Consider the case of a microcapillary of radius R with two microfluidic immiscible. The micro-capillary region 0 < r <
R1 is occupied by the microfluidic less dense and less viscous; while the microcapillary region R1 <0 < R is occupied by
the microfluidic more dense and more viscous. Determine the characteristic impedance of the microcapillary in this case
when both microfluidics are driven by the same pressure gradient as the boundary condition at the wall of the
microcapillary is of the non-Newtonian slip. The Navier Stokes equation is solved for both microfluidic methods using
the Laplace transform. The velocity profiles are expressed in terms of Bessel functions. Similarly, the characteristic
impedance of the microcapillary is expressed by a complex formula Bessel functions. Obtain the analytical results are
important for designing engineering microdevices with applications in pharmaceutical, food engineering,
nanotechnology and biotechnology in general in particular. For future research it is interesting to consider the case of
boundary conditions with memory effects.
The substance 1–methyl–4–phenyl–1, 2, 3, 6 tetrahy dropyridine (MPTP) has been studied as a major cause of neurodegeneration dopaminica, which is specifically related to Parkinson's disease. The analysis is in terms of the diffusion of the substance to the mammalian brain, by evaluating the diffusion equation in a spherical coordinate system, being η (collective diffusion term) spatially modulated. Although the progress of the disease with respect to time has not been established with certainty, an attempt to find a stable pattern of the concentration of MPTP and its effects has been made.
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