Helmholtz-Smoluchowski equation zeta potential determination

The most common method for determining the zeta-potential is the microelectrophoretic procedure in which the movements of individual particles under the influence of a known electric field are followed microscopically. The zeta potential can be calculated from the electrophoretic velocity of the particles using the Helmholtz-Smoluchowski equation. 

Zeta potential is determined Trom electrophoretic mobility (v) with the Helmholtz-Smoluchowski equation (Eq. 13). 

The above equation is a different form of the Helmholtz-Smoluchowski equation. Equation 14 shows that if the average electroosmotic velocity is determined from the experimentally measured current-time relationship, the zeta potential can be calculated. Introducing the electroosmotic mobility concept, Peo = u -vJEx, Eq. 14 can be further simplified in the following format ... 

Particle trajectories are determined by a combination of fluid-flow, electrophoresis and DEP. The fluid-flow is driven by electroosmosis for the case of interest here. For the thin Debye layer approximation, electroosmotic flow may be simply modeled with a slip velocity adjacent to the channel walls that is proportional to the tangential component of the local electric field, as shown by the Helmholtz-Smoluchowski equation 12). Here, the proportionality constant between the velocity and field is called the electroosmotic mobility, tigo- Fluid-flow in microchannels becomes even simpler for ideal flow conditions where the zeta potential, and hence /ieo, is uniform over all walls and where there are no pressure gradients. For these conditions, it can be shown that the fluid velocity at all points in the fluid domain is given by the product of the local electric field and// o(/i). 

The influence of membrane effective fixed charge, Xf, on the transport of ions is estimated by determining the ion / transport number or fraction of the total electric current transported by ion i (TO, that is f = Ij/Ix since Zi h = 1, for single salts L + t. = 1. However, electrical characterization of membrane-surface/electrolyte interface is usually carried out by TSP measurements (A( ) gt), which allows the determination of zeta potential (Q, the electrical potential at the shear plane, by using the Helmholtz-Smoluchowski equation [33] ... 

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the EOF depends on the magnitude of the zeta potential, which is determined by various factors inhuencing the formation of the electric double layer, discussed above. Each of these factors depends on several variables, such as pH, specihc adsorption of ionic species in the compact region of the double layer, ionic strength, and temperature. 

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