Please try this.

* Identify the div element (immediate parent) which holds your chat messages. Example: #chatList 

* At the end of the events (including refresh event of the screen with updated pagelist, if used), which are called on click of the 'Send' button, use the below function.

​function scrollToEnd(){
	var chatList = document.getElementById("chatList");
	chatList.scrollTop = chatList.scrollHeight;
}

* The function should be defined at appropriate JS file