Electroviscous effects in a Carreau liquid flowing through a cylindrical microfluidic contraction

Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cylindrical microfluidic 4:1:4 contraction–expansion at low Reynolds number are investigated numerically by solving the equations governing the flow, the electric field, and ion transport, using a finite volume method. The channel wall is considered to have a uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Predictions are presented for a range of values of the shear-thinning parameters in the Carreau model for various surface charge densities and Debye lengths. The apparent/physical viscosity ratio is shown to increase as the degree of shear-thinning increases. Thus the electroviscous effect is stronger in shear-thinning liquids than it is when the liquid is Newtonian, a result previously obtained for uniform pipe flow of power-law liquids. The trend holds true regardless of the choice of surface charge density or Debye length, although the magnitude of the trend decreases as the surface charge density and/or the Debye length is reduced. Comparison between uniform pipe flow of a Carreau liquid and the corresponding power-law liquid that approximates it at large shear rates shows that the apparent/physical viscosity ratios for the two models are almost identical. A previous prediction that a near-wall region of reduced velocity can occur for pipe flow of a shear-thinning power-law liquid when EDLs are overlapping and surface charge density is elevated is confirmed for a Carreau liquid.