Whales all feed in much the same way. They swallow up water and filter it through fronds in their mouths called baleen. Most of the food they eat is tiny stuff, like krill and other small invertebrates. So some scientists have wondered how big whales manage to put enough tiny bits of food in their bodies to get to such huge sizes.

Fin whale lunge diagram, Nick Pyenson.
The very act of getting that food–diving deep, lunging open-mouthed, and then pushing a school-bus-sized volume of water forwards–requires a lot of energy.
Whales lunge into a cloud of krill and drop open their jaws. Pleats under the lower jaw open up, engulfing huge amounts of water. The whale slows down because of the drag. It behaves, in other words, a lot like a parachute. scientists have found: in one lunge, a fin whale can momentarily double its weight. As the water rushes in, the whales contract muscles in their lower jaw. The water slows down and then reverses direction, so that it’s moving with the whale. Once the water is moving forward inside the whale it can then close its mouth and give an extra squeeze to filter the water through its baleen.
A fin whale can get 20 pounds of krill in a single gulp, but it can gulp every 30 seconds. Because krill live in gigantic swarms, they can keep gulping and get enough food in four hours to fuel their bodies for an entire day
Source: discovermagazine.com