  We fill a viscous liquid in a vertically stood cell of millimeter thickness,
called the Hele-Shaw cell, and insert a disk in the liquid whose thickness is
smaller than the cell thickness. The disk starts falling in the liquid due to
gravity opposed by viscous friction. We focus on the case in which lubricating
films formed in the gap between the cell surface and the disk surface are
thinner than the disk thickness. As a result, we find an apparent scaling
regime for the falling velocity of a disk, in which the thickness of the
lubricating film characterizes the dynamics. We further show that the apparent
scaling regime is explained simply as a result of competition of two scaling
regimes, elucidating the physics of the viscous friction. The present study is
thus relevant to fundamental issues and applications in various fields in which
small-scale physics in the flow at low Reynolds numbers is essential, such as
microfluidics, bioconvection, and active matter. The simple scenario for
explaining an apparent scaling law demonstrated in the present study would be
useful in diverse fields, considering that the generality and strength of
scaling analysis in science and that simple arguments usually lead to a few
different scaling laws for a given problem.
