Stop WiFi adapter using internet, but retain networking capabilities.

I have a wired Ethernet connection directly into my modem, I also have a WiFi dongle connected to a router so that i have network access to other machines. The WiFi network is also providing me with internet, i dont want the internet because i think it my confuse certain applications, how will they know which internet to use? How can i stop internet coming in through the WiFi but still be...