Figure 4.

An analytic model which captures the relevant physics. (A) The simplest model is an infinite cylinder with external and internal axially directed electric fields in opposite directions. This drives electroosmotic flows in opposite directions. The electric field ratio α was set to 0.1 in all of the analytic calculations. (B) The flow profiles inside and outside a cylinder of radius a and wall thickness a, at two different salt concentrations κ = 0.001 (solid lines) and κ = 1.0 (dashed lines), where κ is measured in units of a^–1. The maximum velocity v_max in each case was calculated at r = 0 for the inner flow and at r = λ_D for the outer flow. In the high salt case v_max,in > v_max,out, whereas in the low salt case it is the other way around. (C) The normalized momentum flux generated by the inner (solid line) and outer (dashed line) walls, as a function of salt concentration for an infinite cylinder. As salt is reduced, the inner flux saturates, while the outer flux carries on growing. (D) The normalized net momentum flux exhibits the same qualitative flow reversal behavior as observed in the experiments and simulations.