  We present an approximate treatment of the mixing between $\nu_{\tau}$
($\bar\nu_{\tau}$) and a sterile species $\nu_s$ ($\bar\nu_s$) with a vacuum
mass-squared difference of $\sim$ 10$^2$-10$^3$ keV$^2$ in protoneutron stars
created in core-collapse supernovae. Including production of sterile neutrinos
through both resonant flavor conversion and collisions, we track the evolution
of the $\nu_{\tau}$ lepton number due to both escape of sterile neutrinos and
diffusion. Our approach provides a reasonable treatment of the pertinent
processes discussed in previous studies and serves a pedagogical purpose to
elucidate the relevant physics. We also discuss refinements needed to study
more accurately how flavor mixing with sterile neutrinos affects protoneutron
star evolution.
