  The capillary flow of a Newtonian and incompressible fluid in an axially
symmetric horizontal tube with a non-slowly-varying cross section and a
boundary slip is considered theoretically under the assumption that the
Reynolds number is small enough for the Stokes approximation to be valid.
Combining the Stokes equation with the hydrodynamic model assuming the
Hagen-Poiseulle flow, a general formula for the capillary flow in a
non-slowly-varying tube is derived. Using the newly derived formula, the
capillary imbibition and the time evolution of meniscus in tubes with
non-uniform cross sections such as a conical tube, a power-law-shaped diverging
tube, and a power-law-shaped converging tube are reconsidered. The perturbation
parameters and the corrections due to the non-slowly-varying effects are
elucidated and the new scaling formulas for the time evolution of the meniscus
of these specific examples are derived. Our study could be useful for
understanding various natural fluidic systems and for designing functional
fluidic devices such as a diode and a switch.
