Its pretty common to find people coming to meetings and plonking one (or more!) mobile phones on the table in front of them. I've recently been reading about research which suggests this is a bad idea - which is how it has felt to me all along, but nice to see a proper study.
The study was that Researchers at Essex University had people meet with a stranger, discuss something for a while and then say how well they felt they connected with their partner. It was arranged such that either a mobile phone, or a notebook was visible on the table during the meeting, or the table was bare. Subjects felt the meeting had gone less well when a phone had been visible (Notebook was OK). Here's a newspaper article about the research: http://www.telegraph.co.uk/science/science-news/9589232/Putting-a-mobile...
That makes sense to me - having your phone visible suggests that you're going to be willing to interrupt the meeting, or at least allow yourself to be distracted, to deal with the phone if it goes off (call, email, text, tweet). This research suggests that the empathy damage is done to the meeting whether or not the phone actually goes off. It's the priorities you are implying to the person you are with, I expect. You're suggesting that stuff which might happen on your phone is more interesting than they are; that you are so busy that they are lucky briefly to get your partial attention and so on. So, please, keep the darned thing out of sight, and get it out only if you need it for something related to the current meeting.