Particle clustering and pattern formation during electrophoretic deposition: A hydrodynamic model

Clustering of latex particles 4-10 mu m in diameter during and after electrophoretic deposition of the particles onto flat electrodes has been reported by Bohmer (Langmuir 1996, 12, 5747). The particles interacted over length scales comparable to their size in the formative stages of the clusters. Combinations of two or more clusters already deposited approached each other to form larger agglomerates. A model based on electroosmotic flow about charged particles near surfaces is developed here to explain these observations. A charged, nonconducting particle near or on a flat conducting surface creates flow in the adjacent fluid due to electroosmosis about the particle's surface. Fluid is drawn laterally toward the particle near the electrode and pushed outward from the particle farther away from the electrode above the particle. Another particle near the electrode will be drawn toward the central particle by this convection. We first solve for the flow field about a single particle and then compute the rearrangement of neighboring particles in response to the flows. The clustering times for different initial configurations of sets of particles (e.g., regular versus irregular spacing) are calculated. The average clustering times for irregular configurations are greater than those for regular arrays. The qualitative and quantitative features of the experimental observations are captured by this model if the hindrance effect of the solid wall is taken into account. For example, the model correctly predicts the observed declustering (separation) of particles when the polarity of the electric field is reversed as well as the observed cluster-to-cluster motion.