Select Menu: Window / Workspace / Dual Monitor - Large Viewer
Drag the two different windows now showing to the individual monitor you want each to display on.
If the single image "Viewer" is still there above the browser thumbnails then select - View / Hide Viewer to only show the thumbnails and tool tab. When I select that workspace using the above menu, the Viewer automatically goes away.
You can close whatever tools tab you have open on the left such as the Library to allow more thumbnails to show with - View / Hide Tools (or CTRL T). Repeat to switch back but it will now read "Show Tools" or "Show Viewer"
Another way to do it - though the Viewer will still remain above the Browser thumbnails
Hit F10 key to open the large viewer window, move it to the display where you want it.
On the other window choose - View / Hide Viewer - This will get rid of the single image view above the browser thumbnails. Remove the tools tab the same way, View / Hide tools or CTRL-T
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You can also assign a keystroke to show or hide the Viewer in Edit / Preferences / Commands, but make sure you don't over-ride a command that is in use somewhere else. If you do, it will warn you that you changed a command, but it will still make the change. If you didn't want to change the command then you have to go and re-assign the command to what it was before, then try some other keystroke. Pretty cumbersome in my view. It would be better if it warned you BEFORE changing it rather than AFTER, but it doesn't.
Be aware that the Color Editor when in dual monitor mode may not work properly on displays that don't meet the requirements for said editor to function properly. On my Win8 tablet, because it has a lower than 1920x1080 display, the color editor will only work on the external 1920x1080 display. With my Win 8 notebook a Sony Flip 15, which has a 2880x1620 display the color editor works on both screens.