, Mariano López de Haro, Douglas Henderson
The mean spherical approximation (MSA), introduced by Lebowitz and Percus [10], may be used in connection with fluids whose intermolecular potentials consist of a hard-core and a tail and have the following general form where σ is the distance of closest approach between two particles. It is defined by the relations and with the radial distribution function (rdf) and the direct correlation function (dcf) related to the total correlation function through the well-known OZ expression, namely Furthermore, in Equation (3) , ( being the Boltzmann constant and T the absolute temperature). The name of the MSA derives from the fact that it is related to the solution of the PY equation for hard-sphere fluids since the intermolecular potential of the hard-sphere fluid is recovered when .