The sink in my kitchen drains very slowly. If the dishwasher is running, the waste water from the dishwasher flows into the kitchen sink. Eventually it will drain but it takes a while. I cleaned the plumbing, there is no issue there. I believe the issue is that the exit hole for the waste water is too high in the wall and there is no real downward flow after the sink trap.
The riffled hose that goes into the wall should have a downward slope to get a good water flow. In my case it is essentially level. How can I fix that?
The height of the hole in the wall is fixed. I don't want to increase the height of the kitchen counter that has the sink in it because my wife is only 5 feet tall and it should be at a convenient height for her to work on it. I could replace the sink with a different sink with less depth but that would also be less nice. I already switched the plumbing for a set where the exit of the trap is high relatively to the input (the limit is the entry for the dishwasher from the grey hose coming in from the back).
What else can I do to get my sink to drain properly?
A little more background and results. When I wrote 'I cleaned the plumbing' I meant the parts from the sink until it disappears in the wall. I disassembled these parts and cleaned them, there is no clogging issue there.
However, as suggested in some answers, the issue is clogging further down the pipes. The pipe in the hole in the wall has a 90° turn after a few centimeters and goes directly downwards. Poking in there with a wire it seems to go down maybe 20 centimeters or so and that is the spot where a lot of gunk accumulated. I'm in a multi floor apartment building so the building main waste water pipe will be much thicker but aparently my pipe has another bend there before it drains in the main pipe.
I poured some pipe cleaner directly into the whole in the wall and that seems to have fixed the issue. Drainage is much better and faster now. I haven't run the dishwasher yet but I hope this issue is solved as well.