"放任情绪"的英文表达可以用"indulge one's emotions"来表示。

"Indulge"是英文动词,意思是沉溺于、满足(某种欲望或嗜好)。"One's emotions"是指个人的情绪。

例句:

She indulged her emotions and cried for hours after breaking up with her boyfriend. (她放任情绪,和男友分手后哭了几个小时。)
He couldn't help but indulge his emotions and express his anger when he heard the news. (当他听到这个消息时,他忍不住放任情绪,表达了他的愤怒。)