Electroosmotic flow of a Phan-Thien-Tanner fluid in a wavy-wall microchannel

In this paper the electroosmotic flow (EOF) of a viscoelastic fluid in a wavy-wall microchannel is asymptotically analyzed. The rheological behavior of the fluid corresponds to the simplified Phan-Thien-Tanner model (sPTT). By using the lubrication theory, the governing equations of the flow are considerably simplified, which are written in dimensionless form. For obtaining the solution for the flow and electric fields, and assuming small amplitudes of the waviness of the microchannel walls, the domain perturbation method is used. The EOF is mainly characterized by the following dimensionless parameters: δ modulates the waviness of the walls; n denotes the number of waves along the microchannel and eDe_κ², which reflects the viscoelastic character of the fluid. The principal results show that the volumetric flow rate is increased when eDe_κ² is increased, due to this parameter influences in an important manner on the velocity gradient at the microchannel wall. Also, for very small values of δ, the volumetric flow rate increases linearly. In contrast, for increasing values of n, the volumetric flow rate diminishes.