In the classical Bayesian persuasion model an informed player and an uninformed one engage in a static interaction. The informed player, the sender, knows the state of nature, while the uninformed one, the receiver, does not. The informed player partially shares his private information with the receiver and the latter then, based on her belief about the state, takes an action. This action, together with the state of nature, determines the utility of both players. This paper analyzes a dynamic Bayesian persuasion model where the state of nature evolves according to a Markovian law. Here, the sender always knows the realized state, while the receiver randomly gets to know it. We discuss the value of the sender when he becomes more and more patient and its relation to the revelation rate, namely the probability at which the true state is revealed to the receiver at any stage.