Streaming potential of viscoelastic fluids with the pressure-dependent viscosity in nanochannel

The plane Poiseuille flow of viscoelastic fluids with pressure-dependent viscosity is analyzed through a narrow nanochannel, combining with the electrokinetic effect. When the fluid viscosity depends on pressure, the common assumption of unidirectional flow is unsuitable since the secondary flow may exist. In this case, we must solve the continuity equation and two-dimensional (2D) momentum equation simultaneously. It is difficult to obtain the analytical electrokinetic flow characteristics due to the nonlinearity of governing equations. Based on the real applications, we use the regular perturbation expansion method and give the second-order asymptotic solutions of electrokinetic velocity field, streaming potential, pressure field, and electrokinetic energy conversion (EKEC) efficiency. The result reveals a threshold value of Weissenberg number (Wi) exists. The strength of streaming potential increases with the pressure-viscosity coefficient when Wi is smaller than the threshold value. An opposite trend appears when Wi exceeds this threshold value. Besides, the Weissenberg number has no effect on the zero-order flow velocity, but a significant effect on the velocity deviation. A classical parabolic velocity profile transforms into a wavelike velocity profile with the further increase in Wi. Finally, the EKEC efficiency reduces when pressure-dependent viscosity is considered. Present results are helpful to understand the streaming potential and electrokinetic flow in the case of the fluid viscosity depending on pressure.