I'm creating t-shirts with designs printed on them (which have gradient colors).
Can screen printing be used for this? Our printer uses a DTG printer, but it's too slow & expensive.
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You have two main (only?) options for gradients with screen printing...
The same method used in offset printing, but keep in mind that a screen printing generally uses a lower line count (or LPI) than regular printing. This basically means you'll have bigger dots and a courser gradient. This'll be more noticeable with more contrasting colors (e.g. black and white)...
This essentially boils down to the printer applying two (or more) inks to the same screen and creating the gradient by allowing them to mix in the middle. You're relying on the printer the create the gradient by hand so you need to find someone you trust to do this well... but it's worth it. You can get some really cool effects with a split fountain and it can look really good when done well so it's definitely something to consider.
Whichever way you go, speak to the printers first and find out what they can do for you, how they need the files prepared etc. Generally speaking there shouldn't be any special preparation for either method though, as long as you communicate with your printer.