Or HaChaim on Genesis 18:3/אור החיים על בראשית י״ח:ג׳

1 ויאמר, אדני, אם נא מצאתי חן, He said: "my lords, if I have found favour, etc." We need to know why Abraham did not speak to all three of them at the same time. Bereshit Rabbah 48,10 mentions that Abraham said to the leader, Michael, that "a little water should be taken, etc." This is merely a homiletical explanation. How would Michael know that Abraham's invitation was addressed to all three of them when Abraham spoke to Michael in the singular?

2The reason Abraham addressed only Michael was that he felt that the other two were going to come to him even without a specific invitation, seeing that G'd had despatched them with messages for him. One was meant to cure him, the other to inform him of the impending birth of Isaac. The same did not apply to the third angel Gabriel, whose function it was to destroy Sodom. He had no task to perform in Abraham's home. This is why Abraham appealed to him not to depart until he had partaken of his hospitality. Gabriel consented.