Autonomous filling of a viscoelastic fluid in a microfluidic channel: Effect of streaming potential

We study the streaming potential modulated autonomous filling dynamics of a viscoelastic fluid in a microfluidic channel. To describe the rheology of viscoelastic fluid, we consider a simplified Phan-Thien-Tanner (sPTT) model. Considering the electroviscous effect, along with the effects of surface tension force and viscous resistance, we derive a reduced-order model for obtaining the variations in the filling dynamics for different physical parameters of the system. We observe that a complex competition between the viscoelasticity and the electroviscous effect leads to the non-trivial behaviour in the temporal evolution of the filling dynamics. Moreover, our analysis unveils that an enhancement in the electroviscous effect due to increasing viscoelasticity of the fluid leads to a non-linear reduction in the filling length of the fluid in the channel. Consequently, the notion of having a higher filling length for more elastic nature of the fluid is contradicted here due to the presence of the electroviscous effect. Finally, we establish a regime (x similar to root t) at the later stage of filling in the channel. We show that this regime is unique to the surface tension driven filling of viscoelastic fluids in a charged fluidic pathways under the influence of electroviscous effect.