  We study the reaction of low-mass stars to anisotropic irradiation and its
importance for the long-term evolution of compact binaries binaries. We show by
means of a simple homology model that if the energy outflow through the surface
layers of a low-mass main sequence star is blocked over a fraction s_eff < 1 of
its surface it will inflate only modestly and that the maximum contribution to
mass transfer is s_eff times what one obtains in the isotropic case. The
duration of this mass transfer phase is roughly -0.1 ln(1-s_eff) times the
thermal time scale of the convective envelope. Numerical computations confirm
these results. Second, we present a simple analytic one-zone model for
computing the blocking effect by irradiation which gives results in acceptable
quantitative agreement with detailed numerical computations. Third, we show
that unless mass transfer is strongly enhanced by consequential angular
momentum losses, cataclysmic variables are stable against mass transfer if the
mass of the main sequence donor is less than about 0.7 solar masses. Otherwise
systems may be unstable, subject to the efficiency of irradiation. We argue
that low-mass X-ray binaries are even less susceptible to this instability. In
case of instability, mass transfer must evolve through a limit cycle in which
phases of high mass transfer alternate with phases of small (or no) mass
transfer.
