The one thing about plunging, that makes it more effective, is if you close off one compartment of the sink with a wrag stuffed into the strainer. Someone needs to hold it (no drain cleaner) while your plunging. Then the pressure is put against the clog, instead of diverted up the other side of the sink. In addition, if the clog is down the drain past the vent, no amount of plunging will uncork it. You will need either a hand snake or an electric snake. I much prefer the Roto-Rooter type snake, as it completely removes the clog. Grease and sludge clogs cannot be removed by plunging. All you do is pop a hole through the center. A drain snake uses blades to scrape all of the gunk to the full interior diameter of the pipe. That is the only way to be clog free for a longer period of time.
By the way, a word on drain cleaners. Try not to use acid type drain cleaners like draino and liquid plumber. They eat right through metal piping. If your pipes are galvanized, cast iron or copper, you will be replacing your piping as holes will develop. In addition, acid drain cleaners are unsafe for our environment. They polute and destroy groundwater. Water, that you will eventually be drinking. All water eventually reaches the underground water tables, taking with it any polutant we put into the ground. If you have to use a drain cleaner, use an enzyme type. They are non-hazardous so far. And they are not for cleaning the drain, but keeping it clean once cleaned by a Roto-Rooter machine.
Raymond VinZant Plumbing Prof.