The following depends on:
- Their reasons for staying quiet
- Are they shy & afraid of public speaking? Or busy & annoyed to be there?
- The culture you're in
- Do you have authority to ask them to do things, or will they be offended?
- Is there some seniority or cultural reason they might not voice concerns or ideas?
- How much time you have for the meeting.
If you can do so ...
- Shut off the Wi-Fi :)
- Set a clear end time for the meeting (to placate the annoyed ones)
- Do like airlines do & request that they shut off their laptops/phones/tablets
- If it's appropriate, provide some small snacks or water/coffee/tea, etc
Given that they're scientists you could frame the whole meeting in terms of a scientific process ... Your goal is to identify problems & their causes, develop some hypotheses based on available data, and come up with a solution. Their input is the required data.
Presumably you're meeting with them because there's room for improvement.
Do they not have any complaints at all? (If so, are they hiring?). You're there to make their lives easier but you need their input.
You could start by passing out slips of paper & asking:
"What is the #1 thing you would change about [X]?" Please write it down.
"What is #2?" Please write it down as well.
No need to talk, and initial input would be anonymous (unless they write something too specific/identifiable). Could be about your specific product, or their work processes in general - whatever you want to focus on.
*If they refuse to even write anything, skip to the last paragraph below...
Once you have all their comments, have 1 of them collect the slips & mix them up in a box or hat.
At this point, you could split up the 15 scientists into smaller groups (of 3 or so) & give each group a subset of comments to rank order ... Get them up & moving around, and impose a a 5-10min time limit. Once they're done, ask 1 from each group to write down the comments in rank order. Look for common themes as a large group. You could assign each ranked item a score & use that to determine an overall priority list.
If there's no room/time for small groups, pick the most talkative person to mix up & read all the comments aloud. Have a 2nd person write them down on a whiteboard or something. Then see if you can get to some consensus on a rank order or some clear/repeated themes.
Remind them: their input provides the parameters of the experiment, without which the group cannot effectively test any assumptions/hypotheses or come to a conclusive solution to make their lives easier. If there's time & interest, work with them to come up w/solutions to the top concerns - either in small groups again, or as a larger group (which tend to be dominated by 2-3 people).
*Alternative to the above - come in with some suggestions ready on slips of paper & get them to rank order and (in)validate them for you. No talking, again, but you still get their opinions. As that's done maybe they'll be more open to offering additional suggestions.