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Microchannel impedance for quasi Newtonian fluids with spatial modulated viscosity

Using the Navier-Stokes equation and assuming a viscosity radially modulated for a quasi-Newtonian fluid, we obtain the impedance of a fluid through microchannels and their corresponding electrical analogs. To solve the Navier-Stokes equation will use the Laplace transform, the Bromwich integral, the residue theorem and Bessel functions. This will give a formula for the impedance in terms of Bessel functions and from these equations to be constructed equivalent electrical circuits. These solutions correspond to the case of quasi-Newtonian fluid it is to say a fluid that does not stagnate in the channel wall as is the case if the fluid is Newtonian. The formulas obtained may have applications in the general theory of microfluidics and microscopic systems design for drug delivery.