Discrete-element model of electrophoretic deposition in systems with small Debye length: effective charge, lubrication force, characteristic scales, and early-stage transport

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Electrophoresis was recently proposed as a new method for controlling properties and structure of the interface between cement and steel elements in petroleum and construction industries (Lavrov A et al., 2018). Cement slurries typically contain a wide range of particle sizes (micron to hundred micron), and the particles have small Debye lengths (nanometer). The relative magnitude of different forces acting on particles in such systems was examined. A formulation based on the DLVO theory was used to calculate van der Waals forces and electric repulsion forces between particles. It was shown that the following forces need to be included in a discrete-element model of electrophoretic deposition in this case: viscous drag force, force due to the external electric field, gravity + buoyancy force, lubrication force, van der Waals force, and direct mechanical contact force. The recommended cut-off gaps for van der Waals and lubrication forces are equal to the radius of the larger particle participating in the interaction. An example DEM simulation has revealed that deposition starts with deposing finer particles. Shortly after, larger particles are deposited on the finer substrate. This is due to the larger speed-up time of larger particles. The difference in the speed-up time leads to some size segregation at the early stage of deposition, even though the particle mobility is independent of the particle size. The model enables some insight into the processes that take place during the earlier stages of electrophoretic deposition that are difficult to capture and analyze in laboratory experiments.