  We describe a general correspondence between injective (resp. projective)
recollements of triangulated categories and injective (resp. projective)
cotorsion pairs. This provides a model category description of these
recollement situations. Our applications focus on displaying several
recollements that glue together various full subcategories of K(R), the
homotopy category of chain complexes of modules over a general ring R. When R
is (left) Noetherian ring, these recollements involve complexes built from the
Gorenstein injective modules. When R is a (left) coherent ring for which all
flat modules have finite projective dimension we obtain the duals. These
results extend to a general ring R by replacing the Gorenstein modules with the
Gorenstein AC-modules introduced recently in the work of Bravo-Gillespie-Hovey.
We also see that in any abelian category with enough injectives, the Gorenstein
injective objects enjoy a maximality property in that they contain every other
class making up the right half of an injective cotorsion pair.
