Fluid motion generated by phoretic transport mechanisms can explain two apparently different experimental observations: the aggregation of particles on an electrode during electrophoretic deposition, and a special bubble coalescence pattern on an electrode during electrolytic gas evolution. An externally imposed field (the gradient of electrical potential, temperature, or concentration of a solute), interacting with the surface of particles or bubbles very near a planar conducting surface, drives the convection of fluid that causes particles and bubbles to approach each other on the electrode. Analysis of this flow shows that the long-range lateral attraction observed in ensembles of solid particles and gas bubbles on electrodes can be understood as entrainment in the flow generated by each. In the case of particle aggregation during electrophoretic deposition, the flow has its origin in electroosmosis about each deposited particle, while with bubbles the flow is generated by thermocapillary stresses about the bubble surfaces. The flows in both cases are circulatory and, in the case of electrophoretic deposition, reversible upon reversal of the direction of the electric field. This unified hydrodynamic theory of aggregation on electrodes fits experimental observations qualitatively and quantitatively.