In which 2011 'Pirates of the Caribbean' movie does Captain Jack Sparrow embark on a quest to find the legendary Fountain of Youth, encountering mermaids, Blackbeard, and a mysterious woman from his past?

The 2011 film in the "Pirates of the Caribbean" series that features Captain Jack Sparrow on a quest for the Fountain of Youth, encountering mermaids, Blackbeard, and a mysterious woman from his past, is "Pirates of the Caribbean: On Stranger Tides". This fourth installment in the popular franchise sees Jack Sparrow (Johnny Depp) drawn into a thrilling race to find the mythical Fountain of Youth. His journey becomes complicated when he crosses paths with Angelica (Penélope Cruz), a cunning pirate and a woman from his romantic past, who forces him aboard the ship of the formidable and legendary pirate Blackbeard (Ian McShane).

The quest for the Fountain of Youth is central to the plot, with multiple factions, including the British Navy led by Captain Barbossa, the Spanish Navy, and Blackbeard, all vying to reach it first. Along the way, the characters encounter dangerous and alluring mermaids, whose tears are a crucial component for activating the Fountain's power. Blackbeard, known for his ruthless nature and voodoo magic, is a formidable antagonist, intent on using the Fountain to avert a prophecy of his demise.

"On Stranger Tides" marked a new chapter for the "Pirates of the Caribbean" series, being the first film not directed by Gore Verbinski, with Rob Marshall taking the helm. The movie was loosely based on Tim Powers' 1987 novel of the same name, and it was also the first in the franchise to be shot entirely in 3D. The production involved extensive filming in diverse locations, including Hawaii, Puerto Rico, and historical sites in Great Britain, contributing to the film's grand scale and adventurous feel.