  We predict the dynamics and shapes of nanobubbles growing in a supersaturated
solution confined within a tapered, Hele-Shaw device with a small opening angle
$\Phi \ll 1$. Our study is inspired by experimental observations of the growth
and translation of nanoscale bubbles, ranging in diameter from tens to hundreds
of nanometers, carried out with liquid-cell transmission electron microscopy.
In our experiments, the electron beam plays a dual role: it supersaturates the
solution with gaseous radiolysis products, which lead to bubble nucleation and
growth, and it provides a means to image the bubbles in-situ with nanoscale
resolution. To understand our experimental data, we propose a migration
mechanism, based on Blake-Haynes theory, which is applicable in the asymptotic
limits of zero capillary and Bond numbers and high confinement. Consistent with
experimental data, our model predicts that in the presence of confinement,
growth rates are orders of magnitude slower compared to a bubble growing in the
bulk and that the combination of a tapered channel and contact line pinning
create tear-drop shaped bubbles.
