Does a woman's touching her vulva with the palm of her hand while performing ablution invalidate the ablution?

According to the Shafi'is and Hanbalis, a woman's ablution (wudu') is invalidated if she touches her private parts with the palm of her hand. The Hanbalis even extend this to invalidating wudu' if she touches her private parts with the back of her hand. The Hanafis and the preferred view among the Malikis hold that touching the private parts does not invalidate wudu' at all. Some Malikis are of the opinion that a woman touching her private parts invalidates wudu' if she inserts her hand into it or grasps it. However, touching the private parts through a barrier does not invalidate wudu'.