food photography - Why isn't the background towel visible in this still life?

She said (in comments) that she has used a towel here as a background: http://500px.com/photo/4934925
That is a macro shot.

But, the towel isn't simply "visible" (except very faintly on the right corner). Is it possible to make the towel invisible without any post processing?

Answer

For some reason I can't see the image linked above. But anyways based on what I've read from few responses I assume the towel is pure white or blown out in the background.

Here is a quick diagram to help you visualize: top view.

All you need is two lights. Set up your main light first, get the exposure you like. Then add second light that is 1 or more stops brighter than your main light. You should consider snooting second light. Snooting helps you direct light where you want it. In this case you might not want to add more light to your current exposure of your subject but you want to overexpose the background.

EDITED TO ADD: Resources

One Light DVD by Zack Arias. And Strobist (Free)