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In other words, zeta potential is the potential difference between the dispersion medium and the stationary layer of fluid attached to the dispersed particle. The zeta potential is caused by the net electrical charge contained within the region bounded by the slipping plane, and also depends on the location of that plane. Thus, it is widely ...
In 1923, Peter Debye and Erich Hückel reported the first successful theory for the distribution of charges in ionic solutions. [7] The framework of linearized Debye–Hückel theory subsequently was applied to colloidal dispersions by S. Levine and G. P. Dube [8] [9] who found that charged colloidal particles should experience a strong medium-range repulsion and a weaker long-range attraction.
Smoluchowski's sedimentation potential is defined where ε 0 is the permitivity of free space, D the dimensionless dielectric constant, ξ the zeta potential, g the acceleration due to gravity, Φ the particle volume fraction, ρ the particle density, ρ o the medium density, λ the specific volume conductivity, and η the viscosity. [8]
where ε r is the dielectric constant of the dispersion medium, ε 0 is the permittivity of free space (C 2 N −1 m −2), η is dynamic viscosity of the dispersion medium (Pa s), and ζ is zeta potential (i.e., the electrokinetic potential of the slipping plane in the double layer, units mV or V).
For very low values of the ionic strength the value of the denominator in the expression above becomes nearly equal to one. In this situation the mean activity coefficient is proportional to the square root of the ionic strength. This is known as the Debye–Hückel limiting law. In this limit the equation is given as follows [14]: section 2.5.2
Substituting this length scale into the Debye–Hückel equation and neglecting the second and third terms on the right side yields the much simplified form () = ().As the only characteristic length scale in the Debye–Hückel equation, sets the scale for variations in the potential and in the concentrations of charged species.
is the Riemann zeta function ((/) [18]). Interactions shift the value, and the corrections can be calculated by mean-field theory. This formula is derived from finding the gas degeneracy in the Bose gas using Bose–Einstein statistics.
The equation says the matter wave frequency in vacuum varies with wavenumber (= /) in the non-relativistic approximation. The variation has two parts: a constant part due to the de Broglie frequency of the rest mass ( ℏ ω 0 = m 0 c 2 {\displaystyle \hbar \omega _{0}=m_{0}c^{2}} ) and a quadratic part due to kinetic energy.