Island fixture vent
An island fixture vent, sometimes colloquially called a "Chicago Loop" is an alternate way of venting the trap installed on an under counter island sink or other similar applications where a conventional vertical vent stack or air admittance valve is not feasible or allowed.
Function
As with all drains, ventilation must be provided to allow the flowing waste water to displace the sewer gas in the drain, and then to allow air (or some other fluid) to fill the vacuum which would otherwise form as the water flows down the pipe.
An island fixture vent provides an elegant solution for this necessity: when the drain is opened, water displaces the sewer gas up to the sanitary tee, the water flows downward while sewer gas is displaced upward and toward the vent. The vent can also provide air to fill any vacuum created.
The key to a functional island fixture vent is that the top elbow must be at least as high as the "flood level" (the peak possible drain water level in the sink). This ensures that the vent never becomes waterlogged.
Cost
The cost of installation is high because of the number of elbows and small pieces of pipe required. The largest cost outlay with modern plastic drain pipes is labor. Use of Street elbows is helpful.
Alternately if moving sink to an island sink, install the P-trap below the floor of the island and vent off the top of the drain. Attach toward the trap and reverse 180 degrees so any water in the vent flows down the drain. Slope drain down, slope vent up, and attach to existing vent from previous existing fixture that is now abandoned. Patch previously existing drain to become vent. In Canada, the national plumbing code requires that the minimum trap arm be at least 2 times the pipe diameter, (e.g. 1.25 inch pipe needs a 2.5 inch trap arm, 1.5 pipe needs a 3 inch trap arm etc.) and that the vent pipe be one size larger than the drain that it serves, also a cleanout is required on both the vent and the drain. The reason for this is in the event of a plugged sink, the waste water will back up and go down the vent, possibly plugging the vent (as it is under the countertop)for that reason a clean-out would permit the cleaning of the pipes.