  A residual-based lubrication method is used in this paper to find the flow
rate and pressure field in converging-diverging rigid tubes for the flow of
time-independent category of non-Newtonian fluids. Five converging-diverging
prototype geometries were used in this investigation in conjunction with two
fluid models: Ellis and Herschel-Bulkley. The method was validated by
convergence behavior sensibility tests, convergence to analytical solutions for
the straight tubes as special cases for the converging-diverging tubes,
convergence to analytical solutions found earlier for the flow in
converging-diverging tubes of Newtonian fluids as special cases for
non-Newtonian, and convergence to analytical solutions found earlier for the
flow of power-law fluids in converging-diverging tubes. A brief investigation
was also conducted on a sample of diverging-converging geometries. The method
can in principle be extended to the flow of viscoelastic and
thixotropic/rheopectic fluid categories. The method can also be extended to
geometries varying in size and shape in the flow direction, other than the
perfect cylindrically-symmetric converging-diverging ones, as long as
characteristic flow relations correlating the flow rate to the pressure drop on
the discretized elements of the lubrication approximation can be found. These
relations can be analytical, empirical and even numerical and hence the method
has a wide applicability range.
