  Let $R$ be a ring with identity. Inspired by recent work of Emmanouil, we
show that the derived category of $R$ is equivalent to the chain homotopy
category of all K-flat complexes with pure-injective components. This is
implicitly related to a recollement we exhibit. It expresses
$\mathcal{D}_{pur}(R)$, the pure derived category of $R$, as an attachment of
the usual derived category $\mathcal{D}(R)$ with Emmanouil's quotient category
$\mathcal{D}_{K-flat}(R):=K(R)/K-Flat$, which here we call the K-flat derived
category. It follows that this Verdier quotient is a compactly generated
triangulated category. We obtain our results by using methods of cotorsion
pairs to construct (cofibrantly generated) monoidal abelian model structures on
the exact category of chain complexes along with the degreewise pure exact
structure. In fact, most of our model structures are obtained as corollaries of
a general method which associates an abelian model structure to any class of
so-called $\mathcal{C}$-acyclic complexes, where $\mathcal{C}$ is any given
class of chain complexes. Finally, we also give a new characterization of
K-flat complexes in terms of the pure derived category of $R$.
