We anticipate that such a non-linear increase in the volume flow rate with the electric field must be reflected in the corresponding variation in the EOS flow profile. Fig. (c) provides the velocity profiles of the counterions for different electric field strengths. We find that the velocity profile of the water molecules (EOS flow profile) matches very closely with the velocity profile of the counterions, including the non-linear increase in the maximum strength of the counterion with the electric field strength as well as a finitely large ion velocity inside the brush layer. This confirms that the EOS flow is entirely counterion-driven, as is seen in brush-free nanochannels, and is unlike the EOS flow in PAA-brush-grafted nanochannels, where the presence of the overscreening effect leads to a coion-driven EOS flow.