It depends on which blue and which brown you use. There are a wide variety. For example if you mix ulra marine blue and burnt umber you will get black. Adding blue to a reddish brown will make the brown darker, but also more violet. Using a yellowish brown and blue will give you more of a greenish brown.
You have to experiment with the colors on your pallet to see exactly which one you get.
The related link below will help you understand more about mixing colors to get the ones you want.
blue green and brown make a darker color red.
Blue gray and brown would make a grayed brown color. It would be a very muddy neutral. The blue would make it a cool color.
you can make brown color by mixing blue color and green color.........
It would make a dull grey color.
Brown, being a tertiary color (made from the combination of a primary and secondary, or two secondary colors) and blue would make black (if the proportions are equal) or a slightly blue tinted brown.