The problem of identifying the cause of this effect has been featured in Scientific American magazine, with several theories given to explain the phenomenon but no definite conclusion.
By pushing the curtain in towards the shower, the (short range) vortex and Coandă effects become more significant.
[3][1] David Schmidt of the University of Massachusetts was awarded the 2001 Ig Nobel Prize in Physics for his partial solution to the question of why shower curtains billow inwards.
[4] The Coandă effect, also known as "boundary layer attachment", is the tendency of a moving fluid to adhere to an adjacent wall.
They may have adhesive suction cups on the bottom edges of the curtain, which are then pushed onto the sides of the shower when in use.
Hanging the curtain rod higher or lower, or especially further away from the shower head, can reduce the effect.