Pouring ink in a porcelain sink is always a bad idea especially if it's made from white porcelain. The stain that the ink causes has blueish color that ruins the look of your sink.
To get rid of it you'll have to use some special cleaning techniques and of course, the right products for the job. Fortunately porcelain is quite resistant to all sorts of cleaning products and it will be easy to get rid of the ink stain.
First we'll try a more unconventional method for cleaning and we'll use hairspray to remove the stain. It's best you use the cheapest variety because it is proven to work best on ink stains. Spray the stained area with a good amount of the hairspray and leave it to sit for a couple of minutes. But do not let it dry because it will stick to the surface and it will be harder to remove. Wipe the stain with a soft cloth and apply more hairspray to keep the area saturated. Repeat the procedure until you get the stain out.
If this recipe doesn't work and the stain still remains you'll have to use a more powerful cleaning product. Your choices are acetone or nail polish remover. Take a soft cloth and dampen it with one of the products. Be sure to not soak it too much. Rub the stained area using circular motions. Apply more cleaning fluid if it's need until you get the stain out.
The final cleaning recipe is with rubbing alcohol. The first two should work flawlessly but just in case if any of the stain is left you can finish the cleaning procedure with rubbing alcohol. As you know alcohol lifts stains even on clothes, so it should work quite nicely on porcelain. Dampen a soft cloth with the cleaning solution and rub the stain until it's transferred onto it.
An additional tip is to always rinse the sink after with plenty of water after the usage of such cleaning products. The reason is that if they're left on the surface for too long they can cause discoloration or other damage. Add some dish soap to the water to be sure that the products you used are gone. Rinse with hot water.
I hope these cleaning tips work for you and your porcelain sink will be back to it's normal looks.