Viscoelastic phase separation can be observed in binary mixtures, whose two components have strongly different aggregation time scales. The morphology exhibits features such as volume shrinking, thin network-like structures and phase inversion. Such effects play a crucial role for instance, in the formation of membraneless protein organelles.

We consider a non-degenerate variant of a model proposed by Zhou et al.\ 2006 with gradient-flow structure, that comprises a Cahn--Hilliard equation for the phase variable $u$ with a nonlinear cross-coupling to the spherical bulk stress $q$, which itself obeys relaxational dynamics.
Introducing a small characteristic size $q_c:=\varepsilon$ of $q$ and rescaling the relaxation coefficient and the time, we rigorously pass to the limit $\varepsilon\to0$. We show that $q\to0$ and, depending on the scaling relations, $u$ converges to a solution of either (i) the Cahn--Hilliard equation, (ii) the viscous Cahn--Hilliard equation, or (iii) the mass-preserving Allen--Cahn equation. The analysis is based on the gradient-flow equation and a precise determination of the limiting subdifferential in each scaling regime.