Christophanies in the Old Testament?
Augustine countered the Arian interpretation by emphasising that the Son is no less invisible than the Father, and therefore either of them could well have been appearing to the patriarchs. On the other hand, there is no reason it could not also have been “the Father, or the Son, or the Holy Spirit,” or “sometimes the Father, sometimes the Son, sometimes the Holy Spirit,” or “simply the one and only God, that is the Trinity without any distinction of persons” ...
Augustine’s judgment is that we do not have clear enough warrant to say what is actually happening in these most mysterious events of the Old Testament. But his more substantive reason for rejecting the idea that these are appearances of the Son (not the Father or the Spirit) has to do with the uniqueness of the visible mission of the Son in the incarnation. If the Father sent the Son repeatedly during the old covenant, it derogates in some way from the uniqueness of the incarnation as sending. The question is not so much where the Old Testament Jesus got the body he appeared to the patriarchs in (though that surely calls for some speculation). It is more a matter of the unrepeatable uniqueness of the incarnation of the Son.
—Fred Sanders, The Triune God, 224-5