Yes, there is a way of making it open on a specific monitor if you want that application to always open on that monitor.
Open a PDF, any PDF, and once Preview is opened, right-click on it's icon in the Dock. Select Options and under the Assign To section, choose which display you want to assign Preview to.
Now, every time you launch Preview by itself or through a file it can load, it will automatically jump to the display you've chosen. If you have multiple spaces on your displays, one you select a specific display, it will automatically chose the space as well and always jump to that space & display.