verb

(with reference to moisture or a smell) discharge or be discharged slowly and steadily.

the beetle exudes a caustic liquid

give off/out,discharge,release,send out,send forth,emit,issue,emanate,ooze,weep,leak,leach,secrete,excrete,extravasate,seep,trickle,filter,percolate,escape,flow,well,drip,dribble,drain,bleed,sweat,filtrate,transude,exudate