You can send out chase up e-mails as frequently as you like, but recall, that each time they receive amail from you there's a link at the bottom that announces 'un-subscribe'. So be cautious that you continue to offer them something they can benefit from and not only a sales pitch.
Naturally, the whole point of gathering your website visitors name is to hopefully turn them into a purchasing buyer. It's estimated that up to 98% of the people who visit your site won't make a purchase on their first visit. And they will not ever come back. That is the reason why using an opt in e-mail list is important. To monetize your list you have 2 basic options: you can send out a sales message say for every 5 or so informative mails, or you can add a short sales message as a post script to each email you send out.
Remember that the folks on your list likely get a lot of e-mails every day and you want to set yourself apart, you need to show them that the info in your emails will help them and that it's worth their effort to open and read your e-mails. If you can do that your emails will be the ones that get opened on a consistent basis.
To build up trust and rapport with your internet site visitors use an automated auto-responder system and opt in e-mails.