Slow drain in un-vented kitchen sink
We re-modeled our kitchen, changing the sink from a double to a single bowl. It is located in the same spot as previously, with a dishwasher connected. No disposal. There is no vent in this part of the house - the sink drain goes about 20 feet before joining into the main drain under the bathroom, where there is a vent through the roof. There is another vent for the laundry area, which is on the other side of the bath.
We are now having slow drainage in the kitchen sink. It is clear and drains well for the first few minutes, but as soon as the s-drain is full and the bowl starts to fill, the drainage is very slow. This does not change if the dishwasher is running or not. There doesn't appear to be a problem with drainage for the dishwasher - it does not back up into the sink. The sink and dishwasher are located in a peninsula.
Did the old, 2 bowl sink provide venting to allow the water to continue to drain? There is not room in the new cabinets to replace the sink with a 2 bowl - it is not wide enough and there is no room to expand.
Our first thought was to add an air gap for the dishwasher - but we looked at the purpose and function of those and now question that as a solution.
What can we do?