  We study tidal interactions in white dwarf binaries in the limiting case of
quasi-static tides. The formalism is valid for arbitrary orbital eccentricities
and therefore applicable to white dwarf binaries in the Galactic disk as well
as globular clusters. In the quasi-static limit, the total perturbation of the
gravitational potential shows a phase shift with respect to the position of the
companion, the magnitude of which is determined primarily by the efficiency of
energy dissipation through convective damping. We determine rates of secular
evolution of the orbital elements and white dwarf rotational angular velocity
for a 0.3 solar mass helium white dwarf in binaries with orbital frequencies in
the LISA gravitational wave frequency band and companion masses ranging from
0.3 to 10^5 solar masses. The resulting tidal evolution time scales for the
orbital semi-major axis are longer than a Hubble time, so that convective
damping of quasi-static tides need not be considered in the construction of
gravitational wave templates of white dwarf binaries in the LISA band. Spin-up
of the white dwarf, on the other hand, can occur on time scales of less than
10Myr, provided that the white dwarf is initially rotating with a frequency
much smaller than the orbital frequency. For semi-detached white dwarf binaries
spin-up can occur on time scales of less than 1Myr. Nevertheless, the time
scales remain longer than the orbital inspiral time scales due to gravitational
radiation, so that the degree of asynchronism in these binaries increases. As a
consequence, tidal forcing eventually occurs at forcing frequencies beyond the
quasi-static tide approximation. For the shortest period binaries, energy
dissipation is therefore expected to take place through dynamic tides and
resonantly excited g-modes.
