  We construct a new spectral sequence beginning at the Khovanov homology of a
link and converging to the Khovanov homology of the disjoint union of its
components. The page at which the sequence collapses gives a lower bound on the
splitting number of the link, the minimum number of times its components must
be passed through one another in order to completely separate them. In
addition, we build on work of Kronheimer-Mrowka and Hedden-Ni to show that
Khovanov homology detects the unlink.
