Hashem appeared to him (Avraham) by the plains of Mamre, and he was sitting at the entrance of the tent in the heat of the day. (18:1)
The Ohr Hachaim asks three questions concerning this Posuk. 1) Chazal teach us that Hashem came to visit Avraham after fulfilling the mitzvah of Bris Milah. If this is correct why then is there no mention or hint of this in the Posuk. 2) Previously in Parshas Lech Lecha, Hashem also appeared to Avraham. However, the order of the words is different. This expression has three words. There, Hashem's name is positioned immediately after the first word of the expression. Here, in our Posuk, Hashem's name is moved to the end of the expression. Why the difference? 3) Why is it that after Avraham fulfilled the Bris Milah we no longer find Hashem appearing to Avraham? We do have many instances of Hashem speaking to Avraham, however, an expression including the term "appearing" is no longer mentioned.
The Ohr Hachaim answers by explaining that the Mitzvah of Bris Milah is unique in that via its fulfillment a person achieves an impactful connection with Hashem. The Divine Presence of Hashem permanently devolves upon that individual. The nuanced wording of this Posuk subtly expresses this concept. The word 'eilav' mentioned here doesn't simply mean that Hashem appeared 'to' him, but rather that Hashem 'rested' upon him. The structure of the expression brings out this idea. By moving Hashem's name to the end of the expression and replacing it with 'eilav,' highlights the unique meaning of this word in this context. This was not just a casual encounter between Hashem and Avraham, it was a significant change in the spiritual composition of Avraham. Avraham was now a person upon whom Hashem rested his Divine Presence. We can now answer the other two questions as well.
In the previous encounter, Avraham was not yet circumcised. Hashem simply appeared 'to' Avraham. When Hashem left, Avraham was the same person as before. The order of the words is likewise structured to make that point. Furthermore, after the Bris Milah, the Divine Presence never left. Hashem was perpetually appearing to Avraham. The term 'appear' would no longer be appropriate. From this point onwards, the Torah only needs to mention that Hashem spoke to Avraham.
