  We study the surface tension of hot, highly magnetized three flavor quark
matter droplets, focusing specifically on the thermodynamic conditions
prevailing in neutron stars, hot lepton rich protoneutron stars and neutron
star mergers. We explore the role of temperature, baryon number density,
trapped neutrinos, droplet size and magnetic fields within the multiple
reflection expansion formalism (MRE), assuming that astrophysical quark matter
can be described as a mixture of free Fermi gases composed by quarks $u$, $d$,
$s$, electrons and neutrinos, in chemical equilibrium under weak interactions.
We find that the total surface tension is rather unaffected by the size of the
drop, but is quite sensitive to the effect of baryon number density,
temperature, trapped neutrinos and magnetic fields (specially above $eB \sim 5
\times 10^{-3} \mathrm{GeV}^2$). Surface tensions parallel and transverse to
the magnetic field span values up to $\sim$ 25 MeV/fm$^2$. For $T \lesssim 100$
MeV the surface tension is a decreasing function of temperature but above 100
MeV it increases monotonically with $T$. Finally, we discuss some astrophysical
consequences of our results.
