Add the Run to TextBlock in logic file

Something like this:

string lineToAppend = //... new Run(str) is probably incorrect, but something method returning string
tb.Text = string.Format("{0}{1}{2}", tb.Text, System.Environment.NewLine, lineToAppend);

This is simple, but performance can be a problem if you do it repeatedly and and collect a lot of text (see below). Try this for better performance:

//this is where performance is compromised,
//but at teast twice less than in previous sample:
tb.SelectionStart = tb.Text.Length;

tb.SelectionLength = 0;
tb.SelectedText = lineToAppend;

Unfortunately, text box types do not support access by line directly; and appending performance is not good (because every time you append the whole Text it is copied back and forth again and again). For equivalent of such functionality, use ListBox and add or modify items of string type.

ListBox myListBox = new ListBox();

//...

myListBox.Items.Add(lineToAppend); //much faster; can hold many items without loss of performance

ListBox is much better then TextBox if you want appending some output results programmatically.

—SA