Electro-osmosis is a phenomenon that occurs when an electric field is applied to a fluid that contains charged particles or ions, causing the fluid to move through a porous medium or a gel. This movement is driven by the interaction between the electric field and the charged species in the fluid, leading to the bulk flow of the liquid.
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Electro-osmosis is fluid motion driven by an applied electric field acting on mobile electric charge near a surface. A charged interface attracts a diffuse population of counterions in an electric double layer. A field component tangent to the interface exerts a force density on that mobile charge; momentum transfer to the surrounding solvent drives flow opposed by viscous stress. In a capillary electrophoresis measurement, this flow advects the sample as well as its electrical drift relative to the fluid. Locally, the measured axial velocity is , where is the electroosmotic fluid velocity and is the electrophoretic mobility. [ref]
https://ocw.mit.edu/courses/6-777j-design-and-fabrication-of-microelectromechanical-devices-spring-2007/ecbd3da50020e79e0cbb85a43a9604c1_07lecture15.pdf. MIT OpenCourseWare, lecture 15: electroosmotic flow driven by the force on diffuse-double-layer charge