Tight closure/Arithmetische Deformation/Dimension 1/Generisch solid closure/Problem/en

Let ${}D$ denote an onedimensional domain of mixed characteristic (of finite type over ${}\mathbb {Z}$) and let ${}D\subseteq S$ be a domain of finite type of relative dimension ${}2$. Let ${}I\subseteq S$ be an ideal and ${}f\in S$. Suppose that ${}f$ belongs to the solid closure of ${}I$ inside the generic ring ${}S_{Q(D)}$ (in characteristic ${}0$). Is it true that ${}f\in I^{*}$ holds for infinitely many points ${}{\mathfrak {m}}\in \operatorname {Spec} {\left(D\right)}$ (in positive characteristic)?