Studies

Study #1
In this study, researchers Tang and Wang looked at the way that bloggers self-disclose on social media sites. In their findings, they found out that people discuss nine different types of conversations online. They found that the younger you are, the more likely you are to self-disclose online and the more likely use of breadth, but the range of depth will stay the same.
(Tang & Wang, 2012)

Study #2
In a study by Gibbs, Ellison, and Lai (2011), the researchers wanted to learn about how online dating users self-disclose. Using a nationwide sample of 562 participants, they were able to see the potential for users to continue to self-disclose as the conversations continued. What they found was that online users were more likely to disclose in hopes of reducing concerns in personal security, misrepresentation, and recognition.
(Gibbs & Ellison & Lai, 2011)

Study #3
Using Facebook and instant messenger, researchers Quan-Haase and Young (2010) examined the difference between self-disclosing with the two different platforms. Using 77 surveys and 21 interviews of undergraduate students, they found that Facebook is about having fun, giving information that ends at the orientation stage, whereas instant messenger is about building relationships, meaning you are going to continue self-disclosing among one another in a more intimate way.
(Quan-Haase and Young, 2010)
In these studies about Social Penetration Theory, they all study self-disclosure online.