The problem becomes even more complex under a non-equilibrium setting, namely in the presence of an applied electric field (applied to a brush layer grafted on a single surface or the walls of a nanochannel) or in the presence of a background pressure-driven flow (applied to a brush layer grafted on the walls of a nanochannel). Due to the varying characteristics of different polyelectrolyte (PE) chains, their responses to an externally applied electric field (or their steadystate configurations) will differ, influencing the surrounding environment in distinct ways. For example, as we had recently shown, in the presence of externally added salt, there occurred a presence of a greater number of counterions (Na + ions) than required to neutralize the charges inside the sodium-counterion-screened anionic poly (acrylic acid) (PAA) brush layer grafted to the walls of a nanochannel. This effect, also known as the overscreening (OS) effect, was manipulated by varying the strength of the applied electric field enforcing (1) a coion-driven electroosmotic (EOS) transport and (2) switching the EOS transport from being coion-driven to becoming counterion-driven (i.e., changing the direction of the EOS transport) by merely changing the strength of the applied electric field. In another related study, we showed that this OS effect in nanochannels grafted with anionic PAA brushes leads to simultaneous energy generation and flow enhancement in the presence of a pressure-driven background transport. In a separate study, we unravelled how the change in the nature of the counterions affected the presence/absence of the OS effect and the associated EOS transport in nanochannel grafted with the PAA brushes. Finally, in a separate study, we probed the deformation behavior of different anionic brushes (e.g., PAA, poly(styrenesulfonate) or PSS brushes) to applied axial electric fields. There are several theoretical studies from our group and by other researchers that try to predict the flow behavior and the brush configuration of a soft nanochannel (i.e., nanochannel whose inner walls are grafted with PE brushes) subjected to an external field (pressure, temperature, or electric field) using theories such strong stretching theory or self-consistent field theory. However, neglecting the detailed resolution of water and counterions renders these theories unable to capture certain critical hydrodynamic effects. As noted by Hickey et al., ignoring them (free-draining approximation) can result in significant inaccuracies in predicting flow and brush behavior.