  We study droplets of chromonic liquid crystals squeezed between parallel
plates inducing degenerate tangential anchoring on the nematic director. In the
coexistence regime, where droplets in the nematic phase are at equilibrium with
the surrounding melt, our two-dimensional theoretical model predicts a regime
of shape bistability for sufficiently large bipolar droplets, where tactoids
(pointed shapes) and discoids (smooth shapes) coexist in equilibrium. This
phenomenon has not yet been observed. Two-dimensional droplets of disodium
cromoglycate (DSCG) have been the object of a thorough experimental study
[Y.-K. Kim et al., J. Phys.: Condens. Matter 25, 404202 (2013)]. We show that
our theory is in good quantitative agreement with these data and extract from
them what promises to be a more accurate estimate for the isotropic surface
tension at the nematic/melt interface of DSCG.
