to which the wide-gap theory demonstrated a robust applicability in prediction over a wide range of $\varepsilon$.

The present simulation consistently served as bridge between the wide- and narrow-gap theories (see figure \[fig:migvel\_comp\_lub\]) as long as the bubble deformation is assumed to be infinitesimal. However, in spite of the qualitative success of the simulation in revealing the narrow-gap repulsive force, the deformation-induced migration velocity in the experiment is considerably higher by a factor of about 3 than the simulated one, as shown in figure \[fig:migvel\_comp\_exp\]. The experiment may inevitably involve unknown factors such as unsteadiness, imperfection from the infinite plate-fluid system, and measurement uncertainty, which cannot be captured by the simulation. Nevertheless, we have not expected such a large discrepancy because firstly the quantitative agreement between the interfacial deflections of the experiment and the simulation has been confirmed in figures \[fig:scale\_deform\] and \[fig:deformationr\_kap\], secondly the consistent inertia-driven migration velocity of a rigid sphere with the available theories ([@vas1976; @mag2003]) has been obtained by [@tak2004] using the same experimental setup, and thirdly considerable uncertainty seems not to be introduced into such a simple system as illustrated in figure \[fig:schem\]. Further joint researches among theory, numerics and experiment are needed to resolve 