Rheometry of non-Newtonian electrokinetic flow in a microchannel T-junction

Two-dimensional finite element simulations of electrokinetic flow in a microchannel T-junction of a fluid with a Carreau-type nonlinear viscosity are presented. The motion of the electrical double layer at the channel walls is approximated by velocity wall slip boundary conditions. The fluid experiences a range of shear rates as it turns the corner, and the flow field is shown to be sensitive to the non-Newtonian characteristics of the Carreau model. A one-to-one mapping between the Carreau parameters and the end wall pressure is demonstrated through statistical analysis of the pressure profile for a broad range of physical and operating parameters. Such a mapping allows the determination of the Carreau parameters of an unknown fluid if the end wall pressure profile is known; thus a highly efficient viscometric device may be constructed. A graphical technique to show that the inverse problem is well posed is shown, and a method for solving the inverse problem is presented. The challenges that must be overcome before a practical device can be constructed are discussed.