The Dynamic Mobility for Thin Double Layer Systems

The Dynamic Mobility for Thin Double Layer Systems 

The double layer thickness around a charged particle depends on the electrolyte concentration (c). For a 1 1 symmetric electrolyte in water, the double layer thickness is approximately given by  

In this chapter we focus on the dynamic mobility of particles with thin double layers, although we will discuss the important case of nanopartides, which do not have thin double layers. Owing to lack of space we will not discuss colloids in nonpolar fluids. 

The particle motion is driven by the action of the electric field on the double layer. Although the total electric force on the particle and double layer is zero - because the particle charge is balanced by the diffuse layer charge - a motion is still generated, for the field pushes the particle in one direction and it pulls the double layer ions, and the surrounding fluid, in the opposite direction. As described above, this motion is spatially uniform, except close to the electrodes, and so there is no ESA except from the electrodes. 

In a frame of reference fixed to the particle, the double layer liquid moves with a tangential velocity that increases from zero at the shear surface to a limiting value Au beyond the double layer. This motion is called an electro-osmotic flow. The relative velocity Au is proportional to the tangential component of the electric field 

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