Electroosmosis surface charge density

Electroosmotic mobility is proportional to the surface charge density on the silica and inversely proportional to the square root of ionic strength. Electroosmosis decreases at low pH (Si—O —> Si—OH decreases surface charge density) and high ionic strength. At pH 9 in 20 mM borate buffer, electroosmotic flow is 2 mm/s. At pH 3, flow is reduced by an order of magnitude. 

Finite-element simulations are useful to understand the mechanism of NDR and its dependence on the composition in the internal and external solutions, pore geometry, and nanopore surface charge density. Similar to modeling flow effects on nanopore ICR described earlier, the Nernst-Planck equation governing the diffusional, migrational, and convective fluxes of ions (Equation 2.18), the Navier-Stokes equation for low-Reynolds number flow engendered by the external pressure and electroosmosis (Equation 2.20), and Poisson s equation relating the ion distributions to the local electric field (Equation 2.19) were simultaneously solved to obtain local values of the fluid... 

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

It may be appreciated that electrokinetic phenomena are determined by electric properties at the plane of shear rather than at the real surface. In the following sections of this chapter, the relation between the measured property and is further analyzed. This is done for electroosmosis, electrophoresis, streaming current, and streaming potential. The sedimentation potential will not be discussed any further, because in practice this phenomenon does not play an important role. The electrokinetic charge density may then be derived from using the theory for the diffuse electrical double layer. 

As described in the article on nonlinear elec-trokinetic phenomena, electroosmosis of the second arises when the bulk salt concentration goes to zero at a surface passing a diffusion-limited current. Under conditions of super-limiting current, the density of counterions in the electric double layer loses its classical quasiequilibrium profile, and a region of dilute space charge extends into the solution to the... 

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