A kinematic model describing particle movement near a surface as effected by Brownian motion and electrostatic and Van der Waals forces

Nanoparticle movement near a surface is greatly influenced by electrostatic and Van der Waals forces between the particle and the surface,as well as by Brownian motion.In this paper,several precise equations are derived to describe the Van der Waals and electrostatic forces between a particle and a surface when the particle is removed from the surface.These include an equation for particle displacement under the electrostatic force,and a numerical calculation for particle displacement under the Van der Waals force.Finally,a kinematic model is constructed to describe the particle distribution under the effects of the electrostatic and Van der Waals forces,as well as the particle’s Brownian motion.The results show that increasing the multiply of the particle and surface zeta potential values and decreasing the ionic strength of the detergent can prevent a particle from redepositing onto a surface.