The influence of changes in the cross-sections of nanochannels on their electrohydrodynamic characteristics

The description of electrolyte solution flows in nanochannels with variable cross-section is one of the open problems in microelectrohydrodynamics. This problem has become especially important because of the possibility of fabricating narrow channels - as thin as 10 nm - and their practical significance. In addition to an external electric field that appears due to a potential difference between the inlet and outlet of the channel, the field generated by the surface charge on the channel walls is also essential. The assumption of smallness of the Debye layer thickness, which is commonly used to simplify the problem, is often invalid for nanochannels. Besides, there are difficulties connected with the validity of a continuity hypothesis and no-slip wall conditions. This paper presents a simplified approach that relies on the smallness of surface charge density along the channel rather than on the smallness of the Debye layer thickness. The flow parameters are assumed to vary much slower in the wall-tangential direction than in the wall-normal direction. In the Nernst-Planck, Poisson, Navier-Stokes system describing the flow, this makes it possible to implement the normal coordinate averaging, which is similar to the Kármán-Pohlhausen averaging, and to eventually reduce the system to a nonlinear differential equation with respect to a one-dimensional function. For the resulting equation, the sequences of ignoring the boundary no-slip conditions and those of anisotropy of diffusivity and viscosity coefficients are qualitatively analyzed. Stationary flows in simple diffuser/nozzle-shaped channels are modelled numerically in order to understand the behavior of more complex systems. The model proposed can be extended to describe electrolytes with an arbitrary number of charged species (specifically, to a ternary electrolyte), thus enabling to predict more sophisticated effects like local concentration of charged particles.