Made some tea using a drip style coffee maker by placing tea bag where coffee would normally go, namely on the standard fibrous (paper) coffee filter. After the tea has been on the warmer for a while, it develops dregs. Actually it's not so much dregs as particles that sometimes sink to the bottom and sometimes float and stick to the side of the carafe. The tea also develops an oil slick on top. It makes for some nasty looking stuff which sticks to the sides of my cup as well. I fail to understand how these dregs got through the coffee filter in the first place. I pour it back through the filter, but it then drips slowly, as if the filter were clogged. Any clues as to what is happening here? It has happened with 3 different kinds of tea (all in bags).
Regarding the oil film, this is called 'tea scum' and it's completely safe.
The filter gets clogged because the tea particles are small and fill up the spaces in the filter. Then it gets in touch with water and expand. At this point, the filer will get clogged.
There's generally no reason to use a coffee filter as the tea bag itself functions as a filter.