Layer Debye

For large values of k, the first two terms in the square brackets are substantially nonzero only in the Debye layer vicinity of the walls, whereas everywhere else the EOF profile is dominated by the last two linear terms in the square brackets. Therefore, the asymmetric EOF profile can be close to trapezoidal or close to triangular depending on the exact values of the zeta-potentials of the walls. If the signs of the zeta-potentials of the walls are different, then the liquid moves in one direction near one wall and in the opposite direction near another wall (this case can be interesting for the preseparation of the particles having different den-sities).The last term in Eq. (2) corresponds to the pressure-driven Poiseuille flow. 

Exchange current density Equilibrium constant Thermal energy Rate constant Boltzmann constant Thickness of Debye layer... 

Membrane-Induced Deionzation, Debye Layer Extension,... 

In many oxides and halides Debye layers and impurity segregation near free surfaces are known to exist. A polished surface is not likely to be in... 

Figure 6.5.3 Debye layer location in a cylindrical pore (A) A small (B) A large.

Integration of the Langmuir relation (2-135) shows that most of the electrons are located in the thin layer about r r around the macro-particle. These electrons are confined in the Debye layer by a strong electric field, which according to the preceding relations can be expressed as... 

The electric double layer sometimes is called the Debye layer, and Ap is known as the thickness (or radius) of the Debye layer. For water solution of symmetric... 

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 ... 

Direct the x-axis along the capillary axis (toward the cathode). Suppose the velocity has only one component u(y). For a very narrow capillary, such an assumption is valid. Let the thickness of the Debye layer at the capillary wall be small in comparison with the capillary radius a, that is, a. Then in the region adjacent to the wall, the curvature of the capillary wall can be neglected, and Eq. (7.70) reduces to... 

The expression for electrophoresis velocity of a particle, whose size is small in comparison with the thickness of the Debye layer, is called the Huckel equation. 

Debye layer on the analyte backbone, and the frictional force from the surrounding fluid. Therefore, it is not a trivial matter to determine or calculate the electrophoretic mobility of a given protein/peptide a priori from the sequence information. Also, electrophoretic mobilities of many proteins among a given proteome can be similar. Therefore, the CZE is not an ideal technique for separating a very complex protein mixture for sample preparation purposes. 

Disjoining Pressure, Fig. 5 and 2 are electrical potentials of charged surfaces. and 2 are both negative, (a) The distance between two negatively charged surfaces, h, is bigger than the thickness of the Debye layers, R. Electrical double layers do not overlap and there is no electrostatic interaction between these surfaces, (b) The... 

The Equilibrium Debye Layer Suppose that the system is in the steady state and that there is no fluid flow or imposed electric fields. Further suppose that the geometry is such that the electrolyte-substrate interface is an iso-surface of /k. Then, it readily follows from Eqs. 5 and 10 and the boundary condition of no flux into the wall that V /k = 0 everywhere. Therefore, nk = n °° exp(-Zke4>/A BT) where nk °° is the ion concentration where the potential 4) = 0, usually chosen as a point very far from the wall. Using the solution for nk in the charge density pe and substituting in Eq. 4, we get the nonlinear Poisson-Boltzmann equation for determining the potential... 

If the solution to the problem of the equilibrium double layer is known, then the velocity is determined by the above formula. Thus, the solutions to the respective flow problems for the equilibrium situations considered in the previous subsection are readily written down. Solution to the electrokinetic equations is facilitated if the Debye layer thickness may be assumed small compared to the characteristic channel width Wq. This however is not usually the case in nanochannels since wq and are both on the order of nanometers. Exact analytical solutions... 

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