  We introduce a stochastic partial differential equation (SPDE) with elliptic
operator in divergence form, with measurable and bounded coefficients and
driven by space-time white noise. Such SPDEs could be used in mathematical
modelling of diffusion phenomena in medium consisting of different kinds of
materials and undergoing stochastic perturbations. We characterize the solution
and, using the Stein--Malliavin calculus, we prove that the sequence of its
recentered and renormalized spatial quadratic variations satisfies an almost
sure central limit theorem. Particular focus is given to the interesting case
where the coefficients of the operator are piecewise constant.
